CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW323+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n027.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 05:31:38 PM UTC 2026

% Result   : Theorem 31.84s 22.38s
% Output   : CNFRefutation 32.80s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6070)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
    ! [X90,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),X5),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),tc_Int_Oint),c_COMBB(tc_fun(X5,X5),X5,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,X5),X5),tc_Int_Oint),c_HOL_OLet(X5,X5)),c_Int_Oring__1__class_Oof__int(X5)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X5)),tc_Int_Oint),c_COMBS(X5,X5,X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),tc_Int_Oint),c_COMBB(X5,tc_fun(X5,X5),X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5)))),c_Groups_Oone__class_Oone(X5))))),c_Divides_Odivmod__int(X90,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__num) ).

fof(fact_not__sum__power2__lt__zero,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__less__0,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [X122,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).

fof(fact_negDivAlg__eqn__number__of,axiom,
    ! [X126,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [X126,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
         => c_Divides_OnegDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
         => c_Divides_OnegDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OnegDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
         => c_Divides_OposDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
         => c_Divides_OposDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OposDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_hd__dropWhile,axiom,
    ! [X224,X30,X5] :
      ( c_List_OdropWhile(X5,X30,X224) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X30,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X30,X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [X75,X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).

fof(fact_takeWhile__eq__filter,axiom,
    ! [X224,X30,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X30,X224))))
         => ~ hBOOL(hAPP(X30,X3)) )
     => c_List_OtakeWhile(X5,X30,X224) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_power__number__of__odd,axiom,
    ! [X26,X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),X26))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__odd) ).

fof(fact_zpower__number__of__odd,axiom,
    ! [X26,X84] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26))),c_COMBI(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__number__of__odd) ).

fof(fact_irrefl__tranclI,axiom,
    ! [X20,X78,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X78)),c_Transitive__Closure_Ortrancl(X5,X78)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X20)),c_Transitive__Closure_Otrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_dropWhile__append1,axiom,
    ! [X223,X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X30,X224)),X223) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_acyclic__def,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Oacyclic(X5,X78)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [X122,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_acyclicI,axiom,
    ! [X78,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X78)))
     => c_Wellfounded_Oacyclic(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_OdropWhile(X5,X30,X224) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [X84] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).

fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
    ! [X95,X96,X30] :
      ( c_List_Olist__ex(tc_Nat_Onat,X30,c_List_Oupt(X96,X95))
    <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X30),X96,X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).

fof(fact_upt__rec__number__of,axiom,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [X126,X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Int_Oring__char__0(X56) )
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [X223,X24,X224,X30,X5] :
      ( c_List_OdropWhile(X5,X30,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)
    <=> ( X224 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X30,X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))
        & ~ hBOOL(hAPP(X30,X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_removeAll__id,axiom,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => hAPP(c_List_OremoveAll(X5,X20),X224) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__id) ).

fof(fact_removeAll__filter__not,axiom,
    ! [X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => hAPP(c_List_OremoveAll(X5,X20),hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [X92,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122))),X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_upt__Suc,axiom,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X94)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X94),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X94)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__rec,axiom,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,X94) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X94)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,X94) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X122)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_member__rec_I2_J,axiom,
    ! [X57,X56] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X56),c_List_Olist_ONil(X56)),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).

fof(fact_adjust__def,axiom,
    ! [X21] : c_Divides_Oadjust(X21) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X21))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X21))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adjust__def) ).

fof(fact_succ__Bit0,axiom,
    ! [X93] : c_Int_Osucc(c_Int_OBit0(X93)) = c_Int_OBit1(X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [X93] : c_Int_OBit0(X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),c_Int_OMin) = c_Int_Osucc(X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_prod__fun__imageE,axiom,
    ! [X37,X1,X2,X184,X25,X23,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X23),hAPP(c_Set_Oimage(tc_prod(X25,X184),tc_prod(X5,X17),c_Product__Type_Omap__pair(X25,X5,X184,X17,X2,X1)),X37)))
     => ~ ! [X3,X38] :
            ( X23 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X2,X3)),hAPP(X1,X38))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25,X184)),hAPP(hAPP(c_Product__Type_OPair(X25,X184),X3),X38)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_converse__rtranclE2,axiom,
    ! [X78,X292,X293,X294,X200,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
     => ( hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294) != hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292)
       => ~ ! [X49,X124] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124))),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [X106,X90] :
      ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X90,X106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X106 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X90,X106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90) )
          & ( X106 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X90,X106) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X106))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X106)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X106),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X90,X106)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X106))))),c_Divides_Opdivmod(X90,X106)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_apsnd__def,axiom,
    ! [X2,X5,X25,X17] : c_Product__Type_Oapsnd(X17,X25,X5,X2) = c_Product__Type_Omap__pair(X5,X5,X17,X25,c_Fun_Oid(X5),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__def) ).

fof(fact_divmod__int__code,axiom,
    ! [X106,X90] :
      ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X90,X106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X106 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X90,X106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90) )
          & ( X106 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X90,X106) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X106))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X90)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X106))),c_Divides_Opdivmod(X90,X106)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X106))))),c_Divides_Opdivmod(X90,X106)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__code) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [X78,X145,X5] : c_Nitpick_Oplus__frac(X5,X145,X78) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X5),X145),hAPP(c_Nitpick_Odenom(X5),X78))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X5),tc_Int_Oint),c_Nitpick_Ofrac(X5)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),X145))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X5),X145))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),X78))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X5),X78)))))),c_COMBI(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

fof(fact_Nitpick_Odenom__def,axiom,
    ! [X5] : c_Nitpick_Odenom(X5) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X5,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Odenom__def) ).

fof(fact_Nitpick_Onum__def,axiom,
    ! [X5] : c_Nitpick_Onum(X5) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X5,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Onum__def) ).

fof(fact_reflcl__set__eq,axiom,
    ! [X24,X20,X78,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X78)),c_fequal),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).

fof(fact_rtrancl__empty,axiom,
    ! [X5] : c_Transitive__Closure_Ortrancl(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))) = c_Relation_OId(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__empty) ).

fof(fact_adjust__eq,axiom,
    ! [X78,X145,X21] : hAPP(c_Divides_Oadjust(X21),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X145),X78)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X78),X21)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X145)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X145)),X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adjust__eq) ).

fof(fact_trancl__insert,axiom,
    ! [X78,X20,X24,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),X78)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(hAPP(c_COMBC(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),X24))),c_Transitive__Closure_Ortrancl(X5,X78))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(c_Product__Type_OPair(X5,X5),X20))),c_Transitive__Closure_Ortrancl(X5,X78)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__insert) ).

fof(fact_trancl__unfold__left,axiom,
    ! [X78,X5] : c_Transitive__Closure_Otrancl(X5,X78) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X78),c_Transitive__Closure_Ortrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_SUP2__E,axiom,
    ! [X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => ~ hBOOL(hAPP(hAPP(hAPP(X22,X3),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__E) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X20),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
          & X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [X259,X224,X20,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X259)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X259)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X259)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X224),c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X259))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_concat__conv__foldl,axiom,
    ! [X259,X5] : c_List_Oconcat(X5,X259) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),c_List_Olist_ONil(X5)),X259),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [X259,X224,X20,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X259)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X259)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X224),c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X259))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_odd__power__less__zero,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)))),c_Groups_Ozero__class_Ozero(X56))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_rel__compE,axiom,
    ! [X146,X78,X25,X219,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X219),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X78),X146)))
     => ~ ! [X3,X38,X150] :
            ( X219 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X3),X150)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X25)),hAPP(hAPP(c_Product__Type_OPair(X5,X25),X3),X38)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25,X17)),hAPP(hAPP(c_Product__Type_OPair(X25,X17),X38),X150)),X146)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compE) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [X223,X30,X224,X20,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) = hAPP(c_List_Ofilter(X5,X30),X223)
    <=> ? [X242,X247] :
          ( X223 = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X247))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X242)))
             => ~ hBOOL(hAPP(X30,X3)) )
          & hBOOL(hAPP(X30,X20))
          & X224 = hAPP(c_List_Ofilter(X5,X30),X247) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [X224,X20,X223,X30,X5] :
      ( hAPP(c_List_Ofilter(X5,X30),X223) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)
    <=> ? [X242,X247] :
          ( X223 = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X247))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X242)))
             => ~ hBOOL(hAPP(X30,X3)) )
          & hBOOL(hAPP(X30,X20))
          & X224 = hAPP(c_List_Ofilter(X5,X30),X247) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_power2__sum,axiom,
    ! [X57,X55,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X55)),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).

fof(fact_power2__diff,axiom,
    ! [X57,X55,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X55)),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__diff) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => c_Nitpick_Osetsum_H(X5,X17,X2,X19) = hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X19))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => c_Nitpick_Osetsum_H(X5,X17,X2,X19) = c_Groups_Ozero__class_Ozero(X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X20),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      <=> ( X20 != c_Groups_Ozero__class_Ozero(X5)
          | X24 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_transpose__aux__max,axiom,
    ! [X259,X17,X224,X5] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))),c_List_Ofoldr(tc_List_Olist(X17),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X17)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X17))),X259,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),c_List_Ofoldr(tc_List_Olist(X17),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X17)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X17),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X17)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X17)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X17),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X17)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X17),tc_List_Olist(X17),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X17)))),X259),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_foldr__foldl,axiom,
    ! [X6,X224,X2,X5,X17] : c_List_Ofoldr(X17,X5,X2,X224,X6) = hAPP(c_List_Ofoldl(X5,X17,hAPP(c_COMBC(X17,X5,X5),X2),X6),hAPP(c_List_Orev(X17),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__foldl) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [X96,X224,X19,X5] : hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X19)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X224),c_List_Oupt(X96,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X5,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X96))),X19)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X224),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [X89,X51] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) = c_List_Oupt(X51,X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_Random_Osimps,axiom,
    ! [X265,X1,X5,X266] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X266,X265) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X266,X265) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X265)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X5,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X265))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X5)),c_Product__Type_Ofst(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random_Osimps) ).

fof(fact_Suc__div__eq__add3__div__number__of,axiom,
    ! [X122,X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86)))),X92) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X86)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [X96,X254] : hAPP(c_New__DSequence_Opos__not__seq(X254),X96) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X96))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_mem__splitE,axiom,
    ! [X133,X23,X25,X17,X26,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,tc_fun(X5,tc_HOL_Obool)),X23),X133)))
     => ~ ! [X3,X38] :
            ( X133 = hAPP(hAPP(c_Product__Type_OPair(X17,X25),X3),X38)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(X23,X3),X38))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [X75,X19,X20,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X75))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ~ ! [X38] :
                ( X75 = hAPP(hAPP(X2,X20),X38)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X38)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_int__of__code,axiom,
    ! [X93] :
      ( ( X93 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,X93) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X93 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X93,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X93),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
          & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X93,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X93),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__code) ).

fof(fact_sum__power2__ge__zero,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).

fof(fact_pigeonhole__infinite,axiom,
    ! [X2,X17,X19,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [X223,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X223)
       => ( c_List_Oconcat(X5,X224) = c_List_Oconcat(X5,X223)
        <=> X224 = X223 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_concat__injective,axiom,
    ! [X223,X224,X5] :
      ( c_List_Oconcat(X5,X224) = c_List_Oconcat(X5,X223)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X223)
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X3)) )
         => X224 = X223 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__injective) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [X89,X75,X2,X6,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),X89)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),X89))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X89))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X6,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X89))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_add__Min__right,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),c_Int_OMin) = c_Int_Opred(X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__right) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X60)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).

fof(fact_neg__zdiv__mult__2,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X60)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint))),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X60)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [X89,X75] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) = hAPP(c_Nat_OSuc,X89)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X89))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [X75,X89] :
      ( hAPP(c_Nat_OSuc,X89) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X89))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [X19,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Nitpick_Ocard_H(X5,X19) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X19))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Nitpick_Ocard_H(X5,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_card__less__Suc2,axiom,
    ! [X96,X76] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X96)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X96))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_power2__less__imp__less,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_power2__le__imp__le,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_vimage__if,axiom,
    ! [X22,X17,X27,X19,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = X22 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),X22) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__if) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X60)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [X122,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86))),X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X86),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X92)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X92)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_trancl__Int__subset,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),X146)),X78)),X146))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_setprod__gen__delta,axiom,
    ! [X23,X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),X23)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X21,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X36)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),X23)),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X17),X23),hAPP(c_Finite__Set_Ocard(X5),X36)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_setprod__delta,axiom,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = c_Groups_Oone__class_Oone(X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta) ).

fof(fact_setsum__delta,axiom,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta) ).

fof(fact_less__Suc__number__of,axiom,
    ! [X75,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_le__Suc__number__of,axiom,
    ! [X75,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [X133,X1,X184,X2,X5,X17,X25] : hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),hAPP(c_Product__Type_Oapfst(X184,X5,X25,X1),X133)) = hAPP(c_Product__Type_Oapfst(X184,X5,X17,X1),hAPP(c_Product__Type_Oapsnd(X25,X17,X184,X2),X133)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_apfst__def,axiom,
    ! [X2,X17,X25,X5] : c_Product__Type_Oapfst(X5,X25,X17,X2) = c_Product__Type_Omap__pair(X5,X25,X17,X17,X2,c_Fun_Oid(X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__def) ).

fof(fact_lexord__append__leftD,axiom,
    ! [X78,X75,X102,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X20),X102)),hAPP(hAPP(c_List_Oappend(X5),X20),X75))),c_List_Olexord(X5,X78)))
     => ( ! [X49] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X49),X49)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X102),X75)),c_List_Olexord(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rel__pow__E2,axiom,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X20 != X26 )
       => ~ ! [X38,X99] :
              ( X89 = hAPP(c_Nat_OSuc,X99)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),X37))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X99),X37))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
    ! [X106,X90] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X106))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).

fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
    ! [X21,X6] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
    ! [X106,X90] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X106))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).

fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
    ! [X21,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X6,X21)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).

fof(fact_power__odd__eq,axiom,
    ! [X92,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__odd__eq) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [X20,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X20)),hAPP(c_List_Orev(X5),X224)) = hAPP(c_List_Orev(X5),hAPP(c_List_Otl(X5),c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X20)),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [X224,X30,X5] : c_List_OdropWhile(X5,X30,X224) = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_apsnd__compose,axiom,
    ! [X20,X1,X184,X2,X5,X17,X25] : hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),hAPP(c_Product__Type_Oapsnd(X184,X25,X5,X1),X20)) = hAPP(c_Product__Type_Oapsnd(X184,X17,X5,hAPP(c_Fun_Ocomp(X25,X17,X184,X2),X1)),X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__compose) ).

fof(fact_apfst__compose,axiom,
    ! [X20,X1,X184,X2,X17,X5,X25] : hAPP(c_Product__Type_Oapfst(X25,X5,X17,X2),hAPP(c_Product__Type_Oapfst(X184,X25,X17,X1),X20)) = hAPP(c_Product__Type_Oapfst(X184,X5,X17,hAPP(c_Fun_Ocomp(X25,X5,X184,X2),X1)),X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__compose) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X20),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
          & X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_transpose__rectangle,axiom,
    ! [X89,X5,X224] :
      ( ( X224 = c_List_Olist_ONil(tc_List_Olist(X5))
       => X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [X88] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X224),X88)) = X89 )
       => c_List_Otranspose(X5,X224) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_Nat_Onat,X5),tc_Nat_Onat),c_List_Onth(X5)),hAPP(c_List_Onth(tc_List_Olist(X5)),X224))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X49,X124] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X49),X124)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X49),X124)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X30,X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X124))) )
             => hBOOL(hAPP(hAPP(X30,X49),X124)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_setprod__delta_H,axiom,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = c_Groups_Oone__class_Oone(X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_setsum__delta_H,axiom,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X49,X124] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X49),X124)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X49),X124))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X30,X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X124))) )
             => hBOOL(hAPP(hAPP(X30,X49),X124)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_listrel__Cons2,axiom,
    ! [X78,X223,X24,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_List_Olistrel(X5,X78)))
     => ~ ! [X3,X229] :
            ( X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X229)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X24)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X229),X223)),c_List_Olistrel(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37)))
     => ~ ! [X38] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),X37))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [X119,X107,X56] : c_Nitpick_Otimes__frac(X56,X107,X119) = hAPP(hAPP(c_Nitpick_Ofrac(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X56),X107)),hAPP(c_Nitpick_Onum(X56),X119))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X56),X107)),hAPP(c_Nitpick_Odenom(X56),X119))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_rel__pow__E,axiom,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X20 != X26 )
       => ~ ! [X38,X99] :
              ( X89 = hAPP(c_Nat_OSuc,X99)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X99),X37)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),X37)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37)))
     => ~ ! [X38] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [X21,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X21)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X21)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X21)) )
        & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X21)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X21) = hAPP(c_Divides_Oadjust(X21),c_Divides_OnegDivAlg(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [X21,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X21)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X21))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6) )
        & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X21))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X21) = hAPP(c_Divides_Oadjust(X21),c_Divides_OposDivAlg(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [X92,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_arith__series__int,axiom,
    ! [X89,X27,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X27))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X27)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__int) ).

fof(fact_less__number__of__Suc,axiom,
    ! [X89,X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Nat_OSuc,X89)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X89)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_le__number__of__Suc,axiom,
    ! [X89,X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Nat_OSuc,X89)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X89)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_of__nat__double,axiom,
    ! [X55,X56] :
      ( class_Rings_Osemiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X55))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,X55))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,X55))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__double) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [X61,X60] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OnegDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [X61,X60] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OposDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_power__minus1__odd,axiom,
    ! [X92,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92))) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_power__minus__even,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus__even) ).

fof(fact_power__m1__odd,axiom,
    ! [X92,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92))) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__odd) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [X92] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X92))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_ImageE,axiom,
    ! [X19,X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_OImage(X17,X5,X78),X19)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X21)),X78))
           => ~ hBOOL(hAPP(hAPP(c_member(X17),X3),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [X224,X89,X5] : c_Enum_On__lists(X5,hAPP(c_Nat_OSuc,X89),X224) = c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(X5)),c_List_Omap(X5,tc_List_Olist(X5))),hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),X224)),c_Enum_On__lists(X5,X89,X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [X89,X75,X2,X6,X5] : c_Nat_Onat_Onat__case(X5,X6,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),X89)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X5,X6,X2,X89))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X89)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_mod2__gr__0,axiom,
    ! [X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X51,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X51,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod2__gr__0) ).

fof(fact_apsnd__eq__conv,axiom,
    ! [X1,X20,X2,X5,X17,X25] :
      ( hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),X20) = hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X1),X20)
    <=> hAPP(X2,hAPP(c_Product__Type_Osnd(X5,X25),X20)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X25),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_apfst__eq__conv,axiom,
    ! [X1,X20,X2,X17,X5,X25] :
      ( hAPP(c_Product__Type_Oapfst(X25,X5,X17,X2),X20) = hAPP(c_Product__Type_Oapfst(X25,X5,X17,X1),X20)
    <=> hAPP(X2,hAPP(c_Product__Type_Ofst(X25,X17),X20)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X25,X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__eq__conv) ).

fof(fact_Id__def,axiom,
    ! [X5] : c_Relation_OId(X5) = hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X5)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(tc_prod(X5,X5),tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_HOL_Obool)),tc_prod(X5,X5)),c_COMBB(tc_prod(X5,X5),tc_HOL_Obool,X5)),c_fequal)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__def) ).

fof(fact_apsnd__apfst,axiom,
    ! [X20,X1,X184,X2,X5,X17,X25] : hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),hAPP(c_Product__Type_Oapfst(X184,X5,X25,X1),X20)) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X1,hAPP(c_Product__Type_Ofst(X184,X25),X20))),hAPP(X2,hAPP(c_Product__Type_Osnd(X184,X25),X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_apfst__apsnd,axiom,
    ! [X20,X1,X184,X2,X17,X5,X25] : hAPP(c_Product__Type_Oapfst(X25,X5,X17,X2),hAPP(c_Product__Type_Oapsnd(X184,X17,X25,X1),X20)) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X2,hAPP(c_Product__Type_Ofst(X25,X184),X20))),hAPP(X1,hAPP(c_Product__Type_Osnd(X25,X184),X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X78,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber__ring(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X78),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_max__Suc__number__of,axiom,
    ! [X89,X75] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X89))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X89)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).

fof(fact_zero__less__power2,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> X6 != c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).

fof(fact_min__Suc__number__of,axiom,
    ! [X89,X75] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X89)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_nat__rec__number__of,axiom,
    ! [X75,X2,X6,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X6)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X6,X2)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [X259,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X259)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),c_List_Ohd(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X259)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [X259,X5] : c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X259)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otl(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X259)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [X78,X146,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),X146))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X78)),X146)),X78)),X146))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X78)),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_listrel__Cons1,axiom,
    ! [X78,X224,X223,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)),X224)),c_List_Olistrel(X5,X78)))
     => ~ ! [X38,X230] :
            ( X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X38),X230)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X38)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X223),X230)),c_List_Olistrel(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_power__even__eq,axiom,
    ! [X92,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__eq) ).

fof(fact_sublist__def,axiom,
    ! [X19,X224,X5] : c_List_Osublist(X5,X224,X19) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X19)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X224),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__def) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [X72,X33,X34,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X34),X33)),X72))
    <=> ? [X49,X50] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X34),X33) = hAPP(hAPP(c_Set_Oinsert(X5),X49),X50)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X49,X50),X72))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X49),X50)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [X107,X56] : c_Nitpick_Ouminus__frac(X56,X107) = c_Nitpick_OAbs__Frac(X56,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X56),X107))),hAPP(c_Nitpick_Odenom(X56),X107))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_snd__apsnd,axiom,
    ! [X20,X2,X25,X5,X17] : hAPP(c_Product__Type_Osnd(X17,X5),hAPP(c_Product__Type_Oapsnd(X25,X5,X17,X2),X20)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X17,X25),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apsnd) ).

fof(fact_fst__apfst,axiom,
    ! [X20,X2,X25,X17,X5] : hAPP(c_Product__Type_Ofst(X5,X17),hAPP(c_Product__Type_Oapfst(X25,X5,X17,X2),X20)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X25,X17),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apfst) ).

fof(fact_fst__apsnd,axiom,
    ! [X20,X2,X25,X17,X5] : hAPP(c_Product__Type_Ofst(X5,X17),hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),X20)) = hAPP(c_Product__Type_Ofst(X5,X25),X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apsnd) ).

fof(fact_snd__apfst,axiom,
    ! [X20,X2,X25,X5,X17] : hAPP(c_Product__Type_Osnd(X17,X5),hAPP(c_Product__Type_Oapfst(X25,X17,X5,X2),X20)) = hAPP(c_Product__Type_Osnd(X25,X5),X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apfst) ).

fof(fact_nat__case__number__of,axiom,
    ! [X75,X2,X6,X5] : c_Nat_Onat_Onat__case(X5,X6,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X6)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__number__of) ).

fof(fact_max__number__of__Suc,axiom,
    ! [X75,X89] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X89))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X89)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_min__number__of__Suc,axiom,
    ! [X75,X89] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X89)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).

fof(fact_half__gt__zero,axiom,
    ! [X119,X56] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X56)
        & class_Int_Onumber__ring(X56) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X119))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X119),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [X92,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_div__2__gt__zero,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__2__gt__zero) ).

fof(fact_power3__eq__cube,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60)),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_zero__le__power2,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power2) ).

fof(fact_power__minus1__even,axiom,
    ! [X92,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).

fof(fact_power__m1__even,axiom,
    ! [X92,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__even) ).

fof(fact_diff__nat__number__of,axiom,
    ! [X75,X167] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X167),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X167),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X167)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__nat__number__of) ).

fof(fact_dropWhile__map,axiom,
    ! [X224,X2,X17,X30,X5] : c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_OdropWhile(X17,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X17,X30),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__map) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [X26,X147] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X147))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X147)) = hAPP(c_Int_Onat,X26) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X147))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X147)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X147)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__nat__eq__if) ).

fof(fact_dropWhile__neq__rev,axiom,
    ! [X20,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X20)),hAPP(c_List_Orev(X5),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),hAPP(c_List_Orev(X5),c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X20)),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_wf__weak__decr__stable,axiom,
    ! [X78,X2,X5] :
      ( ! [X88] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X88))),hAPP(X2,X88))),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X78))
       => ? [X88] :
          ! [X97] : hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),X97)) = hAPP(X2,X88) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__weak__decr__stable) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [X6,X20,X19,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X21,X19),X20))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_concat__map__singleton,axiom,
    ! [X224,X2,X17,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X17,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(X17,tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X17),c_List_Olist_OCons(X5)),X2)),c_List_Olist_ONil(X5))),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [X78,X145,X5] :
      ( c_Nitpick_Oless__eq__frac(X5,X145,X78)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X145,c_Nitpick_Ouminus__frac(X5,X78)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).

fof(fact_Nitpick_Oless__frac__def,axiom,
    ! [X78,X145,X5] :
      ( c_Nitpick_Oless__frac(X5,X145,X78)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X145,c_Nitpick_Ouminus__frac(X5,X78)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oless__frac__def) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
           => X55 = X57 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_less__2__cases,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X92 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__2__cases) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div2__Suc__Suc) ).

fof(fact_abs__power2,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power2) ).

fof(fact_Nitpick_Oof__frac__def,axiom,
    ! [X107,X56,X161] :
      ( ( class_Rings_Oinverse(X161)
        & class_Rings_Oring__1(X161) )
     => c_Nitpick_Oof__frac(X56,X161,X107) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X161),hAPP(c_Int_Oring__1__class_Oof__int(X161),hAPP(c_Nitpick_Onum(X56),X107))),hAPP(c_Int_Oring__1__class_Oof__int(X161),hAPP(c_Nitpick_Odenom(X56),X107))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_converseE,axiom,
    ! [X78,X220,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X220),hAPP(c_Relation_Oconverse(X17,X5),X78)))
     => ~ ! [X3,X38] :
            ( X220 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X38),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X38)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [X2,X89,X51,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X51)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [X26,X24,X19,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X21,X19),X24))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X26,hAPP(hAPP(c_Set_Oinsert(X5),X21),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [X24,X26,X2,X17,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X24))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),hAPP(hAPP(X2,X20),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_tranclD,axiom,
    ! [X37,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Otrancl(X5,X37)))
     => ? [X150] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X150)),X37))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X150),X24)),c_Transitive__Closure_Ortrancl(X5,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).

fof(fact_tranclD2,axiom,
    ! [X37,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Otrancl(X5,X37)))
     => ? [X150] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X150)),c_Transitive__Closure_Ortrancl(X5,X37)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X150),X24)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).

fof(fact_apfst__conv,axiom,
    ! [X24,X20,X2,X17,X5,X25] : hAPP(c_Product__Type_Oapfst(X25,X5,X17,X2),hAPP(hAPP(c_Product__Type_OPair(X25,X17),X20),X24)) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X2,X20)),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__conv) ).

fof(fact_apsnd__conv,axiom,
    ! [X24,X20,X2,X5,X17,X25] : hAPP(c_Product__Type_Oapsnd(X25,X17,X5,X2),hAPP(hAPP(c_Product__Type_OPair(X5,X25),X20),X24)) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),hAPP(X2,X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__conv) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [X224,X20,X30,X5] :
      ( c_List_Olist__ex1(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))
    <=> ( ( hBOOL(hAPP(X30,X20))
         => c_List_Olist__all(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30))),hAPP(c_fequal,X20)),X224) )
        & ( ~ hBOOL(hAPP(X30,X20))
         => c_List_Olist__ex1(X5,X30,X224) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_transpose__max__length,axiom,
    ! [X224,X5] : c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X224),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__max__length) ).

fof(fact_dropWhile__nth,axiom,
    ! [X224,X30,X5,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X30,X224))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OdropWhile(X5,X30,X224)),X95) = hAPP(hAPP(c_List_Onth(X5),X224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [X126,X122] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_power2__abs,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__abs) ).

fof(fact_power2__minus,axiom,
    ! [X60,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__minus) ).

fof(fact_mod2__Suc__Suc,axiom,
    ! [X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod2__Suc__Suc) ).

fof(fact_finite__subset__induct,axiom,
    ! [X30,X19,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X18),X19))
       => ( hBOOL(hAPP(X30,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X49,X42] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X42))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X49),X42))
                   => ( hBOOL(hAPP(X30,X42))
                     => hBOOL(hAPP(X30,hAPP(hAPP(c_Set_Oinsert(X5),X49),X42))) ) ) ) )
           => hBOOL(hAPP(X30,X18)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_mult__2,axiom,
    ! [X58,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X58) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X58),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).

fof(fact_listsum__map__filter,axiom,
    ! [X2,X30,X224,X5,X17] :
      ( class_Groups_Omonoid__add(X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => ( ~ hBOOL(hAPP(X30,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),hAPP(c_List_Ofilter(X5,X30),X224))) = hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_nat__mult__2,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X58) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X58),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X92) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_length__dropWhile__le,axiom,
    ! [X224,X30,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X30,X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X17),X20),X19)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_RangeE,axiom,
    ! [X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_ORange(X17,X5),X78)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X21)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).

fof(fact_trancl__trans,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Otrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).

fof(fact_trancl__converseI,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [X20,X19,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X19),X20))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [X6,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X5)
      <=> ( X6 = c_Groups_Oone__class_Oone(X5)
          | X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_zero__eq__power2,axiom,
    ! [X6,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_removeAll__append,axiom,
    ! [X221,X222,X55,X56] : hAPP(c_List_OremoveAll(X56,X55),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(c_List_OremoveAll(X56,X55),X222)),hAPP(c_List_OremoveAll(X56,X55),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__append) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [X20,X5] : c_List_OremoveAll(X5,X20) = c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(c_fequal,X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_rotate__rev,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Orotate(X56,X92),hAPP(c_List_Orev(X56),X222)) = hAPP(c_List_Orev(X56),hAPP(c_List_Orotate(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rev) ).

fof(fact_rotate__def,axiom,
    ! [X89,X5] : c_List_Orotate(X5,X89) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X5),tc_List_Olist(X5)),X89),c_List_Orotate1(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__def) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [X26,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X26)),c_Transitive__Closure_Otrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Otrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_Collect__conv__if,axiom,
    ! [X5,X6,X30] :
      ( ( hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X30)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X30)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_foldr__map,axiom,
    ! [X6,X224,X2,X25,X1,X5,X17] : c_List_Ofoldr(X17,X5,X1,hAPP(hAPP(c_List_Omap(X25,X17),X2),X224),X6) = c_List_Ofoldr(X25,X5,hAPP(c_Fun_Ocomp(X17,tc_fun(X5,X5),X25,X1),X2),X224,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__map) ).

fof(fact_fun__upd__image,axiom,
    ! [X24,X2,X17,X19,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Set_Oimage(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24)),X19) = hAPP(hAPP(c_Set_Oinsert(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Set_Oimage(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24)),X19) = hAPP(c_Set_Oimage(X5,X17,X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__image) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [X19,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [X21,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X21)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X21) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
            & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X21)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_foldr__append,axiom,
    ! [X6,X223,X224,X2,X5,X17] : c_List_Ofoldr(X17,X5,X2,hAPP(hAPP(c_List_Oappend(X17),X224),X223),X6) = c_List_Ofoldr(X17,X5,X2,X224,c_List_Ofoldr(X17,X5,X2,X223,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__append) ).

fof(fact_psubset__insert__iff,axiom,
    ! [X22,X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_lexord__irreflexive,axiom,
    ! [X24,X78,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X24),X24)),c_List_Olexord(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X93)),c_Int_OBit1(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X93)),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_inj__on__insert,axiom,
    ! [X19,X6,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19))
    <=> ( c_Fun_Oinj__on(X5,X17,X2,X19)
        & ~ hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__insert) ).

fof(fact_apfst__id,axiom,
    ! [X17,X5] : c_Product__Type_Oapfst(X5,X5,X17,c_Fun_Oid(X5)) = c_Fun_Oid(tc_prod(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__id) ).

fof(fact_apsnd__id,axiom,
    ! [X5,X17] : c_Product__Type_Oapsnd(X17,X17,X5,c_Fun_Oid(X17)) = c_Fun_Oid(tc_prod(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__id) ).

fof(fact_trancl__reflcl,axiom,
    ! [X78,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_subset__insert__iff,axiom,
    ! [X22,X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_eq__special_I4_J,axiom,
    ! [X20,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X20) = c_Groups_Oone__class_Oone(X5)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).

fof(fact_eq__special_I2_J,axiom,
    ! [X24,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Oone__class_Oone(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [X6,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X21) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X21)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [X126,X161] :
      ( ( class_Groups_Omonoid__mult(X161)
        & class_Int_Onumber(X161) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_r__r__into__trancl,axiom,
    ! [X23,X37,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X37))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),X37))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_DomainE,axiom,
    ! [X78,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X17),X78)))
     => ~ ! [X38] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X38)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).

fof(fact_add__self__div__2,axiom,
    ! [X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__self__div__2) ).

fof(fact_mult__2__right,axiom,
    ! [X58,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X58),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).

fof(fact_power2__eq__square,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X55) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_INF2__E,axiom,
    ! [X6,X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X22,X6),X21),X23))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__E) ).

fof(fact_nat__mult__2__right,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X58),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_zero__power2,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).

fof(fact_one__power2,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).

fof(fact_map__fun__upd,axiom,
    ! [X75,X2,X17,X224,X24,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_List_Oset(X5),X224)))
     => hAPP(hAPP(c_List_Omap(X5,X17),c_Fun_Ofun__upd(X5,X17,X2,X24,X75)),X224) = hAPP(hAPP(c_List_Omap(X5,X17),X2),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fun__upd) ).

fof(fact_trancl__mono,axiom,
    ! [X146,X78,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Otrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Otrancl(X5,X146))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X57))),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [X78,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),hAPP(c_Relation_OField(X5),X78)),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_Relation_OField(X5),X78))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_sup2E,axiom,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => ( ~ hBOOL(hAPP(hAPP(X19,X20),X24))
       => hBOOL(hAPP(hAPP(X22,X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2E) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [X37,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X37)))
    <=> ( X20 = X24
        | ( X20 != X24
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Otrancl(X5,X37))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_inf2E,axiom,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => ~ ( hBOOL(hAPP(hAPP(X19,X20),X24))
         => ~ hBOOL(hAPP(hAPP(X22,X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X172)),c_Int_OBit1(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OBit1(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X172)),c_Int_OBit1(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OBit1(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_distinct__removeAll,axiom,
    ! [X55,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),hAPP(c_List_OremoveAll(X56,X55),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__removeAll) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [X224,X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => hAPP(hAPP(c_List_Omap(X5,X17),X2),hAPP(c_List_OremoveAll(X5,X20),X224)) = hAPP(c_List_OremoveAll(X17,hAPP(X2,X20)),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).

fof(fact_dropWhile__append2,axiom,
    ! [X223,X30,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) )
     => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = c_List_OdropWhile(X5,X30,X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_map__removeAll__inj,axiom,
    ! [X224,X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(X5,X17),X2),hAPP(c_List_OremoveAll(X5,X20),X224)) = hAPP(c_List_OremoveAll(X17,hAPP(X2,X20)),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [X224,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => ~ hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_length__transpose,axiom,
    ! [X224,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X224)) = c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__transpose) ).

fof(fact_trancl__power,axiom,
    ! [X37,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Otrancl(X5,X37)))
    <=> ? [X130] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X130))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X130),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__power) ).

fof(fact_concat__append,axiom,
    ! [X221,X222,X56] : c_List_Oconcat(X56,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X56)),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),c_List_Oconcat(X56,X222)),c_List_Oconcat(X56,X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__list__update,axiom,
    ! [X96,X6,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X224),X96)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__list__update) ).

fof(fact_pigeonhole,axiom,
    ! [X19,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X17,X5,X2),X19))),hAPP(c_Finite__Set_Ocard(X17),X19)))
     => ~ c_Fun_Oinj__on(X17,X5,X2,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_rtranclD,axiom,
    ! [X37,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X37)))
     => ( X6 = X21
        | ( X6 != X21
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X37))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [X30,X224,X5,X89] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X89))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => ~ hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X89))) )
       => c_List_OtakeWhile(X5,X30,X224) = hAPP(hAPP(c_List_Otake(X5),X89),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [X84,X23,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [X84,X23,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [X23,X21,X84,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [X23,X21,X84,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_inj__on__fun__updI,axiom,
    ! [X20,X24,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => c_Fun_Oinj__on(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_distinct__concat,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X5)),X224))
     => ( ! [X230] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X230),hAPP(c_List_Oset(tc_List_Olist(X5)),X224)))
           => hBOOL(hAPP(c_List_Odistinct(X5),X230)) )
       => ( ! [X230] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X230),hAPP(c_List_Oset(tc_List_Olist(X5)),X224)))
             => ! [X262] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X262),hAPP(c_List_Oset(tc_List_Olist(X5)),X224)))
                 => ( X230 != X262
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X230)),hAPP(c_List_Oset(X5),X262)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oconcat(X5,X224))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__concat) ).

fof(fact_Collect__conv__if2,axiom,
    ! [X5,X6,X30] :
      ( ( hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X30)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X30)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_rotate__drop__take,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Orotate(X56,X92),X222) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Odrop(X56),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X222)),hAPP(hAPP(c_List_Otake(X56),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_in__set__zipE,axiom,
    ! [X223,X224,X24,X20,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
         => ~ hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_List_Oset(X17),X223))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__zipE) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [X222,X56,X57,X55] :
      ( ( X55 = X57
       => hAPP(c_List_OremoveAll(X56,X55),hAPP(hAPP(c_List_Olist_OCons(X56),X57),X222)) = hAPP(c_List_OremoveAll(X56,X55),X222) )
      & ( X55 != X57
       => hAPP(c_List_OremoveAll(X56,X55),hAPP(hAPP(c_List_Olist_OCons(X56),X57),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X57),hAPP(c_List_OremoveAll(X56,X55),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_acyclic__insert,axiom,
    ! [X78,X20,X24,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),X78))
    <=> ( c_Wellfounded_Oacyclic(X5,X78)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).

fof(fact_wf__insert,axiom,
    ! [X78,X20,X24,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),X78))
    <=> ( c_Wellfounded_Owf(X5,X78)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).

fof(fact_trancl__unfold,axiom,
    ! [X78,X5] : c_Transitive__Closure_Otrancl(X5,X78) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Otrancl(X5,X78)),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold) ).

fof(fact_wf__eq__minimal,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
    <=> ! [X218] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X218))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X218))
              & ! [X38] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X3)),X78))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X38),X218)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X172)),c_Int_OBit0(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OBit0(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OBit0(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X172)),c_Int_OBit0(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [X57,X55] : c_Nitpick_Oint__lcm(X55,X57) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X55)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X57)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [X57,X55] : c_Nitpick_Onat__lcm(X55,X57) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),X57)),c_Nitpick_Onat__gcd(X55,X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [X6,X224,X20,X2,X5,X17] : c_List_Ofoldr(X17,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X17),X20),X224),X6) = hAPP(hAPP(X2,X20),c_List_Ofoldr(X17,X5,X2,X224,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_wf__not__sym,axiom,
    ! [X20,X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X20)),X78))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X6)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [X20,X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X20)),X78))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X6)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [X191,X89,X51] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X51,X89),X191))
    <=> ( X51 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X191)),X89)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191))
        & ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X191) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)),X89)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [X6,X84,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [X6,X84,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_minus__Bit1,axiom,
    ! [X93] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X93)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit1) ).

fof(fact_small__lazy_H_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X121,X88] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X121),X88)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X88))
               => hBOOL(hAPP(hAPP(X30,X121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X88),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X30,X121),X88)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opinduct) ).

fof(fact_less__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X51),X89)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).

fof(fact_quotientE,axiom,
    ! [X78,X19,X40,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
     => ~ ! [X3] :
            ( X40 = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientE) ).

fof(fact_divmod__nat__if,axiom,
    ! [X51,X89] :
      ( ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) )
       => c_Divides_Odivmod__nat(X51,X89) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X51) )
      & ( ~ ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) )
       => c_Divides_Odivmod__nat(X51,X89) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X89),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_divmod__nat__def,axiom,
    ! [X89,X51] : c_Divides_Odivmod__nat(X51,X89) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X51,X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [X248,X249,X250,X251,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X251),X250) = hAPP(hAPP(c_List_Oappend(X5),X249),X248)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)))
         => ( X251 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),X249)
            & X250 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),X249)),X248) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)),X251) = X249
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)),X251)),X250) = X248 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X90)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [X84] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X84))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_length__remdups__concat,axiom,
    ! [X259,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,c_List_Oconcat(X5,X259))) = hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X5)),X259)),c_List_Oset(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_less__special_I2_J,axiom,
    ! [X24,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [X24,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [X84,X21,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [X84,X21,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_sup2CI,axiom,
    ! [X17,X5,X19,X24,X20,X22] :
      ( ( ~ hBOOL(hAPP(hAPP(X22,X20),X24))
       => hBOOL(hAPP(hAPP(X19,X20),X24)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2CI) ).

fof(fact_not__acc__down,axiom,
    ! [X37,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X37)))
     => ~ ! [X150] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X150),X20)),X37))
           => hBOOL(hAPP(hAPP(c_member(X5),X150),c_Wellfounded_Oacc(X5,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).

fof(fact_flat__lub__def,axiom,
    ! [X21,X19,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X21,X19) = X21 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X21,X19) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_flat__lub__def) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X224)),c_List_Olistrel1(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_Nil__notin__lex,axiom,
    ! [X78,X223,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X223)),c_List_Olex(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [X78,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),c_List_Olist_ONil(X5))),c_List_Olex(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [X224,X6,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X224,c_Groups_Ozero__class_Ozero(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Relation_OId(X5)))
    <=> X6 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_finite__induct,axiom,
    ! [X30,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hBOOL(hAPP(X30,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X42] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X42))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X42))
               => ( hBOOL(hAPP(X30,X42))
                 => hBOOL(hAPP(X30,hAPP(hAPP(c_Set_Oinsert(X5),X3),X42))) ) ) )
         => hBOOL(hAPP(X30,X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__induct) ).

fof(fact_one__add__one__is__two,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_set__removeAll,axiom,
    ! [X224,X20,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_OremoveAll(X5,X20),X224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__removeAll) ).

fof(fact_override__on__def,axiom,
    ! [X1,X2,X17,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X1,X6) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X2,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__def) ).

fof(fact_divmod__nat__step,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
       => c_Divides_Odivmod__nat(X86,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_foldl__foldr,axiom,
    ! [X224,X6,X2,X17,X5] : hAPP(c_List_Ofoldl(X5,X17,X2,X6),X224) = c_List_Ofoldr(X17,X5,hAPP(c_COMBC(X5,X17,X5),X2),hAPP(c_List_Orev(X17),X224),X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr) ).

fof(fact_override__on__apply__notin,axiom,
    ! [X1,X2,X17,X19,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X2,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).

fof(fact_distinct__dropWhile,axiom,
    ! [X30,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OdropWhile(X5,X30,X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [X1,X19,X18,X26,X2,X17,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X17,X2,X26,X18)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
         => hAPP(hAPP(X18,X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1),X26),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
         => hAPP(hAPP(X18,X1),X19) = X26 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_in__measure,axiom,
    ! [X2,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(c_Wellfounded_Omeasure(X5),X2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).

fof(fact_measure__def,axiom,
    ! [X5] : c_Wellfounded_Omeasure(X5) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X5),c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measure__def) ).

fof(fact_SigmaE2,axiom,
    ! [X22,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => ~ hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).

fof(fact_map__concat,axiom,
    ! [X224,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Oconcat(X17,X224)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X17),tc_List_Olist(X5)),hAPP(c_List_Omap(X17,X5),X2)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__concat) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X93)),c_Int_OBit0(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X93)),c_Int_OBit0(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [X224,X17,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_List_Oset(X17),X224))))
       => c_List_Olinorder__class_Oinsort__insert__key(X17,X5,X2,X20,X224) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_total__on__diff__Id,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Ototal__on(X5,X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5)))
    <=> c_Relation_Ototal__on(X5,X19,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X92))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact_mult__Bit1,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X93)),X91) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X91))),X91),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).

fof(fact_number__of1,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X92)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X93)),c_Int_OBit1(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),c_Int_Osucc(X91))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OBit1(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X172)),c_Int_OBit1(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X172)),c_Int_OBit1(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OBit1(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_antisym__reflcl,axiom,
    ! [X78,X5] :
      ( c_Relation_Oantisym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5)))
    <=> c_Relation_Oantisym(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__reflcl) ).

fof(fact_finite__trancl,axiom,
    ! [X78,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),c_Transitive__Closure_Otrancl(X5,X78)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__trancl) ).

fof(fact_card__Diff__insert,axiom,
    ! [X22,X6,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X22))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_rev__concat,axiom,
    ! [X224,X5] : hAPP(c_List_Orev(X5),c_List_Oconcat(X5,X224)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Orev(X5)),hAPP(c_List_Orev(tc_List_Olist(X5)),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__concat) ).

fof(fact_fold__image__insert,axiom,
    ! [X26,X1,X6,X19,X5,X17] :
      ( class_Groups_Oab__semigroup__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),X26),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),X26),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__insert) ).

fof(fact_filter__concat,axiom,
    ! [X224,X133,X5] : hAPP(c_List_Ofilter(X5,X133),c_List_Oconcat(X5,X224)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Ofilter(X5,X133)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__concat) ).

fof(fact_in__measures_I1_J,axiom,
    ! [X24,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).

fof(fact_divide__less__eq,axiom,
    ! [X6,X23,X21,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

fof(fact_divide__le__eq,axiom,
    ! [X6,X23,X21,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

fof(fact_distinct__rotate,axiom,
    ! [X224,X89,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate(X5,X89),X224)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rotate) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [X24,X37,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_Relation_ODomain(X5,X5),X37)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X37)))
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X93)),c_Int_OBit1(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [X1,X19,X18,X26,X2,X17,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X17,X2,X26,X18)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(hAPP(X18,X1),X19) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_diff__special_I2_J,axiom,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),c_Groups_Oone__class_Oone(X56)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).

fof(fact_distinct__insort,axiom,
    ! [X224,X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X224)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort) ).

fof(fact_diff__special_I1_J,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_r__into__trancl_H,axiom,
    ! [X78,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Otrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [X222,X55,X56] : c_List_Oconcat(X56,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X56)),X55),X222)) = hAPP(hAPP(c_List_Oappend(X56),X55),c_List_Oconcat(X56,X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X27))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X27)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_insert__partition,axiom,
    ! [X18,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X20),X18))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X20),X18)))
           => ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X63),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X20),X18)))
               => ( X3 != X63
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X63) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X20),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__partition) ).

fof(fact_reflcl__trancl,axiom,
    ! [X78,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X78)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_list__update__append,axiom,
    ! [X55,X221,X222,X56,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92),X55) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X92),X55)),X221) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92),X55) = hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist__update(X56,X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append) ).

fof(fact_less__divide__eq,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

fof(fact_le__divide__eq,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [X278,X6,X149,X28,X17,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X17,X28,X149,c_Lazy__Sequence_Olazy__sequence_OInsert(X17,X6,X278)) = hAPP(hAPP(X149,X6),X278),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_seq__case,axiom,
    ! [X254,X1,X2,X17,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X17,X2,X1,X254) = c_Option_Ooption_Ooption__case(X5,tc_prod(X17,tc_Lazy__Sequence_Olazy__sequence(X17)),X2,hAPP(c_Product__Type_Oprod_Oprod__case(X17,tc_Lazy__Sequence_Olazy__sequence(X17),X5),X1),hAPP(c_Lazy__Sequence_Oyield(X17),X254)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__case) ).

fof(fact_mult__numeral__1,axiom,
    ! [X60,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_list__ex__iff__not__all__inverval__int,axiom,
    ! [X95,X96,X30] :
      ( c_List_Olist__ex(tc_Int_Oint,X30,c_List_Oupto(X96,X95))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X30),X96,X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).

fof(fact_rotate__add,axiom,
    ! [X89,X51,X5] : c_List_Orotate(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orotate(X5,X51)),c_List_Orotate(X5,X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__add) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X27)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_less__special_I4_J,axiom,
    ! [X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_le__special_I4_J,axiom,
    ! [X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_IdE,axiom,
    ! [X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Relation_OId(X5)))
     => ~ ! [X3] : X133 != hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdE) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [X91] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).

fof(fact_IdI,axiom,
    ! [X6,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),c_Relation_OId(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdI) ).

fof(fact_foldl__conv__concat,axiom,
    ! [X259,X224,X5] : hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),X224),X259) = hAPP(hAPP(c_List_Oappend(X5),X224),c_List_Oconcat(X5,X259)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X93)),c_Int_OBit1(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_insort__insert__insort,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X20,X224) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_irrefl__def,axiom,
    ! [X78,X5] :
      ( c_Relation_Oirrefl(X5,X78)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).

fof(fact_wf__not__refl,axiom,
    ! [X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__irrefl,axiom,
    ! [X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__irrefl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [X78,X5] : c_Transitive__Closure_Ortrancl(X5,X78) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X78)),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_INT__E,axiom,
    ! [X6,X22,X19,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(X22,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X17),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__E) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [X84,X75,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Otimes__class_Otimes(X5)),c_COMBI(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [X20,X24,X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X23)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

fof(fact_foldl__foldr1,axiom,
    ! [X224,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X224) = c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X224,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_nth__map__upt,axiom,
    ! [X2,X5,X51,X89,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),X51)))
     => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X51,X89))),X96) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X96)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map__upt) ).

fof(fact_rotate__rotate,axiom,
    ! [X222,X92,X86,X56] : hAPP(c_List_Orotate(X56,X86),hAPP(c_List_Orotate(X56,X92),X222)) = hAPP(c_List_Orotate(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rotate) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [X6,X224,X5] :
      ( class_Groups_Oab__semigroup__add(X5)
     => c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X224,X6) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_lazy__sequence_Osimps_I4_J,axiom,
    ! [X149,X28,X17,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X17,X28,X149,c_Lazy__Sequence_Olazy__sequence_OEmpty(X17)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).

fof(fact_rotate__conv__mod,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Orotate(X56,X92),X222) = hAPP(c_List_Orotate(X56,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_pred__Bit0,axiom,
    ! [X93] : c_Int_Opred(c_Int_OBit0(X93)) = c_Int_OBit1(c_Int_Opred(X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit0) ).

fof(fact_setprod__diff1,axiom,
    ! [X6,X2,X19,X5,X17] :
      ( class_Fields_Ofield(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X17)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__diff1) ).

fof(fact_refl__reflcl,axiom,
    ! [X78,X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__reflcl) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [X224,X30,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X30,X224)),c_List_OdropWhile(X5,X30,X224)) = X224,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_setsum__diff1,axiom,
    ! [X2,X6,X19,X5,X17] :
      ( class_Groups_Oab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1) ).

fof(fact_set__concat,axiom,
    ! [X224,X5] : hAPP(c_List_Oset(X5),c_List_Oconcat(X5,X224)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X5)),X224)),c_List_Oset(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__concat) ).

fof(fact_length__concat,axiom,
    ! [X259,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oconcat(X5,X259)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X259)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__concat) ).

fof(fact_INF1__E,axiom,
    ! [X6,X21,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21))
     => ( ~ hBOOL(hAPP(hAPP(X22,X6),X21))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__E) ).

fof(fact_trans__diff__Id,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => ( c_Relation_Oantisym(X5,X78)
       => c_Relation_Otrans(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__diff__Id) ).

fof(fact_foldr__max__sorted,axiom,
    ! [X24,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),X224))
       => ( ( X224 = c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X224,X24) = X24 )
          & ( X224 != c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X224,X24) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_List_Onth(X5),X224),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_trans__reflclI,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__reflclI) ).

fof(fact_length__filter__less,axiom,
    ! [X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X30),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__less) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [X37,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [X78,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [X78,X5] : c_Relation_Oirrefl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Relation_OId(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_divmod__int__relI,axiom,
    ! [X119,X107,X61,X60] :
      ( X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X119))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [X91] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X91)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [X2,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_wf__converse__trancl,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))
     => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [X259,X5] :
      ( c_List_Oconcat(X5,X259) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X259)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [X259,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oconcat(X5,X259)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X259)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_upt__add__eq__append,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => c_List_Oupt(X98,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X94)),c_List_Oupt(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [X2,X51,X89,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(c_Nat_OSuc,X89))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89))),hAPP(X2,hAPP(c_Nat_OSuc,X89))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_UnE,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnE) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [X224,X30,X5] :
      ( c_List_OdropWhile(X5,X30,X224) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_folding_Oinsert,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X2,X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_sorted__dropWhile,axiom,
    ! [X30,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X224)
       => c_List_Olinorder__class_Osorted(X5,c_List_OdropWhile(X5,X30,X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X230,X262] :
          ( X224 = hAPP(hAPP(c_List_Oappend(X5),X230),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X262))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X262))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X230] :
          ( ? [X262] : X224 = hAPP(hAPP(c_List_Oappend(X5),X230),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X262))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X230))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_succ__Bit1,axiom,
    ! [X93] : c_Int_Osucc(c_Int_OBit1(X93)) = c_Int_OBit0(c_Int_Osucc(X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit1) ).

fof(fact_power__number__of__even,axiom,
    ! [X84,X26,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Otimes__class_Otimes(X5)),c_COMBI(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__even) ).

fof(fact_Diff__iff,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD2,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [X86,X91] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X91),X86) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X91)),c_List_Oembed__list(X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_return__list__def,axiom,
    ! [X106] : c_List_Oreturn__list(X106) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_return__list__def) ).

fof(fact_embed__list__def,axiom,
    ! [X106] : c_List_Oembed__list(X106) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_embed__list__def) ).

fof(fact_card__Suc__eq,axiom,
    ! [X90,X19,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Nat_OSuc,X90)
    <=> ? [X124,X125] :
          ( X19 = hAPP(hAPP(c_Set_Oinsert(X5),X124),X125)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X124),X125))
          & hAPP(c_Finite__Set_Ocard(X5),X125) = X90
          & ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X125 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__eq) ).

fof(fact_distinct__remove1__removeAll,axiom,
    ! [X55,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => c_List_Oremove1(X56,X55,X222) = hAPP(c_List_OremoveAll(X56,X55),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_take__upt,axiom,
    ! [X92,X86,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X86)),X92))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X86),c_List_Oupt(X98,X92)) = c_List_Oupt(X98,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__upt) ).

fof(fact_rotate__map,axiom,
    ! [X224,X2,X17,X89,X5] : hAPP(c_List_Orotate(X5,X89),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Orotate(X17,X89),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__map) ).

fof(fact_trancl__converse,axiom,
    ! [X78,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [X223,X17,X24,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X20)),hAPP(X2,X24)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) = hAPP(hAPP(c_List_Olist_OCons(X17),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X20)),hAPP(X2,X24)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) = hAPP(hAPP(c_List_Olist_OCons(X17),X24),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X223)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_upto__rec__number__of,axiom,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_subset__insert,axiom,
    ! [X22,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).

fof(fact_IntE,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).

fof(fact_upto_Opsimps,axiom,
    ! [X95,X96] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X96),X95)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),X95))
         => c_List_Oupto(X96,X95) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X96),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),X95)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),X95))
         => c_List_Oupto(X96,X95) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Opsimps) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_small__lazy_H_Opsimps,axiom,
    ! [X96,X27] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X27),X96)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X96))
         => c_Lazy__Sequence_Osmall__lazy_H(X27,X96) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X96))
         => c_Lazy__Sequence_Osmall__lazy_H(X27,X96) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X96),c_Lazy__Sequence_Osmall__lazy_H(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opsimps) ).

fof(fact_notin__set__remove1,axiom,
    ! [X24,X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X24,X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_notin__set__sublistI,axiom,
    ! [X111,X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X111)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_nth__upt,axiom,
    ! [X94,X93,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),X94))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X98,X94)),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__upt) ).

fof(fact_zpower__number__of__even,axiom,
    ! [X84,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X84))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__number__of__even) ).

fof(fact_less__fun__def,axiom,
    ! [X1,X2,X5,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X17)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X1),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_pick_Osimps,axiom,
    ! [X222,X55,X56,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55)))
       => hAPP(c_Random_Opick(X56,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X56)),X55),X222)),X98) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X56),X55) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55)))
       => hAPP(c_Random_Opick(X56,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X56)),X55),X222)),X98) = hAPP(c_Random_Opick(X56,X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick_Osimps) ).

fof(fact_UnionE,axiom,
    ! [X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62)))
     => ~ ! [X152] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X19),X152))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X152),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionE) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OBit0(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X172)),c_Int_OBit0(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OBit0(X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X171,X172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X172)),c_Int_OBit0(X171)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X172),X171)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [X55,X56] : hAPP(c_List_OremoveAll(X56,X55),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_add__special_I3_J,axiom,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),c_Groups_Oone__class_Oone(X56)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [X84,X75,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_bot2E,axiom,
    ! [X24,X20,X17,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X20),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [X57,X151,X142,X143] :
      ( X143 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X142),X151)),X57)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X57),X142)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X142),X57))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X142 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X143,X142) = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [X6,X2,X5,X17] : c_List_Ofoldr(X17,X5,X2,c_List_Olist_ONil(X17),X6) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_concat__map__maps,axiom,
    ! [X224,X2,X17,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X17,tc_List_Olist(X5)),X2),X224)) = c_List_Omaps(X17,X5,X2,X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [X224,X2,X5,X17] : c_List_Omaps(X17,X5,X2,X224) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X17,tc_List_Olist(X5)),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__def) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [X141,X57,X142,X143] :
      ( X143 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X142),X57)),X141)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X142)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X142),X141))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X142 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X143),X142) = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_rotate__Suc,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Orotate(X56,hAPP(c_Nat_OSuc,X92)),X222) = hAPP(c_List_Orotate1(X56),hAPP(c_List_Orotate(X56,X92),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__Suc) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),hAPP(hAPP(X2,X20),X26)),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [X224,X20,X95,X96] :
      ( c_List_Oupt(X96,X95) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X20),X224)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X95))
        & X96 = X20
        & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X95) = X224 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [X2,X51,X89,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89))),hAPP(X2,X89)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_sup1E,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => ( ~ hBOOL(hAPP(X19,X20))
       => hBOOL(hAPP(X22,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1E) ).

fof(fact_pred__Bit1,axiom,
    ! [X93] : c_Int_Opred(c_Int_OBit1(X93)) = c_Int_OBit0(X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [X93,X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X93) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X166))),X93) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).

fof(fact_trancl__empty,axiom,
    ! [X5] : c_Transitive__Closure_Otrancl(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__empty) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [X89,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X51,X89))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X51,X89))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [X89,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X51,X89))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X51,X89))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_inf1E,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => ~ ( hBOOL(hAPP(X19,X20))
         => ~ hBOOL(hAPP(X22,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Orotate1(X56),hAPP(c_List_Orotate(X56,X92),X222)) = hAPP(c_List_Orotate(X56,X92),hAPP(c_List_Orotate1(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_number__of__Bit1,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126))),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_DiffI,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [X194,X149,X28,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X28,X149,c_Code__Numeral_OSuc__code__numeral(X194)) = hAPP(hAPP(X149,X194),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X28,X149,X194)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [X93] : c_Code__Numeral_OSuc__code__numeral(X93) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X93))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_card__def,axiom,
    ! [X19,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).

fof(fact_Id__O__R,axiom,
    ! [X37,X17,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X17),c_Relation_OId(X5)),X37) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__O__R) ).

fof(fact_divide__numeral__1,axiom,
    ! [X60,X56] :
      ( ( class_Fields_Ofield(X56)
        & class_Int_Onumber__ring(X56) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_divide__Numeral1,axiom,
    ! [X55,X56] :
      ( ( class_Fields_Ofield(X56)
        & class_Int_Onumber__ring(X56) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_le__supE,axiom,
    ! [X55,X61,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)),X55))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supE) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [X55,X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)),X55))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [X60,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_member__rec_I1_J,axiom,
    ! [X24,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X24))
    <=> ( X20 = X24
        | hBOOL(hAPP(hAPP(c_List_Omember(X5),X224),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).

fof(fact_member__set,axiom,
    ! [X5] : c_List_Omember(X5) = c_List_Oset(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__set) ).

fof(fact_hd__rotate__conv__nth,axiom,
    ! [X92,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Ohd(X56),hAPP(c_List_Orotate(X56,X92),X222)) = hAPP(hAPP(c_List_Onth(X56),X222),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [X93,X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X166))),X93) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_rotate__length01,axiom,
    ! [X92,X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(X56,X92),X222) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__length01) ).

fof(fact_Int__insert__left,axiom,
    ! [X22,X62,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).

fof(fact_UnCI,axiom,
    ! [X19,X22,X23,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnCI) ).

fof(fact_not__square__less__zero,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60)),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [X126,X122] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X122))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_add__leE,axiom,
    ! [X92,X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),X92))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X90)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [X84] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X84))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_Image__Id,axiom,
    ! [X19,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId(X5)),X19) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id) ).

fof(fact_insert__Diff__if,axiom,
    ! [X19,X22,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_le__iff__pred__less,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X90)),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [X91] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_div__if,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).

fof(fact_not__zle__0__negative,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X92))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [X37,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X37)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_upt__Suc__append,axiom,
    ! [X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X94)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X94),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_Int__insert__right,axiom,
    ! [X22,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).

fof(fact_setprod_OF__eq,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = c_Groups_Oone__class_Oone(X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_setsum_OF__eq,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Oplus__class_Oplus(X17)),X1),c_Groups_Ozero__class_Ozero(X17)),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = c_Groups_Ozero__class_Ozero(X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_nth__append,axiom,
    ! [X221,X222,X56,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92) = hAPP(hAPP(c_List_Onth(X56),X222),X92) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92) = hAPP(hAPP(c_List_Onth(X56),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append) ).

fof(fact_Compl__iff,axiom,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplE) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [X84] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X84)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).

fof(fact_max__number__of,axiom,
    ! [X122,X103,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Orderings_Oord(X161) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X122) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X103) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of) ).

fof(fact_min__number__of,axiom,
    ! [X122,X103,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Orderings_Oord(X161) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X103) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X122) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of) ).

fof(fact_not__add__less1,axiom,
    ! [X94,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X98,X94] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X98)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_remove1__append,axiom,
    ! [X223,X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremove1(X5,X20,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X20,X224)),X223) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremove1(X5,X20,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),X224),c_List_Oremove1(X5,X20,X223)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__append) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [X75] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X75))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__pred__iff__0) ).

fof(fact_empty__fold1SetE,axiom,
    ! [X20,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X106,X90] :
      ( c_Int_OBit1(X90) = c_Int_OBit1(X106)
    <=> X90 = X106 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_concat__replicate__trivial,axiom,
    ! [X98,X56] : c_List_Oconcat(X56,c_List_Oreplicate(tc_List_Olist(X56),X98,c_List_Olist_ONil(X56))) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__replicate__trivial) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [X21,X6,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X21)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X21))
            & ~ hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X121] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X121)
              & ~ hBOOL(hAPP(X30,X121)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_length__rotate,axiom,
    ! [X222,X92,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(c_List_Orotate(X56,X92),X222)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [X30,X5] : c_List_OdropWhile(X5,X30,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_setprod__insert,axiom,
    ! [X2,X6,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [X2,X6,X18,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X18))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X18)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__insert) ).

fof(fact_setsum_Oinsert,axiom,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_drop__upt,axiom,
    ! [X94,X98,X86] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X86),c_List_Oupt(X98,X94)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X86),X94),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__upt) ).

fof(fact_filter__empty__conv,axiom,
    ! [X224,X30,X5] :
      ( hAPP(c_List_Ofilter(X5,X30),X224) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => ~ hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_not__int__zless__negative,axiom,
    ! [X86,X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_set__rotate,axiom,
    ! [X224,X89,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate(X5,X89),X224)) = hAPP(c_List_Oset(X5),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate) ).

fof(fact_sup1CI,axiom,
    ! [X5,X19,X20,X22] :
      ( ( ~ hBOOL(hAPP(X22,X20))
       => hBOOL(hAPP(X19,X20)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1CI) ).

fof(fact_partition__P,axiom,
    ! [X255,X256,X224,X30,X5] :
      ( c_List_Opartition(X5,X30,X224) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X256),X255)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X256)))
           => hBOOL(hAPP(X30,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X255)))
           => ~ hBOOL(hAPP(X30,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__P) ).

fof(fact_trancl__domain,axiom,
    ! [X78,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Otrancl(X5,X78)) = hAPP(c_Relation_ODomain(X5,X5),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [X78,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Otrancl(X5,X78)) = hAPP(c_Relation_ORange(X5,X5),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).

fof(fact_le__nat__number__of,axiom,
    ! [X167,X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),X167))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_dvd_Oless__trans,axiom,
    ! [X58,X57,X55] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X55),X57))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X57),X55)) )
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X57),X58))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X58),X57)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X55),X58))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X58),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X93)),c_Int_OBit0(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X93)),c_Int_OBit0(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [X20] :
      ~ ! [X38] :
          ( X20 = hAPP(c_Int_OAbs__Integ,X38)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_upt__conv__Cons,axiom,
    ! [X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => c_List_Oupt(X98,X94) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_filter__insort__triv,axiom,
    ! [X224,X2,X5,X20,X30,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_not__psubset__empty,axiom,
    ! [X19,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_fold1__eq__fold,axiom,
    ! [X6,X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_number__of__Bit0,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126))),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_map__nth,axiom,
    ! [X224,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X224)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))) = X224,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__nth) ).

fof(fact_le__infE,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_length__remove1,axiom,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X20,X224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X20,X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remove1) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [X22,X62,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_nat__of__aux__code,axiom,
    ! [X92,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X98,X92) = X92 )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X98,X92) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [X92,X98] : c_Code__Numeral_Onat__of__aux(X98,X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_sym__trancl,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => c_Relation_Osym(X5,c_Transitive__Closure_Otrancl(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__trancl) ).

fof(fact_wf__trancl,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).

fof(fact_R__O__Id,axiom,
    ! [X37,X17,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X17),X37),c_Relation_OId(X17)) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_R__O__Id) ).

fof(fact_trancl__unfold__right,axiom,
    ! [X78,X5] : c_Transitive__Closure_Otrancl(X5,X78) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X78)),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [X37,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Otrancl(X5,X37)) = c_Transitive__Closure_Ortrancl(X5,X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [X56] : c_List_Oconcat(X56,c_List_Olist_ONil(tc_List_Olist(X56))) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
    ! [X21,X6] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).

fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
    ! [X21,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X20),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_trans__trancl,axiom,
    ! [X78,X5] : c_Relation_Otrans(X5,c_Transitive__Closure_Otrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__trancl) ).

fof(fact_eq__nat__number__of,axiom,
    ! [X167,X75] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)))
             => X75 = X167 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_abs__number__of,axiom,
    ! [X55,X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Rings_Olinordered__idom(X56) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X55) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__number__of) ).

fof(fact_converse__Id,axiom,
    ! [X5] : hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId(X5)) = c_Relation_OId(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id) ).

fof(fact_mod__nat__number__of,axiom,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_mult__Bit0,axiom,
    ! [X91,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X93)),X91) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).

fof(fact_takeWhile__append1,axiom,
    ! [X223,X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = c_List_OtakeWhile(X5,X30,X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_div__nat__number__of,axiom,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [X126,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_fold1__insert,axiom,
    ! [X20,X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert) ).

fof(fact_dvd_OatLeastatMost__empty,axiom,
    ! [X6,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [X86,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X122))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X122))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X89,X30] :
      ( ~ hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X30,X89))
       => ? [X97] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X89))
            & ! [X88] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X97))
               => ~ hBOOL(hAPP(X30,X88)) )
            & hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_greaterThanAtMost__upt,axiom,
    ! [X51,X89] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X89,X51) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X89),hAPP(c_Nat_OSuc,X51))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [X22,X19,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_rotate__id,axiom,
    ! [X222,X56,X92] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(X56,X92),X222) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [X224,X89,X5] :
      ( hAPP(c_List_Orotate(X5,X89),X224) = c_List_Olist_ONil(X5)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_simp__from__to,axiom,
    ! [X96,X95] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X95),X96))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X95),X96))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X96),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),X95)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_simp__from__to) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56))),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit0(X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_insertCI,axiom,
    ! [X21,X22,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X22))
       => X6 = X21 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_Bit1__def,axiom,
    ! [X93] : c_Int_OBit1(X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X93)),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(fact_internal__split__conv,axiom,
    ! [X21,X6,X23,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Ointernal__split(X17,X25,X5),X23),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)) = hAPP(hAPP(X23,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).

fof(fact_internal__split__def,axiom,
    ! [X25,X17,X5] : c_Product__Type_Ointernal__split(X5,X17,X25) = c_Product__Type_Oprod_Oprod__case(X5,X17,X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).

fof(fact_map__replicate__trivial,axiom,
    ! [X96,X20,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_COMBK(X5,tc_Nat_Onat),X20)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X96)) = c_List_Oreplicate(X5,X96,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__trivial) ).

fof(fact_ComplI,axiom,
    ! [X19,X23,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplI) ).

fof(fact_vimage__const,axiom,
    ! [X17,X19,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hAPP(c_Set_Ovimage(X17,X5,hAPP(c_COMBK(X5,X17),X23)),X19) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hAPP(c_Set_Ovimage(X17,X5,hAPP(c_COMBK(X5,X17),X23)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__const) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(X18,X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_map__Suc__upt,axiom,
    ! [X89,X51] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X51,X89)) = c_List_Oupt(hAPP(c_Nat_OSuc,X51),hAPP(c_Nat_OSuc,X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_divmod__int__def,axiom,
    ! [X61,X60] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = c_Divides_OposDivAlg(X60,X61) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( ( X60 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
              & ( X60 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X60,X61) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = c_Divides_OnegDivAlg(X60,X61) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__def) ).

fof(fact_takeWhile__tail,axiom,
    ! [X106,X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X106))) = c_List_OtakeWhile(X5,X30,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_refl__Id,axiom,
    ! [X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Relation_OId(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__Id) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => c_Groups_Oone__class_Oone(X56) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_not__less__eq__eq,axiom,
    ! [X89,X51] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_abs__not__less__zero,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [X84,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Int_Oring__char__0(X5) )
     => ( c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(X84)))
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_add__nat__number__of,axiom,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X166),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X166),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X166)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_power__nat__number__of,axiom,
    ! [X92,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [X91] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X91)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_minus__shift__def,axiom,
    ! [X119,X91,X93] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Random_Ominus__shift(X119,X93,X91) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X119),X93)),X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Random_Ominus__shift(X119,X93,X91) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X93),X91) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__shift__def) ).

fof(fact_split__zmod,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,c_Divides_Odiv__class_Omod(tc_Int_Oint,X89,X90)))
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X30,X89)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X88,X120] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X90))
                & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X120)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X88,X120] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X120))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X120)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).

fof(fact_upto_Osimps,axiom,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
       => c_List_Oupto(X98,X94) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X98),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)),X94)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
       => c_List_Oupto(X98,X94) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Osimps) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X91,X93] : c_Int_OBit0(X93) != c_Int_OBit1(X91),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X91,X93] : c_Int_OBit1(X93) != c_Int_OBit0(X91),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [X92,X86] : c_Divides_Odivmod__nat(X86,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [X194,X149,X28,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X28,X149,c_Code__Numeral_OSuc__code__numeral(X194)) = hAPP(X149,X194),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [X51,X89] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X89,X51) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X89),X51)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_Oremdups(X5,X224) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Oremdups(X5,X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_of__int__of__nat,axiom,
    ! [X93,X56] :
      ( class_Rings_Oring__1(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X56),X93) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X56),X93) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,X93)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_small__lazy_H_Osimps,axiom,
    ! [X98,X73] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X73,X98) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X73,X98) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X98),c_Lazy__Sequence_Osmall__lazy_H(X73,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Osimps) ).

fof(fact_Domain__Id,axiom,
    ! [X5] : hAPP(c_Relation_ODomain(X5,X5),c_Relation_OId(X5)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id) ).

fof(fact_Range__Id,axiom,
    ! [X5] : hAPP(c_Relation_ORange(X5,X5),c_Relation_OId(X5)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Min_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_list__all__iff__all__interval__nat,axiom,
    ! [X95,X96,X30] :
      ( c_List_Olist__all(tc_Nat_Onat,X30,c_List_Oupt(X96,X95))
    <=> c_List_Oall__interval__nat(X30,X96,X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__nat) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [X37,X5] : c_Transitive__Closure_Otrancl(X5,c_Transitive__Closure_Ortrancl(X5,X37)) = c_Transitive__Closure_Ortrancl(X5,X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_sublist__singleton,axiom,
    ! [X20,X5,X19] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)),X19) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)),X19) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__singleton) ).

fof(fact_List_Omember__def,axiom,
    ! [X20,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),X224),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omember__def) ).

fof(fact_in__set__member,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> hBOOL(hAPP(hAPP(c_List_Omember(X5),X224),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__member) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [X166] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).

fof(fact_single__valued__Id,axiom,
    ! [X5] : c_Relation_Osingle__valued(X5,X5,c_Relation_OId(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id) ).

fof(fact_less__le__not__le,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card_Oinsert,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).

fof(fact_split__zdiv,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X89),X90)))
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X88] :
              ( ? [X120] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X90))
                  & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X88)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X88] :
              ( ? [X120] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X120))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X88)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).

fof(fact_insert__ident,axiom,
    ! [X22,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X20),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)
        <=> X19 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_card__insert__if,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Finite__Set_Ocard(X5),X19) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_last__upt,axiom,
    ! [X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(X98,X94)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__upt) ).

fof(fact_Suc__code__numeral__minus__one,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X92)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_not__less__eq,axiom,
    ! [X89,X51] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X51))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_distinct__upt,axiom,
    ! [X94,X98] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X98,X94))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upt) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [X37,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X37) = c_Relation_OId(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_OtakeWhile(X5,X30,X224)) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_int__less__0__conv,axiom,
    ! [X93] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).

fof(fact_rel__simps_I43_J,axiom,
    ! [X106] :
      ( c_Int_OMin = c_Int_OBit1(X106)
    <=> c_Int_OMin = X106 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [X90] :
      ( c_Int_OBit1(X90) = c_Int_OMin
    <=> X90 = c_Int_OMin ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X93] : c_Int_OBit1(X93) != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X91] : c_Int_OPls != c_Int_OBit1(X91),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_sym__Id,axiom,
    ! [X5] : c_Relation_Osym(X5,c_Relation_OId(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id) ).

fof(fact_antisym__Id,axiom,
    ! [X5] : c_Relation_Oantisym(X5,c_Relation_OId(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).

fof(fact_trans__Id,axiom,
    ! [X5] : c_Relation_Otrans(X5,c_Relation_OId(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X122) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(X56) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_infinite__UNIV__listI,axiom,
    ! [X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).

fof(fact_List_Oinsert__def,axiom,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oinsert(X5,X20,X224) = X224 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oinsert(X5,X20,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_xt1_I9_J,axiom,
    ! [X60,X61,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20))
          | X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_linorder__not__less,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_leD,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__le,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_order__less__not__sym,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__asym_H,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__asym,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_mult__nat__number__of,axiom,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X166)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_hd__upt,axiom,
    ! [X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X98,X94)) = X98 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__upt) ).

fof(fact_empty__iff,axiom,
    ! [X23,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X23),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).

fof(fact_emptyE,axiom,
    ! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).

fof(fact_le__SucE,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
       => X86 = hAPP(c_Nat_OSuc,X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [X51,X89] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X89,X51) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X89,hAPP(c_Nat_OSuc,X51))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [X89,X51] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X89),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),hAPP(c_List_Ofilter(X5,X30),X224)) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X51,X89] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X51)))
      <=> X89 = X51 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [X86,X92] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X86))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_OSuc,X86)))
       => X86 = X92 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucE,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => X86 = X92 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [X92,X86] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),c_Divides_Odivmod__nat(X86,X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_code__numeral_Osize_I4_J,axiom,
    ! [X192] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X192)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X192)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I4_J) ).

fof(fact_atMost__upto,axiom,
    ! [X89] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__upto) ).

fof(fact_number__of__pred,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_Opred(X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56))),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__pred) ).

fof(fact_trancl__id,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => c_Transitive__Closure_Otrancl(X5,X78) = X78 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__id) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [X106,X90,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X90,X106)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X90),X106)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [X106,X90,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X90),X106)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_divmod__nat__base,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => c_Divides_Odivmod__nat(X86,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_equalityE,axiom,
    ! [X5,X22,X19] :
      ( X19 = X22
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X92)),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_z3div__def,axiom,
    ! [X93,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3div(X93,X91) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3div(X93,X91) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3div__def) ).

fof(fact_mod__geq,axiom,
    ! [X92,X86] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).

fof(fact_mod__if,axiom,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = X86 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).

fof(fact_not__in__set__insert,axiom,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => c_List_Oinsert(X5,X20,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_part__equivpE,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X37,X3),X3))
         => ( c_Predicate_Osymp(X5,X37)
           => ~ c_Predicate_Otransp(X5,X37) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpE) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [X193,X194] :
      ( c_Code__Numeral_OSuc__code__numeral(X194) = c_Code__Numeral_OSuc__code__numeral(X193)
    <=> X194 = X193 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [X192] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X192)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X192)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I2_J) ).

fof(fact_minus__Bit0,axiom,
    ! [X93] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X93)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_filter__replicate,axiom,
    ! [X89,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),c_List_Oreplicate(X5,X89,X20)) = c_List_Oreplicate(X5,X89,X20) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),c_List_Oreplicate(X5,X89,X20)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__replicate) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [X91] :
      ( c_List_Onat__list(X91)
     => c_List_Oembed__list(c_List_Oreturn__list(X91)) = X91 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_all__not__in__conv,axiom,
    ! [X19,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_remove1__idem,axiom,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => c_List_Oremove1(X5,X20,X224) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__idem) ).

fof(fact_length__upt,axiom,
    ! [X94,X98] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X98,X94)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__upt) ).

fof(fact_sgn__if,axiom,
    ! [X55,X56] :
      ( class_Groups_Osgn__if(X56)
     => ( ( X55 = c_Groups_Ozero__class_Ozero(X56)
         => c_Groups_Osgn__class_Osgn(X56,X55) = c_Groups_Ozero__class_Ozero(X56) )
        & ( X55 != c_Groups_Ozero__class_Ozero(X56)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
             => c_Groups_Osgn__class_Osgn(X56,X55) = c_Groups_Oone__class_Oone(X56) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
             => c_Groups_Osgn__class_Osgn(X56,X55) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_upt__conv__Nil,axiom,
    ! [X98,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X98))
     => c_List_Oupt(X98,X94) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [X95,X96] :
      ( c_List_Oupt(X96,X95) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_z3mod__def,axiom,
    ! [X93,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3mod(X93,X91) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3mod(X93,X91) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3mod__def) ).

fof(fact_abs__if,axiom,
    ! [X60,X56] :
      ( class_Groups_Oabs__if(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = X60 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_not__one__less__zero,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_not__one__le__zero,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_add__diff__inverse,axiom,
    ! [X92,X86] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_atLeast__upt,axiom,
    ! [X89] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__upt) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( X55 != X57
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X20,X24,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( X55 != X57
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__cases,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ( X55 != X57
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_not__leE,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_linorder__le__cases,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_set__upt,axiom,
    ! [X95,X96] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X96,X95)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [X95,X96] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X96,X95)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_succ__pred,axiom,
    ! [X55] : c_Int_Osucc(c_Int_Opred(X55)) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).

fof(fact_number__of__succ,axiom,
    ! [X93,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_Osucc(X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).

fof(fact_equals0D,axiom,
    ! [X6,X5,X19] :
      ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [X20] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_of__nat__cases,axiom,
    ! [X20] :
      ~ ! [X38] :
          ( X20 = hAPP(c_Code__Numeral_Oof__nat,X38)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__cases) ).

fof(fact_nat__eq__iff,axiom,
    ! [X51,X84] :
      ( hAPP(c_Int_Onat,X84) = X51
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X84 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff) ).

fof(fact_nat__eq__iff2,axiom,
    ! [X84,X51] :
      ( X51 = hAPP(c_Int_Onat,X84)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X84 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).

fof(fact_int__nat__eq,axiom,
    ! [X58] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = X58 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__eq) ).

fof(fact_tsub__def,axiom,
    ! [X55,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),X55))
       => c_Nat__Transfer_Otsub(X55,X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X57) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),X55))
       => c_Nat__Transfer_Otsub(X55,X57) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).

fof(fact_of__nat__number__of__eq,axiom,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(X56) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X122) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_mod__nat__def,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__def) ).

fof(fact_remove1__filter__not,axiom,
    ! [X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => c_List_Oremove1(X5,X20,hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_div__nat__def,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__def) ).

fof(fact_int__nat__number__of,axiom,
    ! [X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_zabs__def,axiom,
    ! [X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X98) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = X98 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X57,X55] :
      ( X55 != X57
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [X185,X92,X86] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),X185))
     => c_Divides_Odivmod__nat(X86,X92) = X185 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_zsgn__def,axiom,
    ! [X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).

fof(fact_sorted__upt,axiom,
    ! [X94,X98] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X98,X94)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upt) ).

fof(fact_wf__measure,axiom,
    ! [X2,X5] : c_Wellfounded_Owf(X5,hAPP(c_Wellfounded_Omeasure(X5),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).

fof(fact_order__less__irrefl,axiom,
    ! [X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_beyond__def,axiom,
    ! [X91,X93] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Quickcheck_Obeyond(X93,X91) = X91 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Quickcheck_Obeyond(X93,X91) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__def) ).

fof(fact_rotate0,axiom,
    ! [X5] : c_List_Orotate(X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_not__less0,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__zeroE,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_divmod__nat__zero,axiom,
    ! [X86] : c_Divides_Odivmod__nat(X86,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_less__not__refl,axiom,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [X106,X90] :
      ( c_Int_OBit0(X90) = c_Int_OBit0(X106)
    <=> X90 = X106 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = c_Groups_Oone__class_Oone(X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) = c_Groups_Oone__class_Oone(X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__infinite) ).

fof(fact_setsum__infinite,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19) = c_Groups_Ozero__class_Ozero(X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = c_Groups_Ozero__class_Ozero(X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_not__neg__int,axiom,
    ! [X92] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__int) ).

fof(fact_equivE,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ~ ( c_Relation_Orefl__on(X5,X19,X78)
         => ( c_Relation_Osym(X5,X78)
           => ~ c_Relation_Otrans(X5,X78) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivE) ).

fof(fact_code__numeral_Osimps_I3_J,axiom,
    ! [X195] : c_Code__Numeral_OSuc__code__numeral(X195) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).

fof(fact_code__numeral_Osimps_I2_J,axiom,
    ! [X196] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X196),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(help_c__fimplies__3,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X30),X29))
      | ~ hBOOL(X30)
      | hBOOL(X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).

fof(fact_card__eq__0__iff,axiom,
    ! [X19,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).

fof(help_c__fdisj__3,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X30),X29))
      | hBOOL(X30)
      | hBOOL(X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fconj__2,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X30),X29))
      | hBOOL(X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X30),X29))
      | hBOOL(X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).

fof(fact_empty__Collect__eq,axiom,
    ! [X30,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X30)
    <=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [X30,X5] :
      ( hAPP(c_Set_OCollect(X5),X30) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).

fof(help_c__fequal__1,axiom,
    ! [X24,X20] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X20),X24))
      | X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_nat__of__code,axiom,
    ! [X98] : hAPP(c_Code__Numeral_Onat__of,X98) = c_Code__Numeral_Onat__of__aux(X98,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__code) ).

fof(fact_list__ex1__simps_I1_J,axiom,
    ! [X30,X5] : ~ c_List_Olist__ex1(X5,X30,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).

fof(fact_list__ex__simps_I2_J,axiom,
    ! [X30,X5] : ~ c_List_Olist__ex(X5,X30,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_pred__def,axiom,
    ! [X93] : c_Int_Opred(X93) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__def) ).

fof(fact_succ__def,axiom,
    ! [X93] : c_Int_Osucc(X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).

fof(fact_upt__0,axiom,
    ! [X98] : c_List_Oupt(X98,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__0) ).

fof(help_c__fconj__1,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(X30)
      | ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fconj,X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).

fof(fact_add__Min,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X93) = c_Int_Opred(X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(help_c__fimplies__2,axiom,
    ! [X30,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fimplies,X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fdisj__1,axiom,
    ! [X29,X30] :
      ( ~ hBOOL(X30)
      | hBOOL(hAPP(hAPP(c_fdisj,X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [X30,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fdisj,X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [X106] :
      ( c_Int_OPls = c_Int_OBit0(X106)
    <=> c_Int_OPls = X106 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X90] :
      ( c_Int_OBit0(X90) = c_Int_OPls
    <=> X90 = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [X93] : c_Int_OBit0(X93) != c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [X91] : c_Int_OMin != c_Int_OBit0(X91),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_not__neg__nat,axiom,
    ! [X58] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X58))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = X58 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__nat) ).

fof(fact_card__infinite,axiom,
    ! [X19,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).

fof(help_c__fNot__1,axiom,
    ! [X30] :
      ( ~ hBOOL(hAPP(c_fNot,X30))
      | ~ hBOOL(X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).

fof(fact_not__iszero__1,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => ~ c_Int_Oiszero(X56,c_Groups_Oone__class_Oone(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).

fof(fact_equivpE,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ~ ( c_Predicate_Oreflp(X5,X37)
         => ( c_Predicate_Osymp(X5,X37)
           => ~ c_Predicate_Otransp(X5,X37) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpE) ).

fof(help_c__fNot__2,axiom,
    ! [X30] :
      ( ~ ~ hBOOL(X30)
      | hBOOL(hAPP(c_fNot,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [X22,X168,X169,X2,X25,X162,X163,X17,X164,X165,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X165,X164)
     => ( c_Equiv__Relations_Oequiv(X17,X163,X162)
       => ( c_Equiv__Relations_Ocongruent2(X5,X17,tc_fun(X25,tc_HOL_Obool),X164,X162,X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X169),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X165),X164)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X17,tc_HOL_Obool)),X168),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17),X163),X162)))
             => ( ! [X77] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X77),X165))
                   => ! [X170] :
                        ( hBOOL(hAPP(hAPP(c_member(X17),X170),X163))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(X2,X77),X170)),X22)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X25,tc_HOL_Obool)),X169),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X25,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,tc_HOL_Obool)),X168)),X2))),X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_rtrancl__induct2,axiom,
    ! [X30,X78,X286,X287,X288,X289,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X289),X288)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X287),X286))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
     => ( hBOOL(hAPP(hAPP(X30,X289),X288))
       => ( ! [X49,X124] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X289),X288)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
             => ! [X290,X291] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X290),X291))),X78))
                 => ( hBOOL(hAPP(hAPP(X30,X49),X124))
                   => hBOOL(hAPP(hAPP(X30,X290),X291)) ) ) )
         => hBOOL(hAPP(hAPP(X30,X287),X286)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).

fof(fact_converse__rtrancl__induct2,axiom,
    ! [X30,X78,X286,X287,X288,X289,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X289),X288)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X287),X286))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
     => ( hBOOL(hAPP(hAPP(X30,X287),X286))
       => ( ! [X49,X124,X290,X291] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X290),X291))),X78))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X290),X291)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X287),X286))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
               => ( hBOOL(hAPP(hAPP(X30,X290),X291))
                 => hBOOL(hAPP(hAPP(X30,X49),X124)) ) ) )
         => hBOOL(hAPP(hAPP(X30,X289),X288)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [X22,X19,X1,X2,X17,X5,X25] :
      ( class_Rings_Osemiring__0(X25)
     => ( c_Fun_Oinj__on(tc_prod(X5,X17),X25,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,X25),tc_fun(X17,X25)),hAPP(hAPP(c_COMBB(tc_fun(X25,X25),tc_fun(tc_fun(X17,X25),tc_fun(X17,X25)),X5),c_COMBB(X25,X25,X17)),hAPP(hAPP(c_COMBB(X25,tc_fun(X25,X25),X5),c_Groups_Otimes__class_Otimes(X25)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25),X1),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X25),c_Fun_Oid(X25)),hAPP(c_Set_OCollect(X25),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X25),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X25),hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X17))),hAPP(hAPP(c_COMBC(X25,tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X25),c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X17,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool))),X25),hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_fun(X17,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25),hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj))),hAPP(hAPP(c_COMBC(X25,tc_fun(X5,tc_fun(X17,X25)),tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X25),tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X17,X25)),tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X25),c_COMBB(tc_fun(X17,X25),tc_fun(X17,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(tc_fun(X17,X25),tc_fun(X17,tc_HOL_Obool)),X25),c_COMBB(X25,tc_HOL_Obool,X17)),c_fequal))),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,X25),tc_fun(X17,X25)),hAPP(hAPP(c_COMBB(tc_fun(X25,X25),tc_fun(tc_fun(X17,X25),tc_fun(X17,X25)),X5),c_COMBB(X25,X25,X17)),hAPP(hAPP(c_COMBB(X25,tc_fun(X25,X25),X5),c_Groups_Otimes__class_Otimes(X25)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_rel__comp__def,axiom,
    ! [X146,X78,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X78),X146) = hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_HOL_Obool,X17),c_HOL_OEx(X25))),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),tc_fun(tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool),X17)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X5),c_COMBS(X25,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X5),c_COMBC(X25,tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X5,X25)),tc_fun(X25,tc_fun(tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X25),tc_fun(tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_HOL_Obool),X25),c_member(tc_prod(X5,X25)))),c_Product__Type_OPair(X5,X25)))),X78))))),hAPP(hAPP(c_COMBC(X17,tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X17),c_COMBC(X25,tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X25,X17)),tc_fun(X25,tc_fun(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_HOL_Obool)),X17),hAPP(c_COMBB(tc_prod(X25,X17),tc_fun(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_HOL_Obool),X25),c_member(tc_prod(X25,X17)))),hAPP(c_COMBC(X25,X17,tc_prod(X25,X17)),c_Product__Type_OPair(X25,X17))))),X146))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__def) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X22)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omax(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X22)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omin(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)),c_Big__Operators_Olattice__class_OSup__fin(X5,X22)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),c_Big__Operators_Olattice__class_OInf__fin(X5,X22)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_set__Cons__def,axiom,
    ! [X199,X19,X5] : c_List_Oset__Cons(X5,X19,X199) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X5)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_List_Olist(X5)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBS(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_HOL_Obool,tc_List_Olist(X5))),c_fequal))),c_List_Olist_OCons(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),X199)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__def) ).

fof(fact_image__INT,axiom,
    ! [X95,X22,X19,X25,X62,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X62)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X25),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X22,X3)),X62)) )
       => ( hBOOL(hAPP(hAPP(c_member(X25),X95),X19))
         => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X25),c_Set_Oimage(X5,X17,X2)),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__INT) ).

fof(fact_inf__Int__eq2,axiom,
    ! [X24,X20,X36,X37,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X36)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X37),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_sup__Un__eq2,axiom,
    ! [X24,X20,X36,X37,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X36)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X37),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_lenlex__conv,axiom,
    ! [X78,X5] : c_List_Olenlex(X5,X78) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))))),c_List_Olex(X5,X78)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lenlex__conv) ).

fof(fact_foldl__apply,axiom,
    ! [X146,X1,X16,X2,X17,X25,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hAPP(c_Fun_Ocomp(X25,X25,X17,hAPP(X2,X3)),X16) = hAPP(c_Fun_Ocomp(X17,X25,X17,X16),hAPP(X1,X3)) )
     => hAPP(c_List_Ofoldl(X25,X5,hAPP(c_COMBC(X5,X25,X25),X2),hAPP(X16,X146)),X224) = hAPP(X16,hAPP(c_List_Ofoldl(X17,X5,hAPP(c_COMBC(X5,X17,X17),X1),X146),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__apply) ).

fof(fact_INF__INT__eq2,axiom,
    ! [X24,X20,X78,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),X5),hAPP(c_COMBC(X17,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X17),c_COMBC(X25,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X17,X25)),tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),X17),hAPP(c_COMBB(tc_prod(X17,X25),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool),X25),c_member(tc_prod(X17,X25)))),c_Product__Type_OPair(X17,X25))))),X78)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X25)),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X20),X24)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X17,X25),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [X24,X20,X78,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),X5),hAPP(c_COMBC(X17,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X17),c_COMBC(X25,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X17,X25)),tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),X17),hAPP(c_COMBB(tc_prod(X17,X25),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool),X25),c_member(tc_prod(X17,X25)))),c_Product__Type_OPair(X17,X25))))),X78)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X25)),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X20),X24)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X17,X25),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [X24,X20,X146,X78,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X17,X25,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X78),hAPP(hAPP(c_COMBC(X17,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X17),c_COMBC(X25,tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X17,X25)),tc_fun(X25,tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool)),X17),hAPP(c_COMBB(tc_prod(X17,X25),tc_fun(tc_fun(tc_prod(X17,X25),tc_HOL_Obool),tc_HOL_Obool),X25),c_member(tc_prod(X17,X25)))),c_Product__Type_OPair(X17,X25)))),X146)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X25)),hAPP(hAPP(c_Product__Type_OPair(X5,X25),X20),X24)),hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X78),X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [X43,X40,X2,X17,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X17,tc_HOL_Obool),X78,X2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X40),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X43),X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X43),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
             => ( ! [X3] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
                   => ! [X38] :
                        ( hBOOL(hAPP(hAPP(c_member(X5),X38),X19))
                       => ( hAPP(X2,X3) = hAPP(X2,X38)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X78)) ) ) )
               => X40 = X43 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_finite__image__set,axiom,
    ! [X2,X17,X30,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X30)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X17),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,X17),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X5,X17),tc_fun(X5,tc_HOL_Obool)),X17),c_COMBB(X17,tc_HOL_Obool,X5)),c_fequal)),X2)))),X30))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__image__set) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [X16,X1,X22,X19,X2,X17,X5,X25] :
      ( class_Groups_Ocomm__monoid__add(X25)
     => ( c_Fun_Oinj__on(X5,X17,X2,X19)
       => ( X22 = hAPP(c_Set_Oimage(X5,X17,X2),X19)
         => ( ! [X49] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
               => hAPP(X1,X49) = hAPP(X16,hAPP(X2,X49)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25),X16),X22) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),X1),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_conversep__converse__eq,axiom,
    ! [X24,X20,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X17,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X78)),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X20),X24)),hAPP(c_Relation_Oconverse(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [X16,X1,X22,X19,X2,X17,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( c_Fun_Oinj__on(X5,X17,X2,X19)
       => ( X22 = hAPP(c_Set_Oimage(X5,X17,X2),X19)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X17,X25,X5,X16),X2),X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X25),X16),X22) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X25),X1),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [X1,X2,X27,X21,X23,X6,X5,X17] :
      ( ( class_Groups_Ocomm__monoid__add(X17)
        & class_Orderings_Oord(X5) )
     => ( X6 = X23
       => ( X21 = X27
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X3))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X27))
                 => hAPP(X2,X3) = hAPP(X1,X3) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_minus__int__def,axiom,
    ! [X26] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__int__def) ).

fof(fact_exE__realizer,axiom,
    ! [X25,X2,X29,X133,X5,X17,X30] :
      ( hBOOL(hAPP(hAPP(X30,hAPP(c_Product__Type_Osnd(X17,X5),X133)),hAPP(c_Product__Type_Ofst(X17,X5),X133)))
     => ( ! [X3,X38] :
            ( hBOOL(hAPP(hAPP(X30,X38),X3))
           => hBOOL(hAPP(X29,hAPP(hAPP(X2,X3),X38))) )
       => hBOOL(hAPP(X29,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X5,X25),X2),X133))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__realizer) ).

fof(fact_rp__inv__image__def,axiom,
    ! [X17,X5] : c_FunDef_Orp__inv__image(X5,X17) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),tc_fun(tc_fun(X17,X5),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBS(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),tc_fun(tc_fun(X17,X5),tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool))),tc_fun(X17,X5)),c_Product__Type_OPair(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(tc_prod(X17,X17),tc_HOL_Obool)))),c_Relation_Oinv__image(X5,X17))))),c_Relation_Oinv__image(X5,X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_inv__image__def,axiom,
    ! [X2,X78,X5,X17] : hAPP(hAPP(c_Relation_Oinv__image(X17,X5),X78),X2) = hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X17,X17)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X17,X17),tc_fun(tc_fun(tc_prod(X17,X17),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X17,X17)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X17),tc_fun(X5,tc_prod(X17,X17))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X17,X17)),tc_fun(tc_fun(X5,X17),tc_fun(X5,tc_prod(X17,X17))),X5),c_COMBB(X17,tc_prod(X17,X17),X5)),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_prod(X17,X17)),X5),c_Product__Type_OPair(X17,X17)),X2))),X2)))),X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__def) ).

fof(fact_set__zip,axiom,
    ! [X223,X224,X17,X5] : hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223)) = hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X17)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,X17),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X17)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X5,X17)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X5,X17),tc_fun(tc_Nat_Onat,tc_prod(X5,X17)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X5,X17)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X17)),c_COMBB(tc_prod(X5,X17),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X17,tc_prod(X5,X17)),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_prod(X5,X17)),tc_Nat_Onat),c_Product__Type_OPair(X5,X17)),hAPP(c_List_Onth(X5),X224))),hAPP(c_List_Onth(X17),X223)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip) ).

fof(fact_LoopF,axiom,
    ! [X23,X21,X30,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X5),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X30))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X21))),c_Com_Ocom_OWhile(X21,X23)),X30)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LoopF) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X36,X37,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X36)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X37),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_Pow__Compl,axiom,
    ! [X19,X5] : hAPP(c_Set_OPow(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)) = hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X19)),c_Set_OPow(X5))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Compl) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [X22,X40,X2,X17,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X17,tc_HOL_Obool),X78,X2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X17,tc_HOL_Obool)),hAPP(X2,X3)),X22)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X40),X2)),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_INF2__I,axiom,
    ! [X25,X17,X23,X21,X22,X19,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => hBOOL(hAPP(hAPP(hAPP(X22,X3),X21),X23)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__I) ).

fof(fact_INF2__iff,axiom,
    ! [X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => hBOOL(hAPP(hAPP(hAPP(X22,X3),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__iff) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X5),X20))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X5),X20))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_add__Min__commute,axiom,
    ! [X90,X41,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
       => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X90),c_Big__Operators_Olinorder__class_OMin(X5,X41)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X90))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X41))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__commute) ).

fof(fact_add__Max__commute,axiom,
    ! [X90,X41,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
       => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X90),c_Big__Operators_Olinorder__class_OMax(X5,X41)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X90))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X41))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Max__commute) ).

fof(conj_3,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
   => c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

fof(fact_escape,axiom,
    ! [X29,X23,X4,X5,X30] :
      ( ! [X31,X32] :
          ( hBOOL(hAPP(hAPP(X30,X31),X32))
         => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X32))),X23),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X5),hAPP(X29,X31)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) )
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_escape) ).

fof(fact_listrel__iff__zip,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,X78)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X224),X223))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X78)),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [X20,X78,X17,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X17,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X78)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_Relation_ODomain(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [X20,X78,X17,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X17,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X78)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(c_Relation_ORange(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_accp__acc__eq,axiom,
    ! [X20,X78,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X78)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [X254,X146,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X146),X254) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X5,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X5),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X146))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X146))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X5),X254)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [X70,X34,X33,X71,X72,X17,X5] :
      ( c_Nitpick_Ofold__graph_H(X5,X17,X72,X71,X33,hAPP(hAPP(X72,X34),X70))
    <=> ( ( X33 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
          & hAPP(hAPP(X72,X34),X70) = X71 )
        | ? [X3,X38] :
            ( hAPP(hAPP(X72,X34),X70) = hAPP(hAPP(X72,X3),X38)
            & hBOOL(hAPP(hAPP(c_member(X5),X3),X33))
            & c_Nitpick_Ofold__graph_H(X5,X17,X72,X71,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X33),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X38) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_SUP2__iff,axiom,
    ! [X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
          & hBOOL(hAPP(hAPP(hAPP(X22,X3),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__iff) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [X224,X20,X30,X5] : c_List_Opartition(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_fun(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),hAPP(c_If(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(X30,X20)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_List_Olist_OCons(X5),X20))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_List_Olist(X5))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(c_List_Olist_OCons(X5),X20)))),c_List_Opartition(X5,X30,X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [X89,X78,X5] : hAPP(c_List_Olexn(X5,X78),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X5,tc_List_Olist(X5)),tc_prod(X5,tc_List_Olist(X5))),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),c_Product__Type_Omap__pair(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),c_Wellfounded_Olex__prod(X5,tc_List_Olist(X5),X78,hAPP(c_List_Olexn(X5,X78),X89)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X89))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X89)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_set__sublist,axiom,
    ! [X111,X224,X5] : hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X111)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X224))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X111))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [X90,X37,X15,X17,X146,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X146))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X15))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X17),X3),X15))
             => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X146))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),X37),X3)))) = hAPP(X90,X3) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),c_Set_OCollect(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X15)))),X37)))),X146) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,tc_Nat_Onat),X90),X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_set__conv__nth,axiom,
    ! [X224,X5] : hAPP(c_List_Oset(X5),X224) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X224))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__conv__nth) ).

fof(fact_Sigma__def,axiom,
    ! [X22,X19,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),X22)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X17),c_Set_Oinsert(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__def) ).

fof(fact_setsum__multicount,axiom,
    ! [X90,X37,X110,X17,X36,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X110))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X17),X3),X110))
             => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),X37),X3)))) = X90 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),c_Set_OCollect(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X110)))),X37)))),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),hAPP(c_Finite__Set_Ocard(X17),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [X37,X2,X110,X17,X36,X5,X25] :
      ( class_Groups_Ocomm__monoid__add(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X110))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),X25),hAPP(hAPP(c_COMBB(tc_fun(X17,X25),tc_fun(tc_fun(X17,tc_HOL_Obool),X25),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),c_Set_OCollect(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X110)))),X37)))),X36) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25),hAPP(hAPP(c_COMBS(X17,tc_fun(X5,tc_HOL_Obool),X25),hAPP(hAPP(c_COMBB(tc_fun(X5,X25),tc_fun(tc_fun(X5,tc_HOL_Obool),X25),X17),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25)),hAPP(c_COMBC(X5,X17,X25),X2))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)))),hAPP(c_COMBC(X5,X17,tc_HOL_Obool),X37))))),X110) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_anamorph_Osimps,axiom,
    ! [X20,X2,X5,X17,X90] :
      ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X17,X5,X2),X90),X20) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X17),c_List_Olist_ONil(X5)),X20) )
      & ( X90 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X17,X5,X2),X90),X20) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X5),X17),tc_prod(X5,X17),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X17),c_List_Olist_ONil(X5)),X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_prod(tc_List_Olist(X5),X17)),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_prod(tc_List_Olist(X5),X17)),tc_fun(X17,tc_prod(tc_List_Olist(X5),X17))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X5),X17),tc_prod(tc_List_Olist(X5),X17)),tc_fun(tc_fun(X17,tc_prod(tc_List_Olist(X5),X17)),tc_fun(X17,tc_prod(tc_List_Olist(X5),X17))),X5),c_COMBB(tc_prod(tc_List_Olist(X5),X17),tc_prod(tc_List_Olist(X5),X17),X17)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(X17,tc_prod(tc_List_Olist(X5),X17))),tc_fun(tc_prod(tc_List_Olist(X5),X17),tc_prod(tc_List_Olist(X5),X17)),X5),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),X17,tc_prod(tc_List_Olist(X5),X17))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_fun(X17,tc_prod(tc_List_Olist(X5),X17))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(X17,tc_prod(tc_List_Olist(X5),X17)),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),X17))),c_List_Olist_OCons(X5))))),hAPP(c_Lazy__Sequence_Oanamorph(X17,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X90),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X2,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_sequence__trans,axiom,
    ! [X90,X96,X78,X2,X5] :
      ( ! [X88] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X88))),hAPP(X2,X88))),c_Transitive__Closure_Ortrancl(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90))),hAPP(X2,X96))),c_Transitive__Closure_Ortrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sequence__trans) ).

fof(fact_fun__lub__def,axiom,
    ! [X20,X19,X283,X25,X5,X17] : c_Partial__Function_Ofun__lub(X17,X5,X25,X283,X19,X20) = hAPP(X283,hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25,X17),tc_HOL_Obool),tc_HOL_Obool,X17),c_HOL_OEx(tc_fun(X25,X17))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25,X17),tc_HOL_Obool),tc_fun(tc_fun(X25,X17),tc_HOL_Obool),X17),hAPP(c_COMBS(tc_fun(X25,X17),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X25,X17)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X25,X17),tc_fun(tc_fun(X25,X17),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X25,X17))),X19)))),hAPP(hAPP(c_COMBC(X17,tc_fun(tc_fun(X25,X17),X17),tc_fun(tc_fun(X25,X17),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X25,X17),X17),tc_fun(tc_fun(X25,X17),tc_HOL_Obool)),X17),c_COMBB(X17,tc_HOL_Obool,tc_fun(X25,X17))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X25,X17),X25,X17),c_COMBI(tc_fun(X25,X17))),X20)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__lub__def) ).

fof(fact_Sup__apply,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,X5),X19),X20) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X17,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X17,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X17,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X17,X5))),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X17,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),X17,X5),c_COMBI(tc_fun(X17,X5))),X20)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__apply) ).

fof(fact_Sup__fun__def,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,X5),X19),X20) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X17,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X17,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X17,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X17,X5))),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X17,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),X17,X5),c_COMBI(tc_fun(X17,X5))),X20)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fun__def) ).

fof(fact_Inf__fun__def,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X17,X5),X19),X20) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X17,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X17,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X17,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X17,X5))),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X17,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),X17,X5),c_COMBI(tc_fun(X17,X5))),X20)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fun__def) ).

fof(fact_Inf__apply,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X17,X5),X19),X20) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X17,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X17,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X17,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X17,X5))),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X17,X5),X5),tc_fun(tc_fun(X17,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X17,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X17,X5),X17,X5),c_COMBI(tc_fun(X17,X5))),X20)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__apply) ).

fof(fact_congruent2I_H,axiom,
    ! [X25,X2,X162,X17,X164,X5] :
      ( ! [X295,X296] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X295),X296)),X164))
         => ! [X297,X298] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X297),X298)),X162))
             => hAPP(hAPP(X2,X295),X297) = hAPP(hAPP(X2,X296),X298) ) )
     => c_Equiv__Relations_Ocongruent2(X5,X17,X25,X164,X162,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2I_H) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [X21,X6] : c_Divides_Odivmod__int__rel(X6,X21) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X6))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X21))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__def) ).

fof(fact_setsum__product,axiom,
    ! [X22,X1,X25,X19,X2,X17,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X5),X1),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),tc_fun(tc_fun(X25,tc_HOL_Obool),X5),X17),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,X5),tc_fun(X25,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X25,X5),tc_fun(X25,X5)),X17),c_COMBB(X5,X5,X25)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Otimes__class_Otimes(X5)),X2))),X1))),X22)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__product) ).

fof(fact_fold__image__Sigma,axiom,
    ! [X1,X22,X17,X19,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X3))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X5,c_Groups_Otimes__class_Otimes(X25)),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),X25),hAPP(hAPP(c_COMBC(X5,X25,tc_fun(tc_fun(X17,tc_HOL_Obool),X25)),hAPP(hAPP(c_COMBB(tc_fun(X17,X25),tc_fun(X25,tc_fun(tc_fun(X17,tc_HOL_Obool),X25)),X5),c_Finite__Set_Ofold__image(X25,X17,c_Groups_Otimes__class_Otimes(X25))),X1)),c_Groups_Oone__class_Oone(X25))),X22)),c_Groups_Oone__class_Oone(X25)),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,tc_prod(X5,X17),c_Groups_Otimes__class_Otimes(X25)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),X1)),c_Groups_Oone__class_Oone(X25)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_finite__lists__length__le,axiom,
    ! [X89,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X19))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X89))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [X89,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X19))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X89))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [X22,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X17),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22)))
               => hAPP(X1,X3) = X26 )
           => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_nat__def,axiom,
    ! [X26] : hAPP(c_Int_Onat,X26) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__def) ).

fof(fact_folding__image_Ocong,axiom,
    ! [X16,X1,X19,X18,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X17,X2,X26,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
             => hAPP(X1,X3) = hAPP(X16,X3) )
         => hAPP(hAPP(X18,X1),X19) = hAPP(hAPP(X18,X16),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Ocong) ).

fof(fact_nat__intermed__int__val,axiom,
    ! [X90,X2,X89,X51] :
      ( ! [X88] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X88))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X89)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X88)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X51)),X90))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),hAPP(X2,X89)))
           => ? [X88] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X88))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X89))
                & hAPP(X2,X88) = X90 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_finite__Collect__bex,axiom,
    ! [X29,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),X29)))))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBC(X17,X5,tc_HOL_Obool),X29),X3)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__bex) ).

fof(fact_INT__anti__mono,axiom,
    ! [X1,X2,X17,X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__anti__mono) ).

fof(fact_Sigma__mono,axiom,
    ! [X64,X22,X17,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(X22,X3)),hAPP(X64,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X62),X64))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__mono) ).

fof(fact_mem__splitI2,axiom,
    ! [X23,X26,X25,X17,X5,X133] :
      ( ! [X49,X124] :
          ( X133 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124)
         => hBOOL(hAPP(hAPP(c_member(X25),X26),hAPP(hAPP(X23,X49),X124))) )
     => hBOOL(hAPP(hAPP(c_member(X25),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_fun(X25,tc_HOL_Obool)),X23),X133))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).

fof(fact_converse__def,axiom,
    ! [X78,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),X78) = hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X17,X5)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X17,X5),tc_fun(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X17,X5)))),hAPP(c_COMBC(X17,X5,tc_prod(X17,X5)),c_Product__Type_OPair(X17,X5))))),X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__def) ).

fof(fact_fold__image__UN__disjoint,axiom,
    ! [X1,X19,X17,X111,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X111))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X111))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X19,X3))) )
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X111))
               => ! [X63] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X63),X111))
                   => ( X3 != X63
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(X19,X3)),hAPP(X19,X63)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X17,c_Groups_Otimes__class_Otimes(X25)),X1),c_Groups_Oone__class_Oone(X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X5,c_Groups_Otimes__class_Otimes(X25)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),X25,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X17,c_Groups_Otimes__class_Otimes(X25)),X1),c_Groups_Oone__class_Oone(X25))),X19)),c_Groups_Oone__class_Oone(X25)),X111) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).

fof(fact_INT__eq,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X19)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17)),c_fequal)),X22))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__eq) ).

fof(fact_UN__eq,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X19)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17)),c_fequal)),X22))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__eq) ).

fof(fact_part__equivp__typedef,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
     => ? [X121] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X121),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBS(X5,X5,tc_HOL_Obool),X37),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5)),c_fequal)),X37))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__typedef) ).

fof(fact_card__less__Suc,axiom,
    ! [X96,X76] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
     => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X96))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X96))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc) ).

fof(fact_setsum__image__gen,axiom,
    ! [X2,X25,X1,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X36) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X17),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),X17,X25),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)))),hAPP(c_COMBC(X5,X25,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X25,tc_fun(X25,tc_HOL_Obool),X5),c_fequal),X2)))))),hAPP(c_Set_Oimage(X5,X25,X2),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_refl__on__def_H,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X78))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_zip__Cons,axiom,
    ! [X223,X24,X224,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),X224),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X17)),X5,c_List_Olist_ONil(tc_prod(X5,X17)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X17)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X17)))),X5),c_COMBB(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17))),X5),c_List_Olist_OCons(tc_prod(X5,X17))),hAPP(hAPP(c_COMBC(X5,X17,tc_prod(X5,X17)),c_Product__Type_OPair(X5,X17)),X24)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X17),tc_List_Olist(tc_prod(X5,X17))),c_List_Ozip(X5,X17)),X223))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [X200,X20,X37,X5] :
      ( c_Wellfounded_Omax__extp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X37),X20,X200)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),X200)),c_Wellfounded_Omax__ext(X5,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [X200,X20,X78,X5] :
      ( c_List_Olistrelp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X78),X20,X200)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X200)),c_List_Olistrel(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_UN__Times__distrib,axiom,
    ! [X18,X206,X22,X19,X17,X5,X184,X25] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X25,X184),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X25,X184),X19),hAPP(c_COMBK(tc_fun(X184,tc_HOL_Obool),X25),X22))),hAPP(c_Product__Type_Oprod_Oprod__case(X25,X184,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25,tc_fun(X184,tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),tc_fun(X184,tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),tc_fun(tc_fun(X184,tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),tc_fun(X184,tc_fun(tc_prod(X5,X17),tc_HOL_Obool))),X25),c_COMBB(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),X184)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X25),c_Product__Type_OSigma(X5,X17)),X206))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),X184),c_COMBK(tc_fun(X17,tc_HOL_Obool),X5)),X18)))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),X206)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X184,tc_fun(X17,tc_HOL_Obool)),X22),X18))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_equivp__equiv,axiom,
    ! [X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X19)
    <=> c_Equiv__Relations_Oequivp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__equiv) ).

fof(fact_wfP__wf__eq,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_OwfP(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X78))
    <=> c_Wellfounded_Owf(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X36,X37,X17,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X37) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBC(X17,tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_HOL_Obool),X17),c_member(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),X36)
    <=> X37 = X36 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_map__zip__map2,axiom,
    ! [X223,X1,X184,X224,X2,X5,X25,X17] : hAPP(hAPP(c_List_Omap(tc_prod(X17,X25),X5),X2),hAPP(hAPP(c_List_Ozip(X17,X25),X224),hAPP(hAPP(c_List_Omap(X184,X25),X1),X223))) = hAPP(hAPP(c_List_Omap(tc_prod(X17,X184),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X184,X5),hAPP(hAPP(c_COMBB(tc_fun(X184,tc_prod(X17,X25)),tc_fun(X184,X5),X17),hAPP(c_COMBB(tc_prod(X17,X25),X5,X184),X2)),hAPP(hAPP(c_COMBC(X17,tc_fun(X184,X25),tc_fun(X184,tc_prod(X17,X25))),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X17,X25)),tc_fun(tc_fun(X184,X25),tc_fun(X184,tc_prod(X17,X25))),X17),c_COMBB(X25,tc_prod(X17,X25),X184)),c_Product__Type_OPair(X17,X25))),X1)))),hAPP(hAPP(c_List_Ozip(X17,X184),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [X6,X24,X19,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X24))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => ? [X74] :
              ( X24 = hAPP(hAPP(X2,X6),X74)
              & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X74)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_zip__Cons1,axiom,
    ! [X223,X224,X20,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X223) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X17)),X17,c_List_Olist_ONil(tc_prod(X5,X17)),hAPP(hAPP(c_COMBC(X17,tc_fun(tc_List_Olist(X17),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_List_Olist(X17),tc_List_Olist(tc_prod(X5,X17)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_fun(tc_List_Olist(X17),tc_List_Olist(tc_prod(X5,X17))),tc_fun(tc_List_Olist(X17),tc_List_Olist(tc_prod(X5,X17)))),X17),c_COMBB(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(X17))),hAPP(hAPP(c_COMBB(tc_prod(X5,X17),tc_fun(tc_List_Olist(tc_prod(X5,X17)),tc_List_Olist(tc_prod(X5,X17))),X17),c_List_Olist_OCons(tc_prod(X5,X17))),hAPP(c_Product__Type_OPair(X5,X17),X20)))),hAPP(c_List_Ozip(X5,X17),X224))),X223),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons1) ).

fof(fact_wf__if__measure,axiom,
    ! [X5,X1,X2,X30] :
      ( ! [X3] :
          ( hBOOL(hAPP(X30,X3))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,hAPP(X1,X3))),hAPP(X2,X3))) )
     => c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),X1))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__if__measure) ).

fof(fact_max__ext__compat,axiom,
    ! [X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X36)),X37))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X37)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X36)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X5,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X36)),X37))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X37)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X36)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X5,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__compat) ).

fof(fact_hoare__derivs_OIf,axiom,
    ! [X27,X29,X23,X21,X30,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X30,X21)),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X30,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X21))),X27),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),c_Com_Ocom_OCond(X21,X23,X27)),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_conseq1,axiom,
    ! [X30,X29,X23,X35,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X35),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( ! [X31,X32] :
            ( hBOOL(hAPP(hAPP(X30,X31),X32))
           => hBOOL(hAPP(hAPP(X35,X31),X32)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conseq1) ).

fof(fact_conseq2,axiom,
    ! [X29,X39,X23,X30,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),X23),X39)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( ! [X31,X32] :
            ( hBOOL(hAPP(hAPP(X39,X31),X32))
           => hBOOL(hAPP(hAPP(X29,X31),X32)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conseq2) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [X22,X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),X2)),c_Groups_Ozero__class_Ozero(X17))),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_zip__map__map,axiom,
    ! [X223,X1,X184,X224,X2,X25,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),hAPP(hAPP(c_List_Omap(X25,X5),X2),X224)),hAPP(hAPP(c_List_Omap(X184,X17),X1),X223)) = hAPP(hAPP(c_List_Omap(tc_prod(X25,X184),tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X25,X184,tc_prod(X5,X17)),hAPP(hAPP(c_COMBC(X25,tc_fun(X184,X17),tc_fun(X184,tc_prod(X5,X17))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(tc_fun(X184,X17),tc_fun(X184,tc_prod(X5,X17))),X25),c_COMBB(X17,tc_prod(X5,X17),X184)),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_prod(X5,X17)),X25),c_Product__Type_OPair(X5,X17)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X25,X184),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map__map) ).

fof(fact_finite__psubset__def,axiom,
    ! [X5] : c_Wellfounded_Ofinite__psubset(X5) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_map__pair__imageI,axiom,
    ! [X1,X2,X184,X25,X37,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X37))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X25,X184)),hAPP(hAPP(c_Product__Type_OPair(X25,X184),hAPP(X2,X6)),hAPP(X1,X21))),hAPP(c_Set_Oimage(tc_prod(X5,X17),tc_prod(X25,X184),c_Product__Type_Omap__pair(X5,X25,X17,X184,X2,X1)),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [X264,X265,X266,X2,X37,X5,X17] : c_New__Random__Sequence_Oneg__decr__bind(X17,X5,X37,X2,X266,X265,X264) = c_New__DSequence_Oneg__decr__bind(X17,X5,hAPP(hAPP(hAPP(X37,X266),X265),X264),hAPP(hAPP(c_COMBC(X17,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X2),X266)),X265)),X264)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_INTER__def,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fimplies),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X19)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17)),c_member(X5))),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__def) ).

fof(fact_congruent__def,axiom,
    ! [X2,X78,X17,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X17,X78,X2)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X78))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X17),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X5,X17),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X17,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2))),X2)),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent__def) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [X29,X17,X30,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X30)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X17),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30))),X29)))))
      <=> ! [X38] :
            ( hBOOL(hAPP(X30,X38))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBC(X17,X5,tc_HOL_Obool),X29),X38)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_setprod__Sigma,axiom,
    ! [X2,X22,X17,X19,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X25),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),X25),hAPP(hAPP(c_COMBB(tc_fun(X17,X25),tc_fun(tc_fun(X17,tc_HOL_Obool),X25),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X25)),X2)),X22)),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X17),X25),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__Sigma,axiom,
    ! [X2,X22,X17,X19,X5,X25] :
      ( class_Groups_Ocomm__monoid__add(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),X25),hAPP(hAPP(c_COMBB(tc_fun(X17,X25),tc_fun(tc_fun(X17,tc_HOL_Obool),X25),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25)),X2)),X22)),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X17),X25),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_setsum__restrict__set,axiom,
    ! [X22,X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),X2)),c_Groups_Ozero__class_Ozero(X17))),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_UN__finite2__subset,axiom,
    ! [X22,X90,X19,X5] :
      ( ! [X130] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X130)),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X130),X90))),X22)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [X264,X265,X266,X2,X37,X5,X17] : c_New__Random__Sequence_Opos__decr__bind(X17,X5,X37,X2,X266,X265,X264) = c_New__DSequence_Opos__decr__bind(X17,X5,hAPP(hAPP(hAPP(X37,X266),X265),X264),hAPP(hAPP(c_COMBC(X17,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X2),X266)),X265)),X264)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [X19,X1,X2,X17,X5,X25] : hAPP(c_Set_Oimage(X25,tc_prod(X5,X17),hAPP(hAPP(c_COMBS(X25,X17,tc_prod(X5,X17)),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_prod(X5,X17)),X25),c_Product__Type_OPair(X5,X17)),X2)),X1)),X19) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(c_Set_Oimage(X25,X5,X2),X19)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),c_Set_Oimage(X25,X17,X1)),hAPP(hAPP(c_COMBC(X5,tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(tc_fun(X25,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X25,tc_HOL_Obool),X5),c_Set_Ovimage(X25,X5,X2)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_small__lazy__list_Osimps,axiom,
    ! [X27,X5] :
      ( class_Lazy__Sequence_Osmall__lazy(X5)
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),X27) = c_Lazy__Sequence_Oappend(tc_List_Olist(X5),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),c_Lazy__Sequence_Oproduct(X5,tc_List_Olist(X5),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X27),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X27),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5)),tc_List_Olist(X5)),c_Lazy__Sequence_Osingle(tc_List_Olist(X5)))),c_List_Olist_OCons(X5))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__list_Osimps) ).

fof(fact_Sup__Inf,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,X19) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__Inf) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [X96,X22,X2,X146,X5,X17] :
      ( class_Groups_Oordered__ab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X146))
       => ( ! [X88] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X88),X146))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X88))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X146) = X22
           => ( hBOOL(hAPP(hAPP(c_member(X5),X96),X146))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X96)),X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_Inf__Sup,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,X19) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),c_Orderings_Oord__class_Oless__eq(X5))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__Sup) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [X22,X112,X25,X19,X111,X17,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X112),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X112)),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X25,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X25,tc_fun(X5,tc_HOL_Obool))),X17),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19))),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [X22,X112,X25,X19,X111,X17,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X112),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X112)),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X25,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X25,tc_fun(X5,tc_HOL_Obool))),X17),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X19))),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_neg__bind__def,axiom,
    ! [X264,X265,X266,X2,X37,X5,X17] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X17,X5,X37,X2),X266),X265),X264) = c_New__DSequence_Oneg__bind(X17,X5,hAPP(hAPP(hAPP(X37,X266),X265),X264),hAPP(hAPP(c_COMBC(X17,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X2),X266)),X265)),X264)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__bind__def) ).

fof(fact_Union__eq,axiom,
    ! [X19,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X19)))),c_member(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__eq) ).

fof(fact_Inter__eq,axiom,
    ! [X19,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X19)))),c_member(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__eq) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [X29,X30,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30),X29))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X3)),c_Transitive__Closure_Ortrancl(X5,X30)))
           => ! [X38] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X29))
               => X3 = X38 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [X29,X30,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30),X29))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X21)),c_Transitive__Closure_Ortrancl(X5,X30)))
           => ! [X38] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X3)),X29))
               => X38 = X3 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_zip__map2,axiom,
    ! [X223,X2,X25,X224,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),X224),hAPP(hAPP(c_List_Omap(X25,X17),X2),X223)) = hAPP(hAPP(c_List_Omap(tc_prod(X5,X25),tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X25,tc_prod(X5,X17)),hAPP(hAPP(c_COMBC(X5,tc_fun(X25,X17),tc_fun(X25,tc_prod(X5,X17))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(tc_fun(X25,X17),tc_fun(X25,tc_prod(X5,X17))),X5),c_COMBB(X17,tc_prod(X5,X17),X25)),c_Product__Type_OPair(X5,X17))),X2))),hAPP(hAPP(c_List_Ozip(X5,X25),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map2) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [X90,X2,X89] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X89))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X88)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),hAPP(X2,X89)))
         => ? [X88] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X89))
              & hAPP(X2,X88) = X90 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [X90,X2,X89] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X89))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X88)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),hAPP(X2,X89)))
         => ? [X88] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X89))
              & hAPP(X2,X88) = X90 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__val__lemma) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [X6,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),X6))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).

fof(fact_pos__bind__def,axiom,
    ! [X264,X265,X266,X2,X37,X5,X17] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X17,X5,X37,X2),X266),X265),X264) = c_New__DSequence_Opos__bind(X17,X5,hAPP(hAPP(hAPP(X37,X266),X265),X264),hAPP(hAPP(c_COMBC(X17,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X2),X266)),X265)),X264)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__bind__def) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [X22,X19,X17,X5] : c_Nitpick_Oprod(X5,X17,X19,X22) = hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)))),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [X214,X96,X16,X215,X183,X1,X2,X17,X184,X5,X25] : hAPP(c_Product__Type_Omap__pair(X25,X5,X184,X17,X2,X1),hAPP(c_Product__Type_Omap__pair(X183,X25,X215,X184,X16,X96),X214)) = hAPP(c_Product__Type_Omap__pair(X183,X5,X215,X17,hAPP(c_Fun_Ocomp(X25,X5,X183,X2),X16),hAPP(c_Fun_Ocomp(X184,X17,X215,X1),X96)),X214),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_less,axiom,
    ! [X75,X102,X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X102),X75)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X75)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [X75,X102,X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X102),X75)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X75)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [X17,X16,X2,X36,X5,X25] :
      ( class_Groups_Ocomm__monoid__add(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
             => ! [X38] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X38),X36))
                 => ( X3 != X38
                   => ( hAPP(X2,X3) = hAPP(X2,X38)
                     => hAPP(X16,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X25) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25),X16),hAPP(c_Set_Oimage(X5,X17,X2),X36)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),hAPP(c_Fun_Ocomp(X17,X25,X5,X16),X2)),X36) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_if__image__distrib,axiom,
    ! [X36,X1,X2,X30,X5,X17] : hAPP(c_Set_Oimage(X17,X5,hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBS(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),X30)),X2)),X1)),X36) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X36),hAPP(c_Set_OCollect(X17),X30)))),hAPP(c_Set_Oimage(X17,X5,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X36),hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17),c_fNot),X30))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_if__image__distrib) ).

fof(fact_mult,axiom,
    ! [X75,X102,X24,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X102),X75)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X75))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X75)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X102)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult) ).

fof(fact_fold__image__cong,axiom,
    ! [X26,X16,X1,X19,X5,X17] :
      ( class_Groups_Oab__semigroup__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hAPP(X1,X3) = hAPP(X16,X3) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),X26),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X16),X26),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__cong) ).

fof(fact_wf__map__pair__image,axiom,
    ! [X2,X17,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => c_Wellfounded_Owf(X17,hAPP(c_Set_Oimage(tc_prod(X5,X5),tc_prod(X17,X17),c_Product__Type_Omap__pair(X5,X17,X5,X17,X2,X2)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_inj__on__INTER,axiom,
    ! [X19,X2,X25,X17,X5,X111] :
      ( X111 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ! [X88] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X88),X111))
           => c_Fun_Oinj__on(X17,X25,X2,hAPP(X19,X88)) )
       => c_Fun_Oinj__on(X17,X25,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_listsum__mono,axiom,
    ! [X1,X2,X224,X5,X17] :
      ( ( class_Groups_Omonoid__add(X17)
        & class_Groups_Oordered__ab__semigroup__add(X17) )
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224))),hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X1),X224)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__mono) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [X30,X21,X17,X6,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X21)
     => ( ! [X130] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6)))
           => hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X6),X130)),hAPP(hAPP(c_List_Onth(X17),X21),X130))) )
       => c_List_Olist__all2(X5,X17,X30,X6,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
        & ! [X88] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88)),hAPP(hAPP(c_List_Onth(X17),X223),X88))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_setsum__strict__mono,axiom,
    ! [X1,X2,X19,X5,X17] :
      ( ( class_Groups_Ocomm__monoid__add(X17)
        & class_Groups_Oordered__cancel__ab__semigroup__add(X17) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17),hAPP(X2,X3)),hAPP(X1,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_setsum__mono,axiom,
    ! [X1,X2,X87,X5,X17] :
      ( ( class_Groups_Ocomm__monoid__add(X17)
        & class_Groups_Oordered__ab__semigroup__add(X17) )
     => ( ! [X88] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X88),X87))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X88)),hAPP(X1,X88))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X87)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X87))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono) ).

fof(fact_setsum__cases,axiom,
    ! [X1,X2,X30,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBS(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),X30)),X2)),X1)),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OCollect(X5),X30)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cases) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [X41,X16,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(X2,X3),X38)) = hAPP(hAPP(X2,hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,hAPP(X18,X41)) = hAPP(X18,hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_set__n__lists,axiom,
    ! [X224,X89,X5] : hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X89,X224)) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X89))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),hAPP(c_List_Oset(X5),X224)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__n__lists) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [X96,X16,X1,X2,X17,X5,X184,X25,X215,X183] : hAPP(c_Fun_Ocomp(tc_prod(X183,X215),tc_prod(X25,X184),tc_prod(X5,X17),c_Product__Type_Omap__pair(X183,X25,X215,X184,X2,X1)),c_Product__Type_Omap__pair(X5,X183,X17,X215,X16,X96)) = c_Product__Type_Omap__pair(X5,X25,X17,X184,hAPP(c_Fun_Ocomp(X183,X25,X5,X2),X16),hAPP(c_Fun_Ocomp(X215,X184,X17,X1),X96)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [X216,X217,X215,X149,X28,X183,X184,X17,X25,X5] : c_Product__Type_Omap__pair(X5,X25,X17,X184,hAPP(c_Fun_Ocomp(X183,X25,X5,X28),X149),hAPP(c_Fun_Ocomp(X215,X184,X17,X217),X216)) = hAPP(c_Fun_Ocomp(tc_prod(X183,X215),tc_prod(X25,X184),tc_prod(X5,X17),c_Product__Type_Omap__pair(X183,X25,X215,X184,X28,X217)),c_Product__Type_Omap__pair(X5,X183,X17,X215,X149,X216)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__compose) ).

fof(fact_listrel__iff__nth,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,X78)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223)
        & ! [X130] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X224),X130)),hAPP(hAPP(c_List_Onth(X5),X223),X130))),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37)))
     => ? [X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),X37))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_quotient__def,axiom,
    ! [X78,X19,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),c_Relation_OImage(X5,X5,X78)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__def) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_Image__iff,axiom,
    ! [X19,X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_OImage(X17,X5,X78),X19)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X21)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(X2,X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),hAPP(X18,X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_Image__Collect__split,axiom,
    ! [X19,X30,X5,X17] : hAPP(c_Relation_OImage(X17,X5,hAPP(c_Set_OCollect(tc_prod(X17,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X5,tc_HOL_Obool),X30))),X19) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fconj),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X19)))),hAPP(c_COMBC(X17,X5,tc_HOL_Obool),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Collect__split) ).

fof(fact_quotient__diff1,axiom,
    ! [X6,X19,X78,X5] :
      ( c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X78),X19)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X78) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__diff1) ).

fof(fact_Collect__ball__eq,axiom,
    ! [X30,X19,X17,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBS(X17,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17),c_fimplies),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X19)))),X30))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Set_OCollect(X5)),hAPP(c_COMBC(X5,X17,tc_HOL_Obool),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_sublist__append,axiom,
    ! [X19,X246,X106,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Oappend(X5),X106),X246),X19) = hAPP(hAPP(c_List_Oappend(X5),c_List_Osublist(X5,X106,X19)),c_List_Osublist(X5,X246,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X106)))),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__append) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [X30,X223,X17,X224,X5] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223))),X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),hAPP(hAPP(c_List_Otake(X17),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223))),X223))
       => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Ozip(X5,X17),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223))),X224)),hAPP(hAPP(c_List_Otake(X17),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223))),X223)))) )
     => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [X78,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X78),X19)
       => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)) = hAPP(c_Finite__Set_Ocard(X5),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_arith__series__general,axiom,
    ! [X89,X27,X6,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X5),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X5)),c_Nat_Osemiring__1__class_Oof__nat(X5))),X27))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X27)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__general) ).

fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
    ! [X90,X106] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90))
     => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).

fof(fact_dvd_OatLeastLessThan__empty,axiom,
    ! [X6,X21] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6))
     => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).

fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
    ! [X90,X106] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90))
     => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).

fof(fact_reduction__pair__def,axiom,
    ! [X30,X5] :
      ( c_FunDef_Oreduction__pair(X5,X30)
    <=> ( c_Wellfounded_Owf(X5,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_UN__subset__iff,axiom,
    ! [X22,X19,X111,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)),X22))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X111))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X19,X3)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_setsum__bounded,axiom,
    ! [X87,X2,X19,X5,X17] :
      ( ( class_Groups_Oordered__ab__semigroup__add(X17)
        & class_Rings_Osemiring__1(X17) )
     => ( ! [X88] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X88),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X88)),X87)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17),hAPP(c_Finite__Set_Ocard(X5),X19))),X87))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__bounded) ).

fof(fact_map__pair__def,axiom,
    ! [X1,X2,X184,X17,X25,X5] : c_Product__Type_Omap__pair(X5,X25,X17,X184,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_prod(X25,X184)),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,X184),tc_fun(X17,tc_prod(X25,X184))),hAPP(hAPP(c_COMBB(tc_fun(X184,tc_prod(X25,X184)),tc_fun(tc_fun(X17,X184),tc_fun(X17,tc_prod(X25,X184))),X5),c_COMBB(X184,tc_prod(X25,X184),X17)),hAPP(hAPP(c_COMBB(X25,tc_fun(X184,tc_prod(X25,X184)),X5),c_Product__Type_OPair(X25,X184)),X2))),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__def) ).

fof(fact_decr__lemma,axiom,
    ! [X58,X55,X73] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X58))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X73))),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

fof(fact_SUP__le__iff,axiom,
    ! [X102,X76,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),X19),X76)),X102))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X76,X3)),X102)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__le__iff) ).

fof(fact_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).

fof(fact_transfer__nat__int__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olexord(X5,X78)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X20)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X24)))
          & hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X20)),X24) = X20 )
        | ? [X88] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X20)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X24))))
            & hAPP(hAPP(c_List_Otake(X5),X88),X20) = hAPP(hAPP(c_List_Otake(X5),X88),X24)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X20),X88)),hAPP(hAPP(c_List_Onth(X5),X24),X88))),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [X29,X30,X17,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30))),X29))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(c_Set_OCollect(X5),X30)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),c_Set_OCollect(X17)),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_card__less,axiom,
    ! [X96,X76] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X96))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less) ).

fof(fact_Eps__split__eq,axiom,
    ! [X24,X20,X17,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X20)))),hAPP(c_fequal,X24)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_The__split__eq,axiom,
    ! [X24,X20,X17,X5] : c_HOL_OThe(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X20)))),hAPP(c_fequal,X24)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split__eq) ).

fof(fact_setsum__commute,axiom,
    ! [X19,X22,X2,X25,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),tc_fun(tc_fun(X25,tc_HOL_Obool),X5),X17),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X5)),X2)),X22)),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X5),hAPP(hAPP(c_COMBC(X25,tc_fun(X17,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X17,X5),tc_fun(tc_fun(X17,tc_HOL_Obool),X5),X25),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5)),hAPP(c_COMBC(X17,X25,X5),X2))),X19)),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__commute) ).

fof(fact_Collect__split,axiom,
    ! [X29,X30,X17,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30))),X29))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(c_Set_OCollect(X5),X30)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_OCollect(X17),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__split) ).

fof(fact_image__eq__fold__image,axiom,
    ! [X2,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Set_Oimage(X5,X17,X2),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X17,tc_HOL_Obool),X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X17,tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Set_Oinsert(X17)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_card__Diff2__less,axiom,
    ! [X24,X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_Id__on__def_H,axiom,
    ! [X19,X5] : c_Relation_OId__on(X5,X19) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),c_fequal))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_int__ge__less__than__def,axiom,
    ! [X27] : c_Int_Oint__ge__less__than(X27) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__ge__less__than__def) ).

fof(fact_scomp__scomp,axiom,
    ! [X16,X1,X2,X215,X183,X17,X184,X25,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X25,X184,X17),hAPP(hAPP(c_Product__Type_Oscomp(X5,X183,X215,tc_prod(X25,X184)),X2),X1)),X16) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X183,X215,X17),X2),hAPP(hAPP(c_COMBC(X183,tc_fun(X25,tc_fun(X184,X17)),tc_fun(X215,X17)),hAPP(hAPP(c_COMBB(tc_fun(X215,tc_prod(X25,X184)),tc_fun(tc_fun(X25,tc_fun(X184,X17)),tc_fun(X215,X17)),X183),c_Product__Type_Oscomp(X215,X25,X184,X17)),X1)),X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__scomp) ).

fof(fact_wmax__insertI,axiom,
    ! [X199,X20,X198,X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24),X198))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X24)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X199),X198)),c_FunDef_Omax__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X199)),X198)),c_FunDef_Omax__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__insertI) ).

fof(fact_smax__insertI,axiom,
    ! [X40,X20,X43,X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24),X43))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X24)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X40),X43)),c_FunDef_Omax__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X40)),X43)),c_FunDef_Omax__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__insertI) ).

fof(fact_sorted__map__same,axiom,
    ! [X224,X1,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Ofilter(X17,hAPP(hAPP(c_COMBC(X17,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X17),c_fequal),X2)),hAPP(X1,X224))),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__same) ).

fof(fact_Loop,axiom,
    ! [X23,X21,X30,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X30,X21)),X23),X30)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),c_Com_Ocom_OWhile(X21,X23)),c_Hoare__Mirabelle_Opeek__and(X5,X30,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X21)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Loop) ).

fof(fact_max__ext_Osimps,axiom,
    ! [X37,X33,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X34),X33)),c_Wellfounded_Omax__ext(X5,X37)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X34))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X33))
        & X33 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X34))
           => ? [X63] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X63),X33))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X63)),X37)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_wf__union__merge,axiom,
    ! [X36,X37,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36))
    <=> c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X37)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X36),X37))),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__merge) ).

fof(fact_map__pair__surj__on,axiom,
    ! [X208,X22,X1,X25,X184,X67,X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),X19) = X67
     => ( hAPP(c_Set_Oimage(X184,X25,X1),X22) = X208
       => hAPP(c_Set_Oimage(tc_prod(X17,X184),tc_prod(X5,X25),c_Product__Type_Omap__pair(X17,X5,X184,X25,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X17,X184),X19),hAPP(c_COMBK(tc_fun(X184,tc_HOL_Obool),X17),X22))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X25),X67),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X5),X208)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_wmin__insertI,axiom,
    ! [X198,X24,X199,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X199))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X24)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X199),X198)),c_FunDef_Omin__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X199),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24),X198))),c_FunDef_Omin__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [X198,X24,X199,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X199))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X24)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X199),X198)),c_FunDef_Omin__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X199),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24),X198))),c_FunDef_Omin__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__insertI) ).

fof(fact_insert__fold1SetE,axiom,
    ! [X20,X40,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X40)),X20))
     => ~ ! [X49,X50] :
            ( hAPP(hAPP(c_Set_Oinsert(X5),X6),X40) = hAPP(hAPP(c_Set_Oinsert(X5),X49),X50)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X49,X50),X20))
             => hBOOL(hAPP(hAPP(c_member(X5),X49),X50)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_listrel1__iff__update,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
    <=> ? [X38,X130] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X224),X130)),X38)),X78))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
          & X223 = hAPP(hAPP(c_List_Olist__update(X5,X224),X130),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_map__pair__surj,axiom,
    ! [X1,X25,X184,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X184,X25,X1),c_Orderings_Otop__class_Otop(tc_fun(X184,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X17,X184),tc_prod(X5,X25),c_Product__Type_Omap__pair(X17,X5,X184,X25,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X17,X184),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X25),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj) ).

fof(fact_minus__fold__remove,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19) = hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_fst__map__pair,axiom,
    ! [X20,X1,X2,X184,X25,X17,X5] : hAPP(c_Product__Type_Ofst(X5,X17),hAPP(c_Product__Type_Omap__pair(X25,X5,X184,X17,X2,X1),X20)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X25,X184),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__map__pair) ).

fof(fact_snd__prod__fun,axiom,
    ! [X20,X1,X2,X184,X25,X5,X17] : hAPP(c_Product__Type_Osnd(X17,X5),hAPP(c_Product__Type_Omap__pair(X25,X17,X184,X5,X2,X1),X20)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X25,X184),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_lexord__linear,axiom,
    ! [X24,X20,X78,X5] :
      ( ! [X49,X124] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X49),X124)),X78))
          | X49 = X124
          | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X124),X49)),X78)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olexord(X5,X78)))
        | X20 = X24
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X24),X20)),c_List_Olexord(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).

fof(fact_add,axiom,
    ! [X75,X102,X24,X20] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X102),X75)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X75))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add) ).

fof(fact_Id__on__def,axiom,
    ! [X19,X5] : c_Relation_OId__on(X5,X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_prod(X5,X5))),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def) ).

fof(fact_conversep__noteq,axiom,
    ! [X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot)),c_fequal)),X20),X24))
    <=> X20 != X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__noteq) ).

fof(fact_map__zip__map,axiom,
    ! [X223,X224,X1,X184,X2,X5,X25,X17] : hAPP(hAPP(c_List_Omap(tc_prod(X17,X25),X5),X2),hAPP(hAPP(c_List_Ozip(X17,X25),hAPP(hAPP(c_List_Omap(X184,X17),X1),X224)),X223)) = hAPP(hAPP(c_List_Omap(tc_prod(X184,X25),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X184,X25,X5),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_prod(X17,X25)),tc_fun(X25,X5),X184),hAPP(c_COMBB(tc_prod(X17,X25),X5,X25),X2)),hAPP(hAPP(c_COMBB(X17,tc_fun(X25,tc_prod(X17,X25)),X184),c_Product__Type_OPair(X17,X25)),X1)))),hAPP(hAPP(c_List_Ozip(X184,X25),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map) ).

fof(fact_order__fun_I2_J,axiom,
    ! [X1,X2,X5,X17] :
      ( ( class_Orderings_Oorder(X17)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X17)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
          & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBS(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),X1)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__fun_I2_J) ).

fof(fact_sublist__Cons,axiom,
    ! [X19,X106,X20,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X106),X19) = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X5)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5))),c_List_Olist_ONil(X5))),c_List_Osublist(X5,X106,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__Cons) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [X95,X96,X224,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X224))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X224))))
         => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X224)),X96)),X95) = hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X224),X95)),X96) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_INF__less__iff,axiom,
    ! [X6,X2,X19,X17,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),X19),X2)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X3)),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__less__iff) ).

fof(fact_ball__UN,axiom,
    ! [X30,X22,X19,X17,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
         => hBOOL(hAPP(X30,X3)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X63),hAPP(X22,X3)))
             => hBOOL(hAPP(X30,X63)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__UN) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).

fof(fact_max__ext__additive,axiom,
    ! [X64,X62,X37,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),X22)),c_Wellfounded_Omax__ext(X5,X37)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X62),X64)),c_Wellfounded_Omax__ext(X5,X37)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X62)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X64))),c_Wellfounded_Omax__ext(X5,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__additive) ).

fof(fact_SigmaE,axiom,
    ! [X22,X19,X23,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X23),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => ! [X38] :
                ( hBOOL(hAPP(hAPP(c_member(X17),X38),hAPP(X22,X3)))
               => X23 != hAPP(hAPP(c_Product__Type_OPair(X5,X17),X3),X38) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).

fof(fact_foldl__map,axiom,
    ! [X224,X2,X25,X6,X1,X17,X5] : hAPP(c_List_Ofoldl(X5,X17,X1,X6),hAPP(hAPP(c_List_Omap(X25,X17),X2),X224)) = hAPP(c_List_Ofoldl(X5,X25,hAPP(hAPP(c_COMBC(X5,tc_fun(X25,X17),tc_fun(X25,X5)),hAPP(hAPP(c_COMBB(tc_fun(X17,X5),tc_fun(tc_fun(X25,X17),tc_fun(X25,X5)),X5),c_COMBB(X17,X5,X25)),X1)),X2),X6),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__map) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [X146,X78,X111,X184,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X184,tc_fun(tc_prod(X5,X25),tc_HOL_Obool)),X111),X78)),X146) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X184,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBC(X184,tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X25),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X184),c_Relation_Orel__comp(X5,X25,X17)),X78)),X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [X29,X30,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),X30)),X29))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X30)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_inj__transfer,axiom,
    ! [X20,X30,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( ! [X38] :
            ( hBOOL(hAPP(hAPP(c_member(X17),X38),hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
           => hBOOL(hAPP(X30,hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X38))) )
       => hBOOL(hAPP(X30,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__transfer) ).

fof(fact_enum__all__prod__def,axiom,
    ! [X30,X5,X17] :
      ( ( class_Enum_Oenum(X17)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X5,X17)),X30))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__all(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_HOL_Obool,X17),X30)),c_Product__Type_OPair(X5,X17))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [X30,X5,X17] :
      ( ( class_Enum_Oenum(X17)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X5,X17)),X30))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__ex(X17)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_HOL_Obool,X17),X30)),c_Product__Type_OPair(X5,X17))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_listsp__conj__eq,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X19)),X22)),X20))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X19),X20))
        & hBOOL(hAPP(c_List_Olistsp(X5,X22),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_lists__IntI,axiom,
    ! [X22,X19,X106,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X106),c_List_Olists(X5,X19)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X106),c_List_Olists(X5,X22)))
       => hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),X106)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).

fof(fact_UN__equiv__class2,axiom,
    ! [X33,X34,X2,X25,X162,X163,X17,X164,X165,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X165,X164)
     => ( c_Equiv__Relations_Oequiv(X17,X163,X162)
       => ( c_Equiv__Relations_Ocongruent2(X5,X17,tc_fun(X25,tc_HOL_Obool),X164,X162,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X5),X34),X165))
           => ( hBOOL(hAPP(hAPP(c_member(X17),X33),X163))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X25,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X164),hAPP(hAPP(c_Set_Oinsert(X5),X34),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X25,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X17,X162),hAPP(hAPP(c_Set_Oinsert(X17),X33),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X34),X33) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_length__sublist,axiom,
    ! [X111,X224,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Osublist(X5,X224,X111)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X111)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublist) ).

fof(fact_length__filter__conv__card,axiom,
    ! [X224,X133,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X133),X224)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat),X133),hAPP(c_List_Onth(X5),X224))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_fold__image__distrib,axiom,
    ! [X16,X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),hAPP(hAPP(c_COMBS(X5,X17,X17),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Groups_Otimes__class_Otimes(X17)),X1)),X16)),c_Groups_Oone__class_Oone(X17)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X16),c_Groups_Oone__class_Oone(X17)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_Cantor__Bernstein,axiom,
    ! [X1,X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),X22))
       => ( c_Fun_Oinj__on(X17,X5,X1,X22)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X1),X22)),X19))
           => ? [X285] : c_Fun_Obij__betw(X5,X17,X285,X19,X22) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantor__Bernstein) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [X78,X24,X223,X20,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X223),hAPP(hAPP(c_List_Olist_OCons(X5),X24),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X78)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
          & X20 = X24 )
        | ( X224 = X223
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_list__all2__map2,axiom,
    ! [X257,X2,X25,X252,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X252,hAPP(hAPP(c_List_Omap(X25,X17),X2),X257))
    <=> c_List_Olist__all2(X5,X25,hAPP(hAPP(c_COMBC(X5,tc_fun(X25,X17),tc_fun(X25,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X25,X17),tc_fun(X25,tc_HOL_Obool)),X5),c_COMBB(X17,tc_HOL_Obool,X25)),X30)),X2),X252,X257) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map2) ).

fof(fact_UN__finite2__eq,axiom,
    ! [X22,X90,X19,X5] :
      ( ! [X130] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X130)),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X130),X90))),X22)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_max__ext_Ointros,axiom,
    ! [X37,X43,X40,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X40))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X43))
       => ( X43 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X40))
               => ? [X63] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X63),X43))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X63)),X37)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X40),X43)),c_Wellfounded_Omax__ext(X5,X37))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [X72,X34,X146,X78,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X17,X25,X78,X146),X34),X72))
    <=> ? [X124] :
          ( hBOOL(hAPP(hAPP(X78,X34),X124))
          & hBOOL(hAPP(hAPP(X146,X124),X72)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [X2,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ~ ! [X97] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X97))),hAPP(X2,X97))),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
    <=> ~ ? [X68] :
          ! [X88] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X68,hAPP(c_Nat_OSuc,X88))),hAPP(X68,X88))),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [X6,X2,X25,X162,X163,X17,X164,X165,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X165,X164)
     => ( c_Equiv__Relations_Oequiv(X17,X163,X162)
       => ( c_Equiv__Relations_Ocongruent2(X5,X17,tc_fun(X25,tc_HOL_Obool),X164,X162,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X17),X6),X163))
           => c_Equiv__Relations_Ocongruent(X5,tc_fun(X25,tc_HOL_Obool),X164,hAPP(hAPP(c_COMBB(tc_fun(X17,tc_fun(X25,tc_HOL_Obool)),tc_fun(X25,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X17,X162),hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))))),X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [X24,X20,X19,X26,X2,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X24))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),hAPP(hAPP(X2,X20),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_setsum__mono3,axiom,
    ! [X2,X19,X22,X5,X17] :
      ( ( class_Groups_Ocomm__monoid__add(X17)
        & class_Groups_Oordered__ab__semigroup__add(X17) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X22))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__mono2,axiom,
    ! [X2,X19,X22,X5,X17] :
      ( class_Groups_Oordered__comm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => ( ! [X124] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X124))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X22))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono2) ).

fof(fact_INF__INT__eq,axiom,
    ! [X20,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17))),X78)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_SUP__UN__eq,axiom,
    ! [X20,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17))),X78)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_less__add__iff1,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),X79)),X23)),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

fof(fact_le__add__iff1,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),X79)),X23)),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [X24,X26,X2,X17,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( c_Nitpick_Ofold__graph_H(X5,X17,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X24)
       => c_Nitpick_Ofold__graph_H(X5,X17,X2,X26,X19,hAPP(hAPP(X2,X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_INT__greatest,axiom,
    ! [X22,X62,X17,X19,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X62),hAPP(X22,X3))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__greatest) ).

fof(fact_INT__subset__iff,axiom,
    ! [X19,X111,X17,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X111))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(X19,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_refl__on__INTER,axiom,
    ! [X78,X19,X17,X36,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
         => c_Relation_Orefl__on(X17,hAPP(X19,X3),hAPP(X78,X3)) )
     => c_Relation_Orefl__on(X17,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X36),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),X36),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__INTER) ).

fof(fact_refl__on__UNION,axiom,
    ! [X78,X19,X17,X36,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
         => c_Relation_Orefl__on(X17,hAPP(X19,X3),hAPP(X78,X3)) )
     => c_Relation_Orefl__on(X17,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X36),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X17,X17),tc_HOL_Obool)),X36),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__UNION) ).

fof(fact_zminus1__lemma,axiom,
    ! [X78,X145,X21,X6] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6,X21),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X145),X78)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),X21),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X145)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X145)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21),X78))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_INT__iff,axiom,
    ! [X22,X19,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(X22,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__iff) ).

fof(fact_vimage__Times,axiom,
    ! [X22,X19,X2,X25,X17,X5] : hAPP(c_Set_Ovimage(X5,tc_prod(X17,X25),X2),hAPP(hAPP(c_Product__Type_OSigma(X17,X25),X19),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X17),X22))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,hAPP(c_Fun_Ocomp(tc_prod(X17,X25),X17,X5,c_Product__Type_Ofst(X17,X25)),X2)),X19)),hAPP(c_Set_Ovimage(X5,X25,hAPP(c_Fun_Ocomp(tc_prod(X17,X25),X25,X5,c_Product__Type_Osnd(X17,X25)),X2)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Times) ).

fof(fact_size__code,axiom,
    ! [X254,X5] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)),X254) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),X5),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X5),X254)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_size__code) ).

fof(fact_in__lex__prod,axiom,
    ! [X146,X78,X181,X182,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X182),X181))),c_Wellfounded_Olex__prod(X5,X17,X78,X146)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X182)),X78))
        | ( X6 = X182
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X21),X181)),X146)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact_INF1__iff,axiom,
    ! [X21,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => hBOOL(hAPP(hAPP(X22,X3),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__iff) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [X96,X30] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X30)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X96))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_incr__lemma,axiom,
    ! [X55,X58,X73] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X58))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X73)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

fof(fact_le__INF__iff,axiom,
    ! [X76,X19,X17,X102,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X102),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),X19),X76)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X102),hAPP(X76,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__INF__iff) ).

fof(fact_insort__is__Cons,axiom,
    ! [X6,X2,X224,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X6)),hAPP(X2,X3))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X6),X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X6),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [X96,X2,X146,X5,X17] :
      ( class_Groups_Oordered__ab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X146))
       => ( ! [X88] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X88),X146))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X88))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X146) = c_Groups_Ozero__class_Ozero(X17)
           => ( hBOOL(hAPP(hAPP(c_member(X5),X96),X146))
             => hAPP(X2,X96) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_inv__into__def,axiom,
    ! [X20,X2,X19,X17,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),X20) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).

fof(fact_the__inv__into__def,axiom,
    ! [X20,X2,X19,X17,X5] : hAPP(c_Fun_Othe__inv__into(X5,X17,X19,X2),X20) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_listrel1E,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
     => ~ ! [X3,X38] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X78))
           => ! [X242,X247] :
                ( X224 = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X247))
               => X223 != hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X247)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [X24,X20,X19,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X20))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X24))
         => X24 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_listsum__addf,axiom,
    ! [X224,X1,X2,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X224)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X1),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__addf) ).

fof(fact_listsum__subtractf,axiom,
    ! [X224,X1,X2,X17,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X1),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_UN__Pow__subset,axiom,
    ! [X22,X19,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X17),c_Set_OPow(X5)),X22))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [X89,X51,X102,X96,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X96))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X96),X95)),X102)),X51)),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [X89,X51,X102,X96,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X96))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X96),X95)),X102)),X51)),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_listsum__mult__const,axiom,
    ! [X224,X23,X2,X17,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Otimes__class_Otimes(X5)),X2)),X23)),X224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_int__ge__less__than2__def,axiom,
    ! [X27] : c_Int_Oint__ge__less__than2(X27) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__ge__less__than2__def) ).

fof(fact_fold__image__Un__one,axiom,
    ! [X2,X110,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X36),X110)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X17) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X2),c_Groups_Oone__class_Oone(X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X36),X110)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X2),c_Groups_Oone__class_Oone(X17)),X36)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X2),c_Groups_Oone__class_Oone(X17)),X110)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_inf__Int__eq,axiom,
    ! [X20,X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X37),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [X20,X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X37),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_insert__Collect,axiom,
    ! [X30,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Set_OCollect(X5),X30)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)))),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Collect) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [X21,X6,X20,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_measures__def,axiom,
    ! [X263,X5] : c_List_Omeasures(X5,X263) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X5),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X5),c_List_Omap(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X5,tc_Nat_Onat),X5,tc_Nat_Onat),c_COMBI(tc_fun(X5,tc_Nat_Onat))))),X263)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__def) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [X177,X178,X61,X179,X180,X59,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X60,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X180),X179)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X61,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X178),X177)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X59))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X61),X59),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X180),X178)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X179),X177)),X59))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X179),X177),X59)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [X30,X2,X5,X17] : c_Random__Sequence_Omap(X17,X5,X2,X30) = c_Random__Sequence_Obind(X17,X5,X30,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X17,c_Random__Sequence_Osingle(X5)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_setprod__Un,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Fields_Ofield(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
               => hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un) ).

fof(fact_zadd1__lemma,axiom,
    ! [X177,X178,X61,X179,X180,X59,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X180),X179)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X61,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X178),X177)))
       => ( X59 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61),X59),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X180),X178)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X177)),X59))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X177),X59)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [X19,X22,X2,X25,X17,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),tc_fun(tc_fun(X25,tc_HOL_Obool),X5),X17),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25,X5)),X2)),X22)),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X17,X25),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X17,X25),X19),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X17),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [X19,X22,X2,X25,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),tc_fun(tc_fun(X25,tc_HOL_Obool),X5),X17),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25,X5)),X2)),X22)),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X17,X25),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X17,X25),X19),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X17),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_map__pair__inj__on,axiom,
    ! [X22,X1,X184,X25,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( c_Fun_Oinj__on(X25,X184,X1,X22)
       => c_Fun_Oinj__on(tc_prod(X5,X25),tc_prod(X17,X184),c_Product__Type_Omap__pair(X5,X17,X25,X184,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X5,X25),X19),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X5),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [X60,X119,X107,X59,X61] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X61,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X107),X119)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X59))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X61),X59),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X107)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X119)),X59))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X119),X59)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_zmult1__lemma,axiom,
    ! [X60,X119,X107,X59,X61] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X61,X59),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X59 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X61),X59),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X107)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X119)),X59))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X119),X59)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult1__lemma) ).

fof(fact_,axiom,
    ! [X269,X270,X17,X5] : c_Lazy__Sequence_Oproduct(X5,X17,X270,X269) = hAPP(c_Lazy__Sequence_Obind(X5,tc_prod(X5,X17),X270),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X17))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X17)),X5),c_Lazy__Sequence_Obind(X17,tc_prod(X5,X17),X269)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X17))),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X17)),X17),c_Lazy__Sequence_Osingle(tc_prod(X5,X17)))),c_Product__Type_OPair(X5,X17)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [X19,X111,X17,X5] :
    ? [X68] :
      ( c_Fun_Oinj__on(X5,tc_prod(X17,X5),X68,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,tc_prod(X17,X5),X68),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19))),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X111),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [X261,X224,X30,X5] : hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X30),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X5,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X5,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X224),X261))) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X30),c_Product__Type_Osnd(X5,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X224),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X261)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [X1,X2,X17,X5,X184,X25] : hAPP(c_Fun_Ocomp(tc_prod(X25,X184),X25,tc_prod(X5,X17),c_Product__Type_Ofst(X25,X184)),c_Product__Type_Omap__pair(X5,X25,X17,X184,X2,X1)) = hAPP(c_Fun_Ocomp(X5,X25,tc_prod(X5,X17),X2),c_Product__Type_Ofst(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [X1,X2,X17,X5,X25,X184] : hAPP(c_Fun_Ocomp(tc_prod(X184,X25),X25,tc_prod(X5,X17),c_Product__Type_Osnd(X184,X25)),c_Product__Type_Omap__pair(X5,X184,X17,X25,X2,X1)) = hAPP(c_Fun_Ocomp(X17,X25,tc_prod(X5,X17),X1),c_Product__Type_Osnd(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [X62,X22,X25,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X17),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool))),X22)),X62)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,tc_HOL_Obool)),X19),X22)),X62),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [X62,X22,X25,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X17,tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25,tc_HOL_Obool),tc_fun(tc_fun(X25,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X17),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool))),X22)),X62)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,tc_HOL_Obool)),X19),X22)),X62),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [X62,X22,X19,X25,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X25,tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X25),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool))),X22)),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [X62,X22,X19,X25,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X25,tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X25),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool))),X22)),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_UN__UN__flatten,axiom,
    ! [X62,X22,X19,X25,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X25,tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X25),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool))),X22)),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_congruentI,axiom,
    ! [X17,X2,X78,X5] :
      ( ! [X38,X150] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X150)),X78))
         => hAPP(X2,X38) = hAPP(X2,X150) )
     => c_Equiv__Relations_Ocongruent(X5,X17,X78,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentI) ).

fof(fact_finite__less__ub,axiom,
    ! [X102,X2] :
      ( ! [X130] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X130),hAPP(X2,X130)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X2)),X102)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__less__ub) ).

fof(fact_congruent2D,axiom,
    ! [X173,X174,X175,X176,X2,X162,X164,X25,X17,X5] :
      ( c_Equiv__Relations_Ocongruent2(X5,X17,X25,X164,X162,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X176),X175)),X164))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X174),X173)),X162))
         => hAPP(hAPP(X2,X176),X174) = hAPP(hAPP(X2,X175),X173) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2D) ).

fof(fact_Int__Collect__mono,axiom,
    ! [X29,X30,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => ( hBOOL(hAPP(X30,X3))
             => hBOOL(hAPP(X29,X3)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OCollect(X5),X30))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Set_OCollect(X5),X29)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_UN__finite__subset,axiom,
    ! [X62,X19,X5] :
      ( ! [X130] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X130)),X19)),X62))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X19)),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_set__diff__eq,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [X29,X30,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X30)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X29))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30)),X29)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_map__pair__simp,axiom,
    ! [X21,X6,X1,X2,X17,X184,X5,X25] : hAPP(c_Product__Type_Omap__pair(X25,X5,X184,X17,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X25,X184),X6),X21)) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X2,X6)),hAPP(X1,X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__simp) ).

fof(fact_list__all2I,axiom,
    ! [X30,X21,X6,X17,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X3),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X6),X21))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X30),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X21)
       => c_List_Olist__all2(X5,X17,X30,X6,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2I) ).

fof(fact_list__all2__def,axiom,
    ! [X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X3),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X30),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__def) ).

fof(fact_map__pair__ident,axiom,
    ! [X26,X17,X5] : hAPP(c_Product__Type_Omap__pair(X5,X5,X17,X17,c_COMBI(X5),c_COMBI(X17)),X26) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__ident) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [X22,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
         => hAPP(hAPP(X2,hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
               => hAPP(X1,X3) = c_Groups_Oone__class_Oone(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_setprod__Un__one,axiom,
    ! [X2,X110,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X36),X110)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X36),X110)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X36)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X110)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
               => hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__Un__zero,axiom,
    ! [X2,X110,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X36),X110)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X36),X110)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X36)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X110)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_Image__singleton,axiom,
    ! [X6,X78,X5,X17] : hAPP(c_Relation_OImage(X17,X5,X78),hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X17,X5),tc_fun(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X17,X5))),hAPP(c_Product__Type_OPair(X17,X5),X6))),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
         => hAPP(X18,X19) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X17),X20),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_subset__image__iff,axiom,
    ! [X19,X2,X17,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
    <=> ? [X65] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X65),X19))
          & X22 = hAPP(c_Set_Oimage(X17,X5,X2),X65) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_UN__iff,axiom,
    ! [X22,X19,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
          & hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(X22,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__iff) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X17),X20),X19)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X17),X20),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_inv__into__comp,axiom,
    ! [X20,X19,X1,X25,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(c_Set_Oimage(X25,X5,X1),X19))
     => ( c_Fun_Oinj__on(X25,X5,X1,X19)
       => ( hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(c_Set_Oimage(X25,X5,X1),X19))))
         => hAPP(c_Hilbert__Choice_Oinv__into(X25,X17,X19,hAPP(c_Fun_Ocomp(X5,X17,X25,X2),X1)),X20) = hAPP(hAPP(c_Fun_Ocomp(X5,X25,X17,c_Hilbert__Choice_Oinv__into(X25,X5,X19,X1)),c_Hilbert__Choice_Oinv__into(X5,X17,hAPP(c_Set_Oimage(X25,X5,X1),X19),X2)),X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__comp) ).

fof(fact_the__inv__into__comp,axiom,
    ! [X20,X19,X1,X25,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(c_Set_Oimage(X25,X5,X1),X19))
     => ( c_Fun_Oinj__on(X25,X5,X1,X19)
       => ( hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(c_Set_Oimage(X25,X5,X1),X19))))
         => hAPP(c_Fun_Othe__inv__into(X25,X17,X19,hAPP(c_Fun_Ocomp(X5,X17,X25,X2),X1)),X20) = hAPP(hAPP(c_Fun_Ocomp(X5,X25,X17,c_Fun_Othe__inv__into(X25,X5,X19,X1)),c_Fun_Othe__inv__into(X5,X17,hAPP(c_Set_Oimage(X25,X5,X1),X19),X2)),X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [X2,X36,X110,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X110),X36)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X36) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X110) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [X2,X36,X110,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X110),X36)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X110) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X36) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [X2,X36,X110,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X110),X36)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X36) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X110) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [X2,X36,X110,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X110))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X110))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X110),X36)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X110) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X36) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_SUP1__iff,axiom,
    ! [X21,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
          & hBOOL(hAPP(hAPP(X22,X3),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__iff) ).

fof(fact_order__fun_I1_J,axiom,
    ! [X1,X2,X5,X17] :
      ( ( class_Orderings_Oorder(X17)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBS(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_Orderings_Oord__class_Oless__eq(X17)),X2)),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [X37,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Ortrancl(X5,X37)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool)),X37)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_Int__Inter__image,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBS(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X19),X62))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X62))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_Un__Union__image,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBS(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X19),X62))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X62))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Union__image) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [X24,X20,X102,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X102),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X20))),hAPP(hAPP(c_List_Oappend(X5),X102),hAPP(hAPP(c_List_Olist_OCons(X5),X21),X24)))),c_List_Olexord(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_intrel__iff,axiom,
    ! [X75,X102,X24,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X102),X75))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X75) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_intrel__iff) ).

fof(fact_same__fstI,axiom,
    ! [X5,X37,X24,X197,X17,X20,X30] :
      ( hBOOL(hAPP(X30,X20))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X197),X24)),hAPP(X37,X20)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X197)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24))),c_Recdef_Osame__fst(X5,X17,X30,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_less__SUP__iff,axiom,
    ! [X2,X19,X17,X6,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),X19),X2)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(X2,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_split__twice,axiom,
    ! [X133,X1,X183,X184,X2,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X184,X183,tc_prod(X17,X25)),X1),X133)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X184,X183,X5),hAPP(hAPP(c_COMBB(tc_fun(X183,tc_prod(X17,X25)),tc_fun(X183,X5),X184),hAPP(c_COMBB(tc_prod(X17,X25),X5,X183),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2))),X1)),X133),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).

fof(fact_list__size__pointwise,axiom,
    ! [X1,X2,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X3)),hAPP(X1,X3))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X5,X2,X224)),c_List_Olist_Olist__size(X5,X1,X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_inj__graph,axiom,
    ! [X17,X5] : c_Fun_Oinj__on(tc_fun(X5,X17),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X5,X17)),c_Set_OCollect(tc_prod(X5,X17))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X5,X17)),c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool)),hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBC(X17,X17,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X17),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__graph) ).

fof(fact_numeral__3__eq__3,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_max__extp_Osimps,axiom,
    ! [X33,X34,X37,X5] :
      ( c_Wellfounded_Omax__extp(X5,X37,X34,X33)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X34))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X33))
        & X33 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X34))
           => ? [X63] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X63),X33))
                & hBOOL(hAPP(hAPP(X37,X3),X63)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).

fof(fact_max__extp_Oequations,axiom,
    ! [X33,X34,X37,X5] :
      ( c_Wellfounded_Omax__extp(X5,X37,X34,X33)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X34))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X33))
        & X33 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X34))
           => ? [X63] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X63),X33))
                & hBOOL(hAPP(hAPP(X37,X3),X63)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_Int__def,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__def) ).

fof(fact_Un__def,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__def) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [X22,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_less__add__iff2,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X6)),X79)),X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

fof(fact_le__add__iff2,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X6)),X79)),X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

fof(fact_Image__INT__subset,axiom,
    ! [X22,X19,X25,X78,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X78),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Relation_OImage(X17,X5,X78)),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X22,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X22),X19))
         => hAPP(hAPP(X2,hAPP(X18,X22)),hAPP(X18,X19)) = hAPP(X18,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X5,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(X18,X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1),X26),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_map__eq__conv,axiom,
    ! [X1,X224,X2,X5,X17] :
      ( hAPP(hAPP(c_List_Omap(X17,X5),X2),X224) = hAPP(hAPP(c_List_Omap(X17,X5),X1),X224)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),hAPP(c_List_Oset(X17),X224)))
         => hAPP(X2,X3) = hAPP(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__conv) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [X25,X17,X5,X23,X146,X21,X6,X78] :
      ( hBOOL(hAPP(hAPP(X78,X6),X21))
     => ( hBOOL(hAPP(hAPP(X146,X21),X23))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X17,X25,X78,X146),X6),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X22,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
         => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [X6,X2,X162,X25,X17,X164,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X164)
     => ( c_Equiv__Relations_Ocongruent2(X5,X17,X25,X164,X162,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => c_Equiv__Relations_Ocongruent(X17,X25,X162,hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [X13,X228,X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = hAPP(hAPP(c_List_Oappend(X5),X228),X13)
    <=> ? [X242] :
          ( ( X224 = hAPP(hAPP(c_List_Oappend(X5),X228),X242)
            & hAPP(hAPP(c_List_Oappend(X5),X242),X223) = X13 )
          | ( hAPP(hAPP(c_List_Oappend(X5),X224),X242) = X228
            & X223 = hAPP(hAPP(c_List_Oappend(X5),X242),X13) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
       => ( ? [X68] :
              ( c_Fun_Oinj__on(X5,X17,X68,X19)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X68),X19)),X22)) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X17),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
         => hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,X19)) = hAPP(X18,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_sublists_Osimps_I2_J,axiom,
    ! [X224,X20,X5] : c_Enum_Osublists(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_Enum_Osublists(X5,X224)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X5)),tc_fun(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(tc_List_Olist(X5))),c_List_Oappend(tc_List_Olist(X5))),hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Olist_OCons(X5),X20)))),c_COMBI(tc_List_Olist(tc_List_Olist(X5))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists_Osimps_I2_J) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X17),X20),X19)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_INT__Int__distrib,axiom,
    ! [X22,X19,X111,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBS(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_UN__Un__distrib,axiom,
    ! [X22,X19,X111,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBS(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [X20,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X17,X2,X26,X1,X18)
     => hAPP(hAPP(X2,X20),X20) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_smax__emptyI,axiom,
    ! [X43] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X43))
     => ( X43 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X43)),c_FunDef_Omax__strict)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__emptyI) ).

fof(fact_set__filter,axiom,
    ! [X224,X30,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),X224)))),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__filter) ).

fof(fact_sum__diff__distrib,axiom,
    ! [X89,X30,X29] :
      ( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X29,X3)),hAPP(X30,X3)))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X30),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X29),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X30)),X29)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [X67,X17,X5,X19] :
      ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ? [X68] :
            ( c_Fun_Oinj__on(X5,X17,X68,X19)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X68),X19)),X67)) )
      <=> ? [X69] : hAPP(c_Set_Oimage(X17,X5,X69),X67) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_Range__iff,axiom,
    ! [X78,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ORange(X17,X5),X78)))
    <=> ? [X38] : hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X38),X6)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).

fof(fact_wmax__emptyI,axiom,
    ! [X40] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X40))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X40)),c_FunDef_Omax__weak)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = X22 )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = X22 )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))),X22) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [X22,X19,X62,X17,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [X22,X19,X62,X17,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [X22,X19,X62,X17,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [X62,X146,X25,X22,X19,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17,X25),tc_HOL_Obool)),X146),hAPP(hAPP(c_Product__Type_OSigma(X17,X25),X22),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X17),X62))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X25),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X78),X146)),hAPP(hAPP(c_Product__Type_OSigma(X5,X25),X19),hAPP(c_COMBK(tc_fun(X25,tc_HOL_Obool),X5),X62)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [X78,X223,X24,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_List_Olistrel1(X5,X78)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
          & X224 = X223 )
        | ( X20 = X24
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_lexord__cons__cons,axiom,
    ! [X78,X24,X21,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X20)),hAPP(hAPP(c_List_Olist_OCons(X5),X21),X24))),c_List_Olexord(X5,X78)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
        | ( X6 = X21
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olexord(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_Cons__in__lex,axiom,
    ! [X78,X223,X24,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_List_Olex(X5,X78)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223) )
        | ( X20 = X24
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olex(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [X22,X19,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [X22,X19,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [X22,X19,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),hAPP(hAPP(c_COMBS(X5,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool))),X19)),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X73)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X59))),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X61),X73))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [X89,X51,X102,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X96)),X102)),X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [X89,X51,X102,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X96)),X102)),X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [X16,X1,X19,X18,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X17,X2,X26,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(hAPP(X18,hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),X2),X1)),X16)),X19) = hAPP(hAPP(X2,hAPP(hAPP(X18,X1),X19)),hAPP(hAPP(X18,X16),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_arith__series__nat,axiom,
    ! [X89,X27,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X27))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X27)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__nat) ).

fof(fact_Un__Int__crazy,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X62),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [X223,X224,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_image__diff__subset,axiom,
    ! [X22,X19,X2,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),X19)),hAPP(c_Set_Oimage(X17,X5,X2),X22))),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [X30] : hAPP(c_Set_OCollect(tc_Nat_Onat),X30) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X30),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_lenlex__def,axiom,
    ! [X78,X5] : c_List_Olenlex(X5,X78) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X5)),tc_List_Olist(X5)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X5),c_Wellfounded_Oless__than,c_List_Olex(X5,X78))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X5))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_COMBI(tc_List_Olist(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lenlex__def) ).

fof(fact_bij__betw__comp__iff2,axiom,
    ! [X19,X2,X25,X284,X67,X213,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X213,X67,X284)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25,X5,X2),X19)),X67))
       => ( c_Fun_Obij__betw(X25,X5,X2,X19,X67)
        <=> c_Fun_Obij__betw(X25,X17,hAPP(c_Fun_Ocomp(X5,X17,X25,X213),X2),X19,X284) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__comp__iff2) ).

fof(fact_refl__onI,axiom,
    ! [X19,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) )
       => c_Relation_Orefl__on(X5,X19,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onI) ).

fof(fact_refl__on__def,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def) ).

fof(fact_insert__compr__raw,axiom,
    ! [X22,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [X22,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr) ).

fof(fact_listrel_OCons,axiom,
    ! [X223,X224,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_List_Olistrel(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).

fof(fact_smin__emptyI,axiom,
    ! [X40] :
      ( X40 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X40),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__emptyI) ).

fof(fact_minus,axiom,
    ! [X24,X20] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X20)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus) ).

fof(fact_wmin__emptyI,axiom,
    ! [X40] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X40),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__emptyI) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [X24,X19,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X24))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_empty__fold__graphE,axiom,
    ! [X20,X26,X2,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X20))
     => X20 = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_subset__equiv__class,axiom,
    ! [X6,X21,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [X102,X106,X105,X104,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OgreaterThanAtMost(X5,X104,X105,X106,X102)))
    <=> ( hBOOL(hAPP(hAPP(X105,X106),X96))
        & hBOOL(hAPP(hAPP(X104,X96),X102)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [X102,X106,X105,X104,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OatLeastLessThan(X5,X104,X105,X106,X102)))
    <=> ( hBOOL(hAPP(hAPP(X104,X106),X96))
        & hBOOL(hAPP(hAPP(X105,X96),X102)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
    ! [X1,X2,X22,X19,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X19 = X22
       => ( c_Nat__Transfer_Onat__set(X22)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
               => hAPP(X2,X3) = hAPP(X1,X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X22) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [X1,X2,X22,X19,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X19 = X22
       => ( c_Nat__Transfer_Onat__set(X22)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
               => hAPP(X2,X3) = hAPP(X1,X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X22) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [X224,X5] : c_Random_Oselect__weight(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X224)) = c_Random_Oselect__weight(X5,X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [X224,X5] : c_Random_Opick(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X224)) = c_Random_Opick(X5,X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__drop__zero) ).

fof(fact_transfer__int__nat__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).

fof(fact_transfer__nat__int__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).

fof(fact_o__inv__distrib,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(X25,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => c_Hilbert__Choice_Oinv__into(X25,X17,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X5,X17,X25,X2),X1)) = hAPP(c_Fun_Ocomp(X5,X25,X17,c_Hilbert__Choice_Oinv__into(X25,X5,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)),X1)),c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__inv__distrib) ).

fof(fact_Domain__Int__subset,axiom,
    ! [X22,X19,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X17),X19)),hAPP(c_Relation_ODomain(X5,X17),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Range__Int__subset,axiom,
    ! [X22,X19,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X17,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X17,X5),X19)),hAPP(c_Relation_ORange(X17,X5),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_setprod__dividef,axiom,
    ! [X1,X2,X19,X5,X17] :
      ( class_Fields_Ofield__inverse__zero(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBS(X5,X17,X17),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Rings_Oinverse__class_Odivide(X17)),X2)),X1)),X19) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__dividef) ).

fof(fact_setprod_Odistrib,axiom,
    ! [X16,X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBS(X5,X17,X17),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Groups_Otimes__class_Otimes(X17)),X1)),X16)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X16),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_setsum_Odistrib,axiom,
    ! [X16,X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBS(X5,X17,X17),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Groups_Oplus__class_Oplus(X17)),X1)),X16)),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X16),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [X20,X19,X26,X2,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X20))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_rotate1__def,axiom,
    ! [X224,X5] : hAPP(c_List_Orotate1(X5),X224) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).

fof(fact_setprod__timesf,axiom,
    ! [X19,X1,X2,X17,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Otimes__class_Otimes(X5)),X2)),X1)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),X1),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__timesf) ).

fof(fact_setsum__addf,axiom,
    ! [X19,X1,X2,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X1),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__addf) ).

fof(fact_setsum__subtractf,axiom,
    ! [X19,X1,X2,X17,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBS(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X19) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X1),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [X59,X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X107),X119)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X59))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X59)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X107),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X107,X59))),X119)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_lists__Int__eq,axiom,
    ! [X22,X19,X5] : c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X22))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X19))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_select__weight__def,axiom,
    ! [X224,X5] : c_Random_Oselect__weight(X5,X224) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X224)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X5,X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__def) ).

fof(fact_insert__times__insert,axiom,
    ! [X22,X21,X19,X6,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X17),X21),X22))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X17),X21),X22)))),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__times__insert) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [X78,X19,X2,X17,X5] :
      ( class_Fields_Ofield(X5)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)),X78) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Rings_Oinverse__class_Odivide(X5)),X2)),X78)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_setsum__left__distrib,axiom,
    ! [X78,X19,X2,X17,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)),X78) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Groups_Otimes__class_Otimes(X5)),X2)),X78)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_zmult2__lemma,axiom,
    ! [X59,X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X59)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X59))),X119)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [X228,X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X223),X228)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X228)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_pred__subset__eq,axiom,
    ! [X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X37)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X37),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [X36,X37,X30,X5] :
      ( c_FunDef_Oreduction__pair(X5,X30)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X30)))
         => ( c_Wellfounded_Owf(X5,X36)
           => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_Union__Int__subset,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_fun__upd__twist,axiom,
    ! [X27,X21,X51,X17,X5,X23,X6] :
      ( X6 != X23
     => c_Fun_Ofun__upd(X5,X17,c_Fun_Ofun__upd(X5,X17,X51,X6,X21),X23,X27) = c_Fun_Ofun__upd(X5,X17,c_Fun_Ofun__upd(X5,X17,X51,X23,X27),X6,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_Image__subset__eq,axiom,
    ! [X22,X19,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X78),X19)),X22))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X17,hAPP(c_Relation_Oconverse(X17,X5),X78)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_image__eq__UN,axiom,
    ! [X19,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X17,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X17),c_Set_Oinsert(X5)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eq__UN) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [X20,X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X223))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_pair__leqI2,axiom,
    ! [X15,X146,X21,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X15))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X146)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21),X15))),c_FunDef_Opair__leq)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI2) ).

fof(fact_pair__lessI2,axiom,
    ! [X15,X146,X21,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X15))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X146)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21),X15))),c_FunDef_Opair__less)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [X36,X37,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X37)),c_Transitive__Closure_Ortrancl(X5,X36))),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_lexord__trans,axiom,
    ! [X26,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olexord(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X24),X26)),c_List_Olexord(X5,X78)))
       => ( c_Relation_Otrans(X5,X78)
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X26)),c_List_Olexord(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).

fof(fact_Image__Int__subset,axiom,
    ! [X22,X19,X37,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X37),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X37),X19)),hAPP(c_Relation_OImage(X17,X5,X37),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_image__Int__subset,axiom,
    ! [X22,X19,X2,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),X19)),hAPP(c_Set_Oimage(X17,X5,X2),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [X35,X30] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => ( hBOOL(hAPP(X30,X3))
          <=> hBOOL(hAPP(X35,X3)) ) )
     => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X30)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_pair__leqI1,axiom,
    ! [X15,X146,X21,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X21))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X146)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21),X15))),c_FunDef_Opair__leq)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI1) ).

fof(fact_pair__lessI1,axiom,
    ! [X15,X146,X21,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X21))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X146)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21),X15))),c_FunDef_Opair__less)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).

fof(fact_lists__eq__set,axiom,
    ! [X19,X5] : c_List_Olists(X5,X19) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__eq__set) ).

fof(fact_append__listrel1I,axiom,
    ! [X244,X245,X78,X223,X224,X5] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
          & X245 = X244 )
        | ( X224 = X223
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X245),X244)),c_List_Olistrel1(X5,X78))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X224),X245)),hAPP(hAPP(c_List_Oappend(X5),X223),X244))),c_List_Olistrel1(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).

fof(fact_lexord__append__leftI,axiom,
    ! [X20,X78,X75,X102,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X102),X75)),c_List_Olexord(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X20),X102)),hAPP(hAPP(c_List_Oappend(X5),X20),X75))),c_List_Olexord(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_listrel1I2,axiom,
    ! [X20,X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X223))),c_List_Olistrel1(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [X30] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_bij__betw__comp__iff,axiom,
    ! [X284,X213,X25,X67,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X67)
     => ( c_Fun_Obij__betw(X17,X25,X213,X67,X284)
      <=> c_Fun_Obij__betw(X5,X25,hAPP(c_Fun_Ocomp(X17,X25,X5,X213),X2),X19,X284) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__comp__iff) ).

fof(fact_zip__map1,axiom,
    ! [X223,X224,X2,X25,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),hAPP(hAPP(c_List_Omap(X25,X5),X2),X224)),X223) = hAPP(hAPP(c_List_Omap(tc_prod(X25,X17),tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X25,X17,tc_prod(X5,X17)),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_prod(X5,X17)),X25),c_Product__Type_OPair(X5,X17)),X2))),hAPP(hAPP(c_List_Ozip(X25,X17),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map1) ).

fof(fact_mlex__prod__def,axiom,
    ! [X37,X2,X5] : c_Wellfounded_Omlex__prod(X5,X2,X37) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X5),X5),c_Wellfounded_Olex__prod(tc_Nat_Onat,X5,c_Wellfounded_Oless__than,X37)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(tc_Nat_Onat,X5)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_prod(tc_Nat_Onat,X5)),X5),c_Product__Type_OPair(tc_Nat_Onat,X5)),X2)),c_COMBI(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_finite__empty__induct,axiom,
    ! [X30,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(X30,X19))
       => ( ! [X49,X50] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X50))
             => ( hBOOL(hAPP(hAPP(c_member(X5),X49),X50))
               => ( hBOOL(hAPP(X30,X50))
                 => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X50),hAPP(hAPP(c_Set_Oinsert(X5),X49),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(X30,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [X22,X19,X17,X62,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X62))),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X22),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X62))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [X89,X26,X37,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X37))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [X26,X37,X89,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X26)),X37))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_bij__comp,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(X17,X25,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)))
       => c_Fun_Obij__betw(X5,X25,hAPP(c_Fun_Ocomp(X17,X25,X5,X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__comp) ).

fof(fact_image__Pow__mono,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),X19)),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X17,X5,X2)),hAPP(c_Set_OPow(X17),X19))),hAPP(c_Set_OPow(X5),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_select__weight__member,axiom,
    ! [X146,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X224))))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X5,X224),X146))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__member) ).

fof(fact_setsum__abs,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Oabs__class_Oabs(X5)),X2)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs) ).

fof(fact_set__minus__filter__out,axiom,
    ! [X24,X224,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X24))),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__filter,axiom,
    ! [X224,X29,X30,X5] : hAPP(c_List_Ofilter(X5,X30),hAPP(c_List_Ofilter(X5,X29),X224)) = hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X29)),X30)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__filter) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [X22,X19,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X17),X19)),hAPP(c_Relation_ODomain(X5,X17),X22))),hAPP(c_Relation_ODomain(X5,X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [X22,X19,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X17,X5),X19)),hAPP(c_Relation_ORange(X17,X5),X22))),hAPP(c_Relation_ORange(X17,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).

fof(conj_0,hypothesis,
    ! [X304] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X304)),hAPP(v_c0,X304)),hAPP(v_Q_H,X304))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X304)),hAPP(v_c0,X304)),hAPP(v_Q,X304))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [X5] : c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).

fof(fact_card__Diff1__less,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_split__comp__eq,axiom,
    ! [X1,X2,X184,X25,X17,X5] : hAPP(hAPP(c_COMBS(tc_prod(X5,X17),X17,X25),hAPP(hAPP(c_COMBB(X184,tc_fun(X17,X25),tc_prod(X5,X17)),X2),hAPP(hAPP(c_COMBB(X5,X184,tc_prod(X5,X17)),X1),c_Product__Type_Ofst(X5,X17)))),c_Product__Type_Osnd(X5,X17)) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),hAPP(hAPP(c_COMBB(X184,tc_fun(X17,X25),X5),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp__eq) ).

fof(fact_insort__key__remove1,axiom,
    ! [X2,X224,X6,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X224)))
       => ( c_List_Olinorder__class_Osorted(X17,hAPP(hAPP(c_List_Omap(X5,X17),X2),X224))
         => ( hAPP(c_List_Ohd(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(X17,tc_HOL_Obool,X5),hAPP(c_fequal,hAPP(X2,X6))),X2)),X224)) = X6
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X6),c_List_Oremove1(X5,X6,X224)) = X224 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_bij__betw__Disj__Un,axiom,
    ! [X2,X208,X67,X17,X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X67),X208) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))
       => ( c_Fun_Obij__betw(X5,X17,X2,X19,X67)
         => ( c_Fun_Obij__betw(X5,X17,X2,X22,X208)
           => c_Fun_Obij__betw(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X67),X208)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [X24,X20] :
      ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X20),X24)),c_Int_Ointrel)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_setsum__UNION__zero,axiom,
    ! [X2,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X36))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X36))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)) )
         => ( ! [X280] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X280),X36))
               => ! [X281] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X281),X36))
                   => ( X280 != X281
                     => ! [X3] :
                          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X280))
                         => ( hBOOL(hAPP(hAPP(c_member(X5),X3),X281))
                           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X36)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2)),X36) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [X33,X34,X17,X5] : c_Nitpick_Ofold__graph_H(X5,X17,X34,X33,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [X26,X2,X17,X5] : c_Nitpick_Ofold__graph_H(X5,X17,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_map__pair_Oid,axiom,
    ! [X17,X5] : c_Product__Type_Omap__pair(X5,X5,X17,X17,c_Fun_Oid(X5),c_Fun_Oid(X17)) = c_Fun_Oid(tc_prod(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [X17,X5] : c_Product__Type_Omap__pair(X5,X5,X17,X17,c_COMBI(X5),c_COMBI(X17)) = c_Fun_Oid(tc_prod(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [X26,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_bij__betw__trans,axiom,
    ! [X62,X1,X25,X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => ( c_Fun_Obij__betw(X17,X25,X1,X22,X62)
       => c_Fun_Obij__betw(X5,X25,hAPP(c_Fun_Ocomp(X17,X25,X5,X1),X2),X19,X62) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__trans) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__def) ).

fof(fact_card__Diff1__le,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_rel__comp__mono,axiom,
    ! [X146,X201,X25,X78,X157,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X157),X78))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17,X25),tc_HOL_Obool)),X201),X146))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X25),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X157),X201)),hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X78),X146))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_equiv__class__subset,axiom,
    ! [X21,X6,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_the__inv__into__into,axiom,
    ! [X22,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Fun_Othe__inv__into(X5,X17,X19,X2),X20)),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X25,X1,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X17,X5,X1),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X25),hAPP(c_Set_Oimage(X17,X25,hAPP(hAPP(c_COMBB(X5,X25,X17),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_Inter__Un__subset,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X22))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_listrel__subset,axiom,
    ! [X19,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X78)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olists(X5,X19)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_List_Olist(X5)),c_List_Olists(X5,X19))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset) ).

fof(fact_fold__image__reindex,axiom,
    ! [X26,X1,X16,X17,X19,X5,X25] :
      ( class_Groups_Oab__semigroup__mult(X25)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( c_Fun_Oinj__on(X5,X17,X16,X19)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X17,c_Groups_Otimes__class_Otimes(X25)),X1),X26),hAPP(c_Set_Oimage(X5,X17,X16),X19)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25,X5,c_Groups_Otimes__class_Otimes(X25)),hAPP(c_Fun_Ocomp(X17,X25,X5,X1),X16)),X26),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [X107,X61,X119,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X59))),X119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [X23,X21,X19,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X21)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X23),X19)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X21),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [X23,X21,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X21)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X23),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X21),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_bij__betw__combine,axiom,
    ! [X64,X62,X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => ( c_Fun_Obij__betw(X5,X17,X2,X62,X64)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X22),X64) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))
         => c_Fun_Obij__betw(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X62),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X22),X64)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__combine) ).

fof(fact_listrel1I1,axiom,
    ! [X224,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X224))),c_List_Olistrel1(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).

fof(fact_transpose__column,axiom,
    ! [X96,X224,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X96)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X224))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X224),X96) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column) ).

fof(fact_split__paired__Eps,axiom,
    ! [X30,X17,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X17),X30) = c_Hilbert__Choice_OEps(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_HOL_Obool,X17),X30)),c_Product__Type_OPair(X5,X17)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_split__paired__The,axiom,
    ! [X30,X17,X5] : c_HOL_OThe(tc_prod(X5,X17),X30) = c_HOL_OThe(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X17),tc_HOL_Obool,X17),X30)),c_Product__Type_OPair(X5,X17)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__The) ).

fof(fact_Comp,axiom,
    ! [X37,X27,X29,X23,X30,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),X23),X29)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X29),X27),X37)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),c_Com_Ocom_OSemi(X23,X27)),X37)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Comp) ).

fof(fact_total__on__def,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Ototal__on(X5,X19,X78)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X63),X19))
             => ( X3 != X63
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X63)),X78))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X63),X3)),X78)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).

fof(fact_mod__lemma,axiom,
    ! [X107,X61,X119,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X59))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X119),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X107,X59))),X119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).

fof(fact_single__valued__confluent,axiom,
    ! [X26,X24,X20,X78,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),c_Transitive__Closure_Ortrancl(X5,X78)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X26)),c_Transitive__Closure_Ortrancl(X5,X78)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X26),X24)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_reduction__pairI,axiom,
    ! [X36,X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X36)),X37))
       => c_FunDef_Oreduction__pair(X5,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pairI) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [X107,X119,X61,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X119))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X59))),X119)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_select__def,axiom,
    ! [X224,X5] : c_Random_Oselect(X5,X224) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X5),X224)),c_Code__Numeral_Onat__of))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__def) ).

fof(fact_of__int,axiom,
    ! [X95,X96,X5] :
      ( class_Rings_Oring__1(X5)
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X96),X95)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X96)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X95)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int) ).

fof(fact_diff__single__insert,axiom,
    ! [X22,X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__single__insert) ).

fof(fact_nat,axiom,
    ! [X24,X20] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat) ).

fof(fact_inj__on__Un,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))
    <=> ( c_Fun_Oinj__on(X5,X17,X2,X19)
        & c_Fun_Oinj__on(X5,X17,X2,X22)
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19))) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un) ).

fof(fact_in__finite__psubset,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),X22)),c_Wellfounded_Ofinite__psubset(X5)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_Domain__iff,axiom,
    ! [X78,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X17),X78)))
    <=> ? [X38] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X38)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).

fof(fact_Un__Pow__subset,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)),hAPP(c_Set_OPow(X5),X22))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_o__inv__o__cancel,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X17,X25,X5,hAPP(c_Fun_Ocomp(X5,X25,X17,X1),c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2))),X2) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__inv__o__cancel) ).

fof(fact_nat__diff__add__eq1,axiom,
    ! [X92,X86,X103,X98,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X98))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X103)),X86)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X103)),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X94)),X103)),X86)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_pick__member,axiom,
    ! [X224,X5,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X224))))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Random_Opick(X5,X224),X96)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__member) ).

fof(fact_rel__compI,axiom,
    ! [X146,X23,X25,X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X25)),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X21),X23)),X146))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X25)),hAPP(hAPP(c_Product__Type_OPair(X5,X25),X6),X23)),hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X78),X146))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [X20,X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Olinorder__class_Oinsort__insert__key(X17,X5,X2,X20,X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_list__all2__append,axiom,
    ! [X244,X245,X30,X223,X17,X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
     => ( c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X245),hAPP(hAPP(c_List_Oappend(X17),X223),X244))
      <=> ( c_List_Olist__all2(X5,X17,X30,X224,X223)
          & c_List_Olist__all2(X5,X17,X30,X245,X244) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__append) ).

fof(fact_bex__Un,axiom,
    ! [X30,X22,X19,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
          & hBOOL(hAPP(X30,X3)) )
    <=> ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
            & hBOOL(hAPP(X30,X3)) )
        | ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X22))
            & hBOOL(hAPP(X30,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [X30,X22,X19,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
         => hBOOL(hAPP(X30,X3)) )
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(X30,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X22))
           => hBOOL(hAPP(X30,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__Un) ).

fof(fact_INF2__D,axiom,
    ! [X6,X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(hAPP(hAPP(X22,X6),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__D) ).

fof(fact_list__all2__appendI,axiom,
    ! [X27,X23,X21,X6,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X6,X21)
     => ( c_List_Olist__all2(X5,X17,X30,X23,X27)
       => c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Oappend(X5),X6),X23),hAPP(hAPP(c_List_Oappend(X17),X21),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__appendI) ).

fof(fact_nat__2,axiom,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__2) ).

fof(fact_fun__upd__comp,axiom,
    ! [X24,X20,X1,X2,X5,X17,X25] : hAPP(c_Fun_Ocomp(X25,X17,X5,X2),c_Fun_Ofun__upd(X5,X25,X1,X20,X24)) = c_Fun_Ofun__upd(X5,X17,hAPP(c_Fun_Ocomp(X25,X17,X5,X2),X1),X20,hAPP(X2,X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__comp) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).

fof(fact_vimage__def,axiom,
    ! [X22,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),X22) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),X5),c_member(X17)),X2)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__def) ).

fof(fact_zip__append2,axiom,
    ! [X237,X221,X222,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),X222),hAPP(hAPP(c_List_Oappend(X161),X221),X237)) = hAPP(hAPP(c_List_Oappend(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X221)),X222)),X221)),hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X221)),X222)),X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append2) ).

fof(fact_in__listrel1__converse,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [X228,X223,X224,X20,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) = hAPP(hAPP(c_List_Oappend(X5),X223),X228)
    <=> ( ( X223 = c_List_Olist_ONil(X5)
          & hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) = X228 )
        | ? [X239] :
            ( hAPP(hAPP(c_List_Olist_OCons(X5),X20),X239) = X223
            & X224 = hAPP(hAPP(c_List_Oappend(X5),X239),X228) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [X224,X20,X228,X223,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X223),X228) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)
    <=> ( ( X223 = c_List_Olist_ONil(X5)
          & X228 = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) )
        | ? [X239] :
            ( X223 = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X239)
            & hAPP(hAPP(c_List_Oappend(X5),X239),X228) = X224 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_inv__into__into,axiom,
    ! [X19,X2,X17,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(c_Hilbert__Choice_Oinv__into(X17,X5,X19,X2),X20)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_card__SigmaI,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X3))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X17)),X22)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__SigmaI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [X26,X2,X17,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [X26,X2,X17,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_wf__union__compatible,axiom,
    ! [X36,X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
     => ( c_Wellfounded_Owf(X5,X36)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X36)),X37))
         => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_fold1__in,axiom,
    ! [X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__in) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [X119,X107,X135,X136,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X136)),X135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X135),X61))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136),X107)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [X119,X107,X135,X136,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X136)),X135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X119))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X135))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X136)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_distinct__insort__insert,axiom,
    ! [X20,X2,X224,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
       => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X17,X2,X20,X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_nth__transpose,axiom,
    ! [X224,X5,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X224))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X224)),X96) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X96)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__transpose) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X20),hAPP(c_Set_OPow(X5),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),X22))
       => ( c_Fun_Oinj__on(X17,X5,X1,X22)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X1),X22)),X19))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
               => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Finite__Set_Ocard(X17),X22) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_Eps__split,axiom,
    ! [X30,X17,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X30)) = c_Hilbert__Choice_OEps(tc_prod(X5,X17),hAPP(hAPP(c_COMBS(tc_prod(X5,X17),X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_HOL_Obool),tc_prod(X5,X17)),X30),c_Product__Type_Ofst(X5,X17))),c_Product__Type_Osnd(X5,X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split) ).

fof(fact_The__split,axiom,
    ! [X30,X17,X5] : c_HOL_OThe(tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X30)) = c_HOL_OThe(tc_prod(X5,X17),hAPP(hAPP(c_COMBS(tc_prod(X5,X17),X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_HOL_Obool),tc_prod(X5,X17)),X30),c_Product__Type_Ofst(X5,X17))),c_Product__Type_Osnd(X5,X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split) ).

fof(fact_in__measures_I2_J,axiom,
    ! [X263,X2,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X263))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24)))
        | ( hAPP(X2,X20) = hAPP(X2,X24)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,X263))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_inf__period_I3_J,axiom,
    ! [X15,X64,X27,X5] :
      ( ( class_Rings_Ocomm__ring(X5)
        & class_Rings_Odvd(X5) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),X64))
       => ! [X3,X97] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),X15)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X97),X64))),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).

fof(fact_inf__period_I4_J,axiom,
    ! [X15,X64,X27,X5] :
      ( ( class_Rings_Ocomm__ring(X5)
        & class_Rings_Odvd(X5) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),X64))
       => ! [X3,X97] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),X15)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X97),X64))),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).

fof(fact_div__mod__equality,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),X61)),c_Divides_Odiv__class_Omod(X56,X60,X61))),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality) ).

fof(fact_fun__upd__upd,axiom,
    ! [X26,X24,X20,X2,X17,X5] : c_Fun_Ofun__upd(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X20,X26) = c_Fun_Ofun__upd(X5,X17,X2,X20,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_vimage__subset__eq,axiom,
    ! [X19,X22,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),X19))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X5,X17,X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subset__eq) ).

fof(fact_uminus__listsum__map,axiom,
    ! [X224,X2,X17,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(c_Fun_Ocomp(X5,X5,X17,c_Groups_Ouminus__class_Ouminus(X5)),X2)),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_neg__map__def,axiom,
    ! [X30,X2,X5,X17] : c_New__Random__Sequence_Oneg__map(X17,X5,X2,X30) = c_New__Random__Sequence_Oneg__bind(X17,X5,X30,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X17,c_New__Random__Sequence_Oneg__single(X5)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__map__def) ).

fof(fact_listsp__lists__eq,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X20),c_List_Olists(X5,X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Oabs__class_Oabs(X5)),X2)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24))),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
          & X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_Min_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_Max_Oclosed,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X38] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X38)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X19)),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [X1,X16,X19,X18,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X17,X2,X26,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( c_Fun_Oinj__on(X17,X17,X16,X19)
         => hAPP(hAPP(X18,X1),hAPP(c_Set_Oimage(X17,X17,X16),X19)) = hAPP(hAPP(X18,hAPP(c_Fun_Ocomp(X17,X5,X17,X1),X16)),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_transpose__column__length,axiom,
    ! [X96,X224,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X224)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X224))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X224),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column__length) ).

fof(fact_pair__imageI,axiom,
    ! [X2,X25,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X19))
     => hBOOL(hAPP(hAPP(c_member(X25),hAPP(hAPP(X2,X6),X21)),hAPP(c_Set_Oimage(tc_prod(X5,X17),X25,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),X2)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).

fof(fact_length__filter__map,axiom,
    ! [X224,X2,X17,X30,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),hAPP(c_List_Ofilter(X17,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X17,X30),X2)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__map) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [X19,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
       => ( X6 = X21
          | hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [X224,X30,X5] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X30),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30)),X224))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_rtrancl__trans,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [X59,X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X59)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X61),X59))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X59)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X59))),X59)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_div__add1__eq,axiom,
    ! [X59,X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X60),X59)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X61),X59))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X60,X59)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X61,X59))),X59)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).

fof(fact_inf2D1,axiom,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => hBOOL(hAPP(hAPP(X19,X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).

fof(fact_inf2D2,axiom,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => hBOOL(hAPP(hAPP(X22,X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [X224,X5,X30,X95] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X95))
         => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [X23,X78,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [X16,X1,X215,X2,X25,X184,X183,X18,X123,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X123,X18)
     => hAPP(c_Fun_Ocomp(X183,X184,X25,X2),hAPP(c_Fun_Ocomp(X215,X183,X25,X1),X16)) = hAPP(c_Fun_Ocomp(X215,X184,X25,hAPP(c_Fun_Ocomp(X183,X184,X215,X2),X1)),X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [X135,X136,X137,X119,X107,X61] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X137),X61))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136),X107)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [X30] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X30)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X30),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_lexord__lex,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olex(X5,X78)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_List_Olexord(X5,X78)))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X20) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X24) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).

fof(fact_filter__map,axiom,
    ! [X224,X2,X17,X30,X5] : hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Ofilter(X17,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X17,X30),X2)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__map) ).

fof(fact_wfP__SUP,axiom,
    ! [X5,X78,X17] :
      ( ! [X88] : c_Wellfounded_OwfP(X17,hAPP(X78,X88))
     => ( ! [X88,X120] :
            ( hAPP(X78,X88) != hAPP(X78,X120)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),c_Predicate_ODomainP(X17,X17,hAPP(X78,X88))),c_Predicate_ORangeP(X17,X17,hAPP(X78,X120))) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(X17,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X17,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__SUP) ).

fof(fact_partition__filter__conv,axiom,
    ! [X224,X2,X5] : c_List_Opartition(X5,X2,X224) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X2),X224)),hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X2)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_upto_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X88,X120] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X88),X120)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X88),X120))
               => hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X88),c_Groups_Oone__class_Oone(tc_Int_Oint))),X120)) )
             => hBOOL(hAPP(hAPP(X30,X88),X120)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_list__all2__map1,axiom,
    ! [X257,X252,X2,X25,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Omap(X25,X5),X2),X252),X257)
    <=> c_List_Olist__all2(X25,X17,hAPP(hAPP(c_COMBB(X5,tc_fun(X17,tc_HOL_Obool),X25),X30),X2),X252,X257) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map1) ).

fof(fact_measures__lesseq,axiom,
    ! [X263,X5,X24,X20,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,X263)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X263)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).

fof(fact_trans__def,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
    <=> ! [X3,X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X78))
         => ! [X150] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X150)),X78))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X150)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).

fof(fact_transD,axiom,
    ! [X23,X21,X6,X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X23)),X78))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X6)),X6)),c_Groups_Ozero__class_Ozero(X5)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_zdiv__zmod__equality2,axiom,
    ! [X93,X61,X60] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),X61)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61))),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_INFI__set__fold,axiom,
    ! [X2,X224,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),hAPP(c_List_Oset(X17),X224)),X2) = hAPP(c_List_Ofoldl(X5,X17,hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Lattices_Osemilattice__inf__class_Oinf(X5)),X2)),c_Orderings_Otop__class_Otop(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [X2,X224,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),hAPP(c_List_Oset(X17),X224)),X2) = hAPP(c_List_Ofoldl(X5,X17,hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),c_Lattices_Osemilattice__sup__class_Osup(X5)),X2)),c_Orderings_Obot__class_Obot(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_finite__UN__I,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ! [X49] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X49))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN__I) ).

fof(fact_finite__UN,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [X78,X111,X184,X146,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X146),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X184,tc_fun(tc_prod(X25,X17),tc_HOL_Obool)),X111),X78)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X184,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X25,X17),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),X184),hAPP(c_Relation_Orel__comp(X5,X25,X17),X146)),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_o__assoc,axiom,
    ! [X16,X1,X184,X2,X5,X17,X25] : hAPP(c_Fun_Ocomp(X25,X17,X5,X2),hAPP(c_Fun_Ocomp(X184,X25,X5,X1),X16)) = hAPP(c_Fun_Ocomp(X184,X17,X5,hAPP(c_Fun_Ocomp(X25,X17,X184,X2),X1)),X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),X19))),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_bij__image__INT,axiom,
    ! [X22,X19,X25,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X25),c_Set_Oimage(X5,X17,X2)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__INT) ).

fof(fact_in__inv__image,axiom,
    ! [X2,X78,X17,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(hAPP(c_Relation_Oinv__image(X17,X5),X78),X2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),hAPP(X2,X20)),hAPP(X2,X24))),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).

fof(fact_sym__trans__comp__subset,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => ( c_Relation_Otrans(X5,X78)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X78)),X78)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__trans__comp__subset) ).

fof(fact_folding_Oremove,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(X18,X19) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oremove) ).

fof(fact_Image__subset,axiom,
    ! [X62,X22,X19,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X17,X78),X62)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset) ).

fof(fact_tl__append,axiom,
    ! [X223,X224,X5] : hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,hAPP(c_List_Otl(X5),X223),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5)),X223))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append) ).

fof(fact_pos__map__def,axiom,
    ! [X30,X2,X5,X17] : c_New__Random__Sequence_Opos__map(X17,X5,X2,X30) = c_New__Random__Sequence_Opos__bind(X17,X5,X30,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X17,c_New__Random__Sequence_Opos__single(X5)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__map__def) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_bij__imp__bij__inv,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => c_Fun_Obij__betw(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [X96,X24,X20,X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
     => ( hBOOL(hAPP(hAPP(X30,X20),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)))
         => c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X20),hAPP(hAPP(c_List_Olist__update(X17,X223),X96),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [X24,X20,X223,X30,X17,X224,X5,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => ( c_List_Olist__all2(X5,X17,X30,X224,X223)
       => ( hBOOL(hAPP(hAPP(X30,X20),X24))
         => c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X20),hAPP(hAPP(c_List_Olist__update(X17,X223),X96),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_bij__image__Collect__eq,axiom,
    ! [X30,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(c_Set_OCollect(X5),X30)) = hAPP(c_Set_OCollect(X17),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X17),X30),c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).

fof(fact_setprod__pos,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Rings_Olinordered__semidom(X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos) ).

fof(fact_setprod__nonneg,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Rings_Olinordered__semidom(X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),c_Groups_Ozero__class_Ozero(X17)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__nonneg) ).

fof(fact_converse__pred__comp,axiom,
    ! [X146,X78,X25,X5,X17] : c_Predicate_Oconversep(X17,X5,c_Predicate_Opred__comp(X17,X25,X5,X78,X146)) = c_Predicate_Opred__comp(X5,X25,X17,c_Predicate_Oconversep(X25,X5,X146),c_Predicate_Oconversep(X17,X25,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [X1,X25,X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X22)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X19)),X1)) = hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X19)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X22)),X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_inv__def,axiom,
    ! [X24,X2,X17,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X24) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__def) ).

fof(fact_finite__SigmaI,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ! [X49] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X22,X49))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_convex__bound__lt,axiom,
    ! [X122,X103,X57,X60,X55,X56] :
      ( class_Rings_Olinordered__semiring__1__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X103))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X122))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X103),X122) = c_Groups_Oone__class_Oone(X56)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X103),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X122),X57))),X60)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_convex__bound__le,axiom,
    ! [X122,X103,X57,X60,X55,X56] :
      ( class_Rings_Olinordered__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X103))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X122))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X103),X122) = c_Groups_Oone__class_Oone(X56)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X103),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X122),X57))),X60)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

fof(fact_aset_I6_J,axiom,
    ! [X19,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X19))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X148),X63) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X15))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X64)),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I6_J) ).

fof(fact_lazy__sequence_Orecs_I2_J,axiom,
    ! [X278,X6,X149,X28,X17,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X17,X28,X149,c_Lazy__Sequence_Olazy__sequence_OInsert(X17,X6,X278)) = hAPP(hAPP(hAPP(X149,X6),X278),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X17,X28,X149,X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).

fof(fact_max__extp_Ointros,axiom,
    ! [X37,X43,X40,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X40))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X43))
       => ( X43 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X40))
               => ? [X63] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X63),X43))
                    & hBOOL(hAPP(hAPP(X37,X3),X63)) ) )
           => c_Wellfounded_Omax__extp(X5,X37,X40,X43) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [X1,X20,X25,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X19)),X1)) = hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X18,X19)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_listrel1I,axiom,
    ! [X223,X244,X245,X224,X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
     => ( X224 = hAPP(hAPP(c_List_Oappend(X5),X245),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X244))
       => ( X223 = hAPP(hAPP(c_List_Oappend(X5),X245),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X244))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).

fof(fact_bex__reg__right,axiom,
    ! [X30,X29,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ( ! [X3] :
            ( hBOOL(hAPP(X29,X3))
           => hBOOL(hAPP(X30,X3)) )
       => ( ? [X77] : hBOOL(hAPP(X29,X77))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Quotient_ORespects(X5,X37)))
              & hBOOL(hAPP(X30,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__reg__right) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [X20,X30,X224,X5] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88))) )
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hBOOL(hAPP(X30,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [X23,X21,X19,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X21),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X23),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [X23,X21,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X23),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [X89,X90,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X90))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_bij__betw__subset,axiom,
    ! [X208,X22,X67,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X67)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
       => ( hAPP(c_Set_Oimage(X5,X17,X2),X22) = X208
         => c_Fun_Obij__betw(X5,X17,X2,X22,X208) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__subset) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [X36,X37,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X20),c_Transitive__Closure_Ortrancl(X5,X37)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X20),c_Transitive__Closure_Ortrancl(X5,X36))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X20),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [X1,X20,X24,X25,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X24)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),X1)) = hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X24)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_range__ex1__eq,axiom,
    ! [X21,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X21 = hAPP(X2,X3)
            & ! [X38] :
                ( X21 = hAPP(X2,X38)
               => X38 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_setsum__Un,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Groups_Oab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un) ).

fof(fact_rev__update,axiom,
    ! [X57,X222,X56,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(c_List_Orev(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X93),X57)) = hAPP(hAPP(c_List_Olist__update(X56,hAPP(c_List_Orev(X56),X222)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X93)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__update) ).

fof(fact_Collect__imp__eq,axiom,
    ! [X29,X30,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),X30)),X29)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30))),hAPP(c_Set_OCollect(X5),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_single__valued__def,axiom,
    ! [X78,X17,X5] :
      ( c_Relation_Osingle__valued(X5,X17,X78)
    <=> ! [X3,X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X3),X38)),X78))
         => ! [X150] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X3),X150)),X78))
             => X38 = X150 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).

fof(fact_prod__size__simp,axiom,
    ! [X133,X1,X2,X17,X5] : c_Product__Type_Oprod_Oprod__size(X5,X17,X2,X1,X133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,hAPP(c_Product__Type_Ofst(X5,X17),X133))),hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X17),X133)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__size__simp) ).

fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [X89,X90,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X90))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_bset_I8_J,axiom,
    ! [X22,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X22))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X22))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X63) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X64))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I8_J) ).

fof(fact_finite__equiv__class,axiom,
    ! [X40,X78,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X40)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_quotient__eqI,axiom,
    ! [X24,X20,X43,X40,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X43),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X40))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X43))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
               => X40 = X43 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eqI) ).

fof(fact_quotient__eq__iff,axiom,
    ! [X24,X20,X43,X40,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X43),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X40))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X43))
             => ( X40 = X43
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => ( ! [X150] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X150))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X150),c_Groups_Oone__class_Oone(X56)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X150),X55)),X57)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_eq__comp__r,axiom,
    ! [X37,X5] : c_Predicate_Opred__comp(X5,X5,X5,c_fequal,c_Predicate_Opred__comp(X5,X5,X5,X37,c_fequal)) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).

fof(fact_curryD,axiom,
    ! [X21,X6,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X17,tc_HOL_Obool,X2),X6),X21))
     => hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).

fof(fact_curryE,axiom,
    ! [X21,X6,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X17,tc_HOL_Obool,X2),X6),X21))
     => hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).

fof(fact_Image__eq__UN,axiom,
    ! [X22,X78,X5,X17] : hAPP(c_Relation_OImage(X17,X5,X78),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Relation_OImage(X17,X5,X78)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),c_Set_Oinsert(X17)),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_vimage__eq__UN,axiom,
    ! [X22,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Set_Ovimage(X5,X17,X2)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),c_Set_Oinsert(X17)),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_distrib__inf__le,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X58))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X58))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_bij__betw__inv__into,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => c_Fun_Obij__betw(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),X22,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).

fof(fact_bij__betw__the__inv__into,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => c_Fun_Obij__betw(X17,X5,c_Fun_Othe__inv__into(X5,X17,X19,X2),X22,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).

fof(fact_inv__into__inv__into__eq,axiom,
    ! [X6,X67,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X67)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(c_Hilbert__Choice_Oinv__into(X17,X5,X67,c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2)),X6) = hAPP(X2,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).

fof(fact_SUP2__I,axiom,
    ! [X25,X17,X23,X21,X22,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => ( hBOOL(hAPP(hAPP(hAPP(X22,X6),X21),X23))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__I) ).

fof(fact_splitD_H,axiom,
    ! [X23,X21,X6,X37,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_fun(X25,tc_HOL_Obool)),X37),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X23))
     => hBOOL(hAPP(hAPP(hAPP(X37,X6),X21),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).

fof(conj_5,conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [X37,X110,X36,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X25),tc_HOL_Obool)),X36),X110)),X37) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X36),X37)),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X110),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X19),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Lattices_Osemilattice__inf__class_Oinf(X17)),X2)),X22),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X19),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Lattices_Osemilattice__sup__class_Osup(X17)),X2)),X22),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_setsum__Un__nat,axiom,
    ! [X2,X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_finite__Collect__not,axiom,
    ! [X30,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X30)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_bij__vimage__eq__inv__image,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X5,X17,X2),X19) = hAPP(c_Set_Oimage(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__vimage__eq__inv__image) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [X107,X119,X61,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X119))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X59))),X119))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [X92,X86,X103,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X103)),X86)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X103)),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X98)),X103)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_abs__setsum__abs,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Oabs__class_Oabs(X5)),X2)),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Oabs__class_Oabs(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_gt__half__sum,axiom,
    ! [X61,X60,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56)))),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_inv__into__injective,axiom,
    ! [X24,X20,X2,X19,X17,X5] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),X20) = hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),X24)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X20),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => ( hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
         => X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_list__all2__Cons,axiom,
    ! [X223,X24,X224,X20,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223))
    <=> ( hBOOL(hAPP(hAPP(X30,X20),X24))
        & c_List_Olist__all2(X5,X17,X30,X224,X223) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_q__neg__lemma,axiom,
    ! [X135,X136,X137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_zip__same,axiom,
    ! [X224,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X224),X224))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X224)))
        & X6 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [X223,X224,X24,X20,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [X223,X224,X24,X20,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))))
     => hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_List_Oset(X17),X223))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)))),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_odd__less__0,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)),X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(fact_INFI__fold__inf,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X19),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Lattices_Osemilattice__inf__class_Oinf(X17)),X2)),c_Orderings_Otop__class_Otop(X17)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X19),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,hAPP(hAPP(c_COMBB(X17,tc_fun(X17,X17),X5),c_Lattices_Osemilattice__sup__class_Osup(X17)),X2)),c_Orderings_Obot__class_Obot(X17)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_single__valuedD,axiom,
    ! [X26,X24,X20,X78,X17,X5] :
      ( c_Relation_Osingle__valued(X5,X17,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),X78))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X26)),X78))
         => X24 = X26 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).

fof(fact_Collect__disj__eq,axiom,
    ! [X29,X30,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),X30)),X29)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30)),hAPP(c_Set_OCollect(X5),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__conj__eq,axiom,
    ! [X29,X30,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X30)),X29)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30)),hAPP(c_Set_OCollect(X5),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_list__all2__dropI,axiom,
    ! [X89,X257,X252,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X252,X257)
     => c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Odrop(X5),X89),X252),hAPP(hAPP(c_List_Odrop(X17),X89),X257)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__takeI,axiom,
    ! [X89,X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
     => c_List_Olist__all2(X5,X17,X30,hAPP(hAPP(c_List_Otake(X5),X89),X224),hAPP(hAPP(c_List_Otake(X17),X89),X223)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),c_Transitive__Closure_Ortrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_antisymD,axiom,
    ! [X21,X6,X78,X5] :
      ( c_Relation_Oantisym(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X6)),X78))
         => X6 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymD) ).

fof(fact_antisym__def,axiom,
    ! [X78,X5] :
      ( c_Relation_Oantisym(X5,X78)
    <=> ! [X3,X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X78))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X3)),X78))
           => X3 = X38 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).

fof(fact_listsum__const__mult,axiom,
    ! [X224,X2,X23,X17,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),hAPP(c_Groups_Otimes__class_Otimes(X5),X23)),X2)),X224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_Image__mono,axiom,
    ! [X19,X67,X78,X157,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X157),X78))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X67),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X17,X157),X67)),hAPP(c_Relation_OImage(X5,X17,X78),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X37,X5,X24,X20,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X37))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Wellfounded_Omlex__prod(X5,X2,X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_swap__product,axiom,
    ! [X22,X19,X5,X17] : hAPP(c_Set_Oimage(tc_prod(X17,X5),tc_prod(X5,X17),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X5,tc_prod(X5,X17)),hAPP(c_COMBC(X5,X17,tc_prod(X5,X17)),c_Product__Type_OPair(X5,X17)))),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X22))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X22),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__product) ).

fof(fact_quotientI,axiom,
    ! [X78,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientI) ).

fof(fact_Image__singleton__iff,axiom,
    ! [X6,X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_OImage(X17,X5,X78),hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X6),X21)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_list__all2__rev,axiom,
    ! [X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,hAPP(c_List_Orev(X5),X224),hAPP(c_List_Orev(X17),X223))
    <=> c_List_Olist__all2(X5,X17,X30,X224,X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X49,X124] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X49),X124)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(X30,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X124))) )
             => hBOOL(hAPP(hAPP(X30,X49),X124)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_aset_I5_J,axiom,
    ! [X19,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X19))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X19))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X148),X63) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X15))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X64)),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I5_J) ).

fof(fact_div__mod__equality2,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61))),c_Divides_Odiv__class_Omod(X56,X60,X61))),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_list__all2__rev1,axiom,
    ! [X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,hAPP(c_List_Orev(X5),X224),X223)
    <=> c_List_Olist__all2(X5,X17,X30,X224,hAPP(c_List_Orev(X17),X223)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_lexord__Nil__left,axiom,
    ! [X78,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X24)),c_List_Olexord(X5,X78)))
    <=> ? [X49,X3] : X24 = hAPP(hAPP(c_List_Olist_OCons(X5),X49),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_image__vimage__subset,axiom,
    ! [X19,X2,X17,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Ovimage(X17,X5,X2),X19))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [X223,X224,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(c_List_Oset(X5),X223)))
       => ( c_List_Olinorder__class_Osorted(X17,hAPP(hAPP(c_List_Omap(X5,X17),X2),X224))
         => ( hBOOL(hAPP(c_List_Odistinct(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)))
           => ( c_List_Olinorder__class_Osorted(X17,hAPP(hAPP(c_List_Omap(X5,X17),X2),X223))
             => ( hBOOL(hAPP(c_List_Odistinct(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X223)))
               => ( hAPP(c_List_Oset(X5),X224) = hAPP(c_List_Oset(X5),X223)
                 => X224 = X223 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [X107,X61,X119,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X59))),X119))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_finite__quotient,axiom,
    ! [X78,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__quotient) ).

fof(fact_foldl__append,axiom,
    ! [X223,X224,X6,X2,X17,X5] : hAPP(c_List_Ofoldl(X5,X17,X2,X6),hAPP(hAPP(c_List_Oappend(X17),X224),X223)) = hAPP(c_List_Ofoldl(X5,X17,X2,hAPP(c_List_Ofoldl(X5,X17,X2,X6),X224)),X223),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__append) ).

fof(fact_rtrancl__converseI,axiom,
    ! [X78,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_zip__append1,axiom,
    ! [X237,X221,X222,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X237) = hAPP(hAPP(c_List_Oappend(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),hAPP(hAPP(c_List_Otake(X161),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X237))),hAPP(hAPP(c_List_Ozip(X56,X161),X221),hAPP(hAPP(c_List_Odrop(X161),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X237))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append1) ).

fof(fact_Diff__subset__conv,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Oimage(X5,X17,c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2)),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_bset_I5_J,axiom,
    ! [X15,X22,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ! [X3] :
          ( ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X148] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X22))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X63) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X15))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X64)),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I5_J) ).

fof(fact_bset_I6_J,axiom,
    ! [X15,X22,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ! [X3] :
          ( ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X148] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X22))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X63) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X15))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X64)),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I6_J) ).

fof(fact_setprod__Un__Int,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setsum__Un__Int,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_inf2I,axiom,
    ! [X17,X5,X22,X24,X20,X19] :
      ( hBOOL(hAPP(hAPP(X19,X20),X24))
     => ( hBOOL(hAPP(hAPP(X22,X20),X24))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).

fof(fact_vimage__subsetD,axiom,
    ! [X19,X22,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17,X5,X2),X22)),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X17,X5,X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_bset_I7_J,axiom,
    ! [X22,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X22))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X22))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X63) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X64))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I7_J) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [X135,X136,X137,X119,X107,X61] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X135),X137))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X137),X61))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X136)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_converse__INTER,axiom,
    ! [X78,X36,X25,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X36),X78)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X36),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),X25),c_Relation_Oconverse(X17,X5)),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__INTER) ).

fof(fact_converse__UNION,axiom,
    ! [X78,X36,X25,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X36),X78)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X36),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool),X25),c_Relation_Oconverse(X17,X5)),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__UNION) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [X26] :
      ~ ! [X3,X38] : X26 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Abs__Integ) ).

fof(fact_image__iff,axiom,
    ! [X19,X2,X17,X26,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
          & X26 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [X24,X20,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X78) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X78)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X208,X67,X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),X19) = X67
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X208),X67))
       => hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Oimage(X5,X17,c_Hilbert__Choice_Oinv__into(X17,X5,X19,X2)),X208)) = X208 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__iff,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
    <=> hAPP(c_Fun_Ocomp(X17,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__iff) ).

fof(fact_split__comp,axiom,
    ! [X20,X1,X2,X184,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),hAPP(c_Fun_Ocomp(X184,tc_fun(X25,X5),X17,X2),X1)),X20) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X17,X25),X20))),hAPP(c_Product__Type_Osnd(X17,X25),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp) ).

fof(fact_inv__inv__eq,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__inv__eq) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [X22,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X19),X22))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).

fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
    ! [X22,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X19),X22))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X41)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X41)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_list__all2__nthD,axiom,
    ! [X133,X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X133),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
       => hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X133)),hAPP(hAPP(c_List_Onth(X17),X223),X133))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__nthD2,axiom,
    ! [X133,X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X133),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)))
       => hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X133)),hAPP(hAPP(c_List_Onth(X17),X223),X133))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_vimage__subsetI,axiom,
    ! [X19,X22,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_converseD,axiom,
    ! [X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(c_Relation_Oconverse(X17,X5),X78)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X21),X6)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).

fof(fact_converse__iff,axiom,
    ! [X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(c_Relation_Oconverse(X17,X5),X78)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X21),X6)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).

fof(fact_finite__vimage__iff,axiom,
    ! [X18,X16,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X17,X16),X18)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X18)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimage__iff) ).

fof(fact_sup2I1,axiom,
    ! [X22,X17,X5,X24,X20,X19] :
      ( hBOOL(hAPP(hAPP(X19,X20),X24))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I1) ).

fof(fact_sup2I2,axiom,
    ! [X19,X17,X5,X24,X20,X22] :
      ( hBOOL(hAPP(hAPP(X22,X20),X24))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I2) ).

fof(fact_Int__mono,axiom,
    ! [X64,X22,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X64))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),X64))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).

fof(fact_Un__mono,axiom,
    ! [X64,X22,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X64))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X62),X64))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__mono) ).

fof(fact_Diff__mono,axiom,
    ! [X22,X64,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X64),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X62),X64))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).

fof(fact_hom__fold1__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X41)) = hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_setprod_Oreindex,axiom,
    ! [X1,X16,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( c_Fun_Oinj__on(X5,X5,X16,X19)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(c_Set_Oimage(X5,X5,X16),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(c_Fun_Ocomp(X5,X17,X5,X1),X16)),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_setsum_Oreindex,axiom,
    ! [X1,X16,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( c_Fun_Oinj__on(X5,X5,X16,X19)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(c_Set_Oimage(X5,X5,X16),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(c_Fun_Ocomp(X5,X17,X5,X1),X16)),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_acc_OaccI,axiom,
    ! [X78,X20,X5] :
      ( ! [X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X20)),X78))
         => hBOOL(hAPP(hAPP(c_member(X5),X38),c_Wellfounded_Oacc(X5,X78))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).

fof(fact_acc_Osimps,axiom,
    ! [X78,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X78)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X6)),X78))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [X78,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),X24)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X20) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [X75,X96,X224,X20,X5] : hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X96),X75) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X75),X224),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X20)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,tc_List_Olist(X5)),c_List_Olist__update(X5,X224)),X75)),X96),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_split__eta,axiom,
    ! [X2,X25,X17,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_prod(X5,X17)),tc_fun(X17,X25),X5),hAPP(c_COMBB(tc_prod(X5,X17),X25,X17),X2)),c_Product__Type_OPair(X5,X17))) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).

fof(fact_aset_I7_J,axiom,
    ! [X15,X19,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ! [X3] :
          ( ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X148] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X19))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X148),X63) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X64))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I7_J) ).

fof(fact_aset_I8_J,axiom,
    ! [X15,X19,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ! [X3] :
          ( ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X148] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X19))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X148),X63) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X64))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I8_J) ).

fof(fact_nth__take__lemma,axiom,
    ! [X221,X222,X56,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X221)))
       => ( ! [X88] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X93))
             => hAPP(hAPP(c_List_Onth(X56),X222),X88) = hAPP(hAPP(c_List_Onth(X56),X221),X88) )
         => hAPP(hAPP(c_List_Otake(X56),X93),X222) = hAPP(hAPP(c_List_Otake(X56),X93),X221) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_rel__pow__0__E,axiom,
    ! [X37,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X37)))
     => X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_exI__realizer,axiom,
    ! [X5,X17,X20,X24,X30] :
      ( hBOOL(hAPP(hAPP(X30,X24),X20))
     => hBOOL(hAPP(hAPP(X30,hAPP(c_Product__Type_Osnd(X17,X5),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X20),X24))),hAPP(c_Product__Type_Ofst(X17,X5),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X20),X24)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exI__realizer) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [X213,X25,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( c_Fun_Oinj__on(X17,X25,X213,hAPP(c_Set_Oimage(X5,X17,X2),X19))
      <=> c_Fun_Oinj__on(X5,X25,hAPP(c_Fun_Ocomp(X17,X25,X5,X213),X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__surj,axiom,
    ! [X1,X25,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X5,X25,X1),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X17,X25,hAPP(c_Fun_Ocomp(X5,X25,X17,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__surj) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [X93,X60,X61] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61))),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_setprod__reindex,axiom,
    ! [X16,X22,X2,X17,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( c_Fun_Oinj__on(X5,X17,X2,X22)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X25),X16),hAPP(c_Set_Oimage(X5,X17,X2),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X25),hAPP(c_Fun_Ocomp(X17,X25,X5,X16),X2)),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex) ).

fof(fact_setsum__reindex,axiom,
    ! [X16,X22,X2,X17,X5,X25] :
      ( class_Groups_Ocomm__monoid__add(X25)
     => ( c_Fun_Oinj__on(X5,X17,X2,X22)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X25),X16),hAPP(c_Set_Oimage(X5,X17,X2),X22)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X25),hAPP(c_Fun_Ocomp(X17,X25,X5,X16),X2)),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_lexn__length,axiom,
    ! [X89,X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),hAPP(c_List_Olexn(X5,X78),X89)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = X89
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223) = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).

fof(fact_converseI,axiom,
    ! [X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X21),X6)),hAPP(c_Relation_Oconverse(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).

fof(fact_rel__comp__distrib,axiom,
    ! [X110,X36,X37,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X37),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X25,X17),tc_HOL_Obool)),X36),X110)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X37),X36)),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X37),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_bot__empty__eq2,axiom,
    ! [X24,X20,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_transpose__transpose,axiom,
    ! [X224,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224)))
     => c_List_Otranspose(X5,c_List_Otranspose(X5,X224)) = c_List_OtakeWhile(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5))),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__transpose) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olattice__class_OInf__fin(X5,X41)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olattice__class_OSup__fin(X5,X41)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olinorder__class_OMin(X5,X41)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [X41,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X38] : hAPP(X16,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X16,X3)),hAPP(X16,X38))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
         => ( X41 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X16,c_Big__Operators_Olinorder__class_OMax(X5,X41)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,X16),X41)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_periodic__finite__ex,axiom,
    ! [X30,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
     => ( ! [X3,X97] :
            ( hBOOL(hAPP(X30,X3))
          <=> hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X27)))) )
       => ( ? [X77] : hBOOL(hAPP(X30,X77))
        <=> ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X27)))
              & hBOOL(hAPP(X30,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_listrel__Nil1,axiom,
    ! [X78,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X224)),c_List_Olistrel(X5,X78)))
     => X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_the__elem__def,axiom,
    ! [X40,X5] : c_Set_Othe__elem(X5,X40) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),hAPP(c_fequal,X40)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__def) ).

fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).

fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_union__comp__emptyL,axiom,
    ! [X22,X62,X19,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X19),X62) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X22),X62) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X19),X22)),X62) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_int__def,axiom,
    ! [X51] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X51),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__def) ).

fof(fact_distrib__sup__le,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X58)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_min__max_Odistrib__sup__le,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X58)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [X21,X6,X19,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21),X19)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [X21,X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X21),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_set__update__subsetI,axiom,
    ! [X96,X20,X19,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X20))),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [X133,X2,X89,X51,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X133))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X133)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_trans__O__subset,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X78),X78)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__O__subset) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [X62,X22,X19,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X22),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [X62,X22,X19,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X22),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [X62,X22,X19,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X22),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X62))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_card__inj__on__le,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),X22))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X17),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_fold__image__1,axiom,
    ! [X2,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
             => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X17) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X2),c_Groups_Oone__class_Oone(X17)),X36) = c_Groups_Oone__class_Oone(X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__1) ).

fof(fact_list__ball__nth,axiom,
    ! [X30,X224,X5,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => hBOOL(hAPP(X30,X3)) )
       => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ball__nth) ).

fof(fact_listrel__Nil2,axiom,
    ! [X78,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X78)))
     => X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_INF__commute,axiom,
    ! [X2,X22,X25,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),X19),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),X5,X17),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,X5),X22)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,X5),X22),hAPP(hAPP(c_COMBB(tc_fun(X17,X5),X5,X25),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),X19)),hAPP(c_COMBC(X17,X25,X5),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__commute) ).

fof(fact_SUP__commute,axiom,
    ! [X2,X22,X25,X19,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),X19),hAPP(hAPP(c_COMBB(tc_fun(X25,X5),X5,X17),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,X5),X22)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,X5),X22),hAPP(hAPP(c_COMBB(tc_fun(X17,X5),X5,X25),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),X19)),hAPP(c_COMBC(X17,X25,X5),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__commute) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [X24,X20,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
         => ( hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [X2,X19,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),X2),X19) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X2)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [X2,X19,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),X2),X19) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X2)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_listrel__eq__len,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel(X5,X78)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [X78,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X223)),c_List_Olistrel1(X5,X78)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_sym__def,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
    <=> ! [X3,X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X38)),X78))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X3)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__def) ).

fof(fact_symD,axiom,
    ! [X21,X6,X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X6)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symD) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [X15,X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)))
       => hAPP(c_List_Ofilter(X17,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X17),hAPP(c_Orderings_Oord__class_Oless(X5),X15)),X2)),X224) = c_List_OtakeWhile(X17,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X17),hAPP(c_Orderings_Oord__class_Oless(X5),X15)),X2),X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_Sigma__Union,axiom,
    ! [X22,X40,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X40)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X40),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X17,tc_HOL_Obool)),tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),c_Product__Type_OSigma(X5,X17)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Union) ).

fof(fact_bset_I4_J,axiom,
    ! [X22,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X22))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X22))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X63) ) )
           => ( X3 != X15
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X64) != X15 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I4_J) ).

fof(fact_aset_I4_J,axiom,
    ! [X19,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X19))
       => ! [X3] :
            ( ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
               => ! [X148] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X148),X19))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X148),X63) ) )
           => ( X3 != X15
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X64) != X15 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I4_J) ).

fof(fact_fold__def,axiom,
    ! [X19,X26,X2,X5,X17] : hAPP(hAPP(c_Finite__Set_Ofold(X17,X5,X2),X26),X19) = c_HOL_OThe(X5,c_Finite__Set_Ofold__graph(X17,X5,X2,X26,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__def) ).

fof(fact_split__paired__All,axiom,
    ! [X17,X5,X30] :
      ( ! [X77] : hBOOL(hAPP(X30,X77))
    <=> ! [X49,X124] : hBOOL(hAPP(X30,hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).

fof(fact_curryI,axiom,
    ! [X21,X6,X17,X5,X2] :
      ( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)))
     => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X17,tc_HOL_Obool,X2),X6),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_inj__on__Inter,axiom,
    ! [X2,X17,X5,X36] :
      ( X36 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [X50] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X50),X36))
           => c_Fun_Oinj__on(X5,X17,X2,X50) )
       => c_Fun_Oinj__on(X5,X17,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_Bex__set__replicate,axiom,
    ! [X30,X6,X89,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X6))))
          & hBOOL(hAPP(X30,X3)) )
    <=> ( hBOOL(hAPP(X30,X6))
        & X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bex__set__replicate) ).

fof(fact_card__UNIV__bool,axiom,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).

fof(fact_Nitpick_Orefl_H__def,axiom,
    ! [X78,X5] :
      ( c_Nitpick_Orefl_H(X5,X78)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_incr__mult__lemma,axiom,
    ! [X90,X30,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
     => ( ! [X3] :
            ( hBOOL(hAPP(X30,X3))
           => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X27))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X3] :
              ( hBOOL(hAPP(X30,X3))
             => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X27)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_decr__mult__lemma,axiom,
    ! [X90,X30,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
     => ( ! [X3] :
            ( hBOOL(hAPP(X30,X3))
           => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X27))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X3] :
              ( hBOOL(hAPP(X30,X3))
             => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X27)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_measures__less,axiom,
    ! [X263,X5,X24,X20,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X263)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).

fof(fact_nat__1__add__1,axiom,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_folding__idem_Oidem__left__comp,axiom,
    ! [X1,X20,X25,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),X1)) = hAPP(c_Fun_Ocomp(X17,X17,X25,hAPP(X2,X20)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_mem__splitI,axiom,
    ! [X25,X17,X21,X6,X23,X26,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(X23,X6),X21)))
     => hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,tc_fun(X5,tc_HOL_Obool)),X23),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).

fof(fact_Ball__set__replicate,axiom,
    ! [X30,X6,X89,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X6))))
         => hBOOL(hAPP(X30,X3)) )
    <=> ( hBOOL(hAPP(X30,X6))
        | X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_listrel__Cons,axiom,
    ! [X224,X20,X78,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X78)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = c_List_Oset__Cons(X5,hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X78)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),X224),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons) ).

fof(fact_UN__le__add__shift,axiom,
    ! [X90,X76,X89,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool),tc_Nat_Onat),X76),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X90,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X90))),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__le__add__shift) ).

fof(fact_numeral__2__eq__2,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).

fof(fact_semiring__norm_I115_J,axiom,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_bij__image__Compl__eq,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__Compl__eq) ).

fof(fact_override__on__apply__in,axiom,
    ! [X1,X2,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X1,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).

fof(fact_lexord__append__rightI,axiom,
    ! [X78,X20,X5,X24] :
      ( ? [X124,X150] : X24 = hAPP(hAPP(c_List_Olist_OCons(X5),X124),X150)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),hAPP(hAPP(c_List_Oappend(X5),X20),X24))),c_List_Olexord(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [X5,X223,X224] :
      ( X224 = X223
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X224),X223))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_fequal),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_nat__gcd_Opinduct,axiom,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X187),X34)))
     => ( ! [X3,X38] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X38)))
           => ( ( X38 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(X30,X38),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X38))) )
             => hBOOL(hAPP(hAPP(X30,X3),X38)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X19,X22,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X22)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_inj__on__image__Int,axiom,
    ! [X22,X19,X62,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X62)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
         => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [X22,X19,X62,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X62)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
         => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_filter__in__sublist,axiom,
    ! [X146,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X146)))),X224) = c_List_Osublist(X5,X224,X146) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_list__ex1__iff__raw,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex1(X5,X30,X224)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(X30,X3))
          & ! [X38] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X38),hAPP(c_List_Oset(X5),X224)))
                & hBOOL(hAPP(X30,X38)) )
             => X38 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).

fof(fact_list__ex1__iff,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex1(X5,X30,X224)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(X30,X3))
          & ! [X38] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X38),hAPP(c_List_Oset(X5),X224)))
                & hBOOL(hAPP(X30,X38)) )
             => X38 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X5,X2),X19)),X19))
       => ( c_Fun_Oinj__on(X5,X5,X2,X19)
         => hAPP(c_Set_Oimage(X5,X5,X2),X19) = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [X224,X17,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_List_Oset(X17),X224))))
       => c_List_Olinorder__class_Oinsort__insert__key(X17,X5,X2,X20,X224) = X224 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X20,X224)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort__insert) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [X157,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X157))
     => ( c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X157)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X78)),c_List_Olistrel(X5,X157))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [X1,X19,X18,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X17,X2,X26,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(hAPP(X18,X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1),X26),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19) = hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_vimage__compose,axiom,
    ! [X20,X2,X1,X25,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,hAPP(c_Fun_Ocomp(X25,X17,X5,X1),X2)),X20) = hAPP(c_Set_Ovimage(X5,X25,X2),hAPP(c_Set_Ovimage(X25,X17,X1),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__compose) ).

fof(fact_image__compose,axiom,
    ! [X78,X1,X2,X25,X5,X17] : hAPP(c_Set_Oimage(X17,X5,hAPP(c_Fun_Ocomp(X25,X5,X17,X2),X1)),X78) = hAPP(c_Set_Oimage(X25,X5,X2),hAPP(c_Set_Oimage(X17,X25,X1),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__compose) ).

fof(fact_rtrancl__power,axiom,
    ! [X37,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Ortrancl(X5,X37)))
    <=> ? [X130] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X130),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__power) ).

fof(fact_scomp__unfold,axiom,
    ! [X20,X1,X2,X5,X184,X25,X17] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X17,X25,X184,X5),X2),X1),X20) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X25,X184),hAPP(X2,X20))),hAPP(c_Product__Type_Osnd(X25,X184),hAPP(X2,X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__unfold) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [X24,X20,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
      <=> ( hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
          & hBOOL(hAPP(hAPP(c_member(X5),X24),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24))))
      <=> ( X20 != c_Groups_Ozero__class_Ozero(X5)
          | X24 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_rtrancl__is__UN__rel__pow,axiom,
    ! [X37,X5] : c_Transitive__Closure_Ortrancl(X5,X37) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool)),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_takeWhile__append2,axiom,
    ! [X223,X30,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) )
     => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),X224),c_List_OtakeWhile(X5,X30,X223)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_inj__on__imageI,axiom,
    ! [X19,X2,X1,X25,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,hAPP(c_Fun_Ocomp(X25,X17,X5,X1),X2),X19)
     => c_Fun_Oinj__on(X25,X17,X1,hAPP(c_Set_Oimage(X5,X25,X2),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [X2,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
            & hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X63),X19))
               => ( X3 != X63
                 => hAPP(X2,X63) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).

fof(fact_sorted__insort__insert,axiom,
    ! [X20,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X224)
       => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X20,X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_abs__mult__less,axiom,
    ! [X73,X61,X59,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [X20,X26,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_takeWhile__map,axiom,
    ! [X224,X2,X17,X30,X5] : c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_OtakeWhile(X17,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X17,X30),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__map) ).

fof(fact_fun__upd__def,axiom,
    ! [X21,X2,X17,X5,X6,X20] :
      ( ( X20 = X6
       => hAPP(c_Fun_Ofun__upd(X5,X17,X2,X6,X21),X20) = X21 )
      & ( X20 != X6
       => hAPP(c_Fun_Ofun__upd(X5,X17,X2,X6,X21),X20) = hAPP(X2,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).

fof(fact_fun__upd__other,axiom,
    ! [X24,X2,X17,X5,X20,X26] :
      ( X26 != X20
     => hAPP(c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X26) = hAPP(X2,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__apply,axiom,
    ! [X24,X2,X17,X5,X20,X26] :
      ( ( X26 = X20
       => hAPP(c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X26) = X24 )
      & ( X26 != X20
       => hAPP(c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X26) = hAPP(X2,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [X2,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
            & hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X63),X19))
               => ( X3 != X63
                 => hAPP(X2,X63) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X78)),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_fun__upd__same,axiom,
    ! [X24,X20,X2,X5,X17] : hAPP(c_Fun_Ofun__upd(X17,X5,X2,X20,X24),X20) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).

fof(fact_comp__inj__on,axiom,
    ! [X1,X25,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( c_Fun_Oinj__on(X17,X25,X1,hAPP(c_Set_Oimage(X5,X17,X2),X19))
       => c_Fun_Oinj__on(X5,X25,hAPP(c_Fun_Ocomp(X17,X25,X5,X1),X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [X223,X224,X20,X17,X5] : c_Enum_Oproduct(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224),X223) = hAPP(hAPP(c_List_Oappend(tc_prod(X5,X17)),hAPP(hAPP(c_List_Omap(X17,tc_prod(X5,X17)),hAPP(c_Product__Type_OPair(X5,X17),X20)),X223)),c_Enum_Oproduct(X5,X17,X224,X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_elem__le__sum,axiom,
    ! [X231,X89] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X89),hAPP(c_List_Oset(tc_Nat_Onat),X231)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X231))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__sum) ).

fof(fact_rev__ImageI,axiom,
    ! [X78,X21,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78))
       => hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(c_Relation_OImage(X5,X17,X78),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).

fof(fact_map__map,axiom,
    ! [X224,X1,X25,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Omap(X25,X17),X1),X224)) = hAPP(hAPP(c_List_Omap(X25,X5),hAPP(c_Fun_Ocomp(X17,X5,X25,X2),X1)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [X226,X1,X25,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Omap(X25,X17),X1),X226)) = hAPP(hAPP(c_List_Omap(X25,X5),hAPP(c_Fun_Ocomp(X17,X5,X25,X2),X1)),X226),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_take__Cons,axiom,
    ! [X224,X20,X89,X5] : hAPP(hAPP(c_List_Otake(X5),X89),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X20)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otake(X5)),X224)),X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons) ).

fof(fact_Un__Image,axiom,
    ! [X19,X36,X37,X5,X17] : hAPP(c_Relation_OImage(X17,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X37),X36)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X37),X19)),hAPP(c_Relation_OImage(X17,X5,X36),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Image) ).

fof(fact_iterate_Osimps,axiom,
    ! [X20,X2,X5,X17,X90] :
      ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X17,X5,X90,X2),X20) = hAPP(c_Product__Type_OPair(X17,X5),X20) )
      & ( X90 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X17,X5,X90,X2),X20) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X17,X5,tc_prod(X17,X5)),hAPP(X2,X20)),c_Random_Oiterate(X17,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X90),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iterate_Osimps) ).

fof(fact_equiv__class__eq,axiom,
    ! [X21,X6,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [X22,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
        & hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD2,axiom,
    ! [X22,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
     => hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).

fof(fact_listrel__mono,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X78)),c_List_Olistrel(X5,X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel1__mono,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X78)),c_List_Olistrel1(X5,X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).

fof(fact_bij__def,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
    <=> ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
        & hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__def) ).

fof(fact_bij__is__inj,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__is__inj) ).

fof(fact_scomp__def,axiom,
    ! [X20,X1,X2,X5,X184,X25,X17] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X17,X25,X184,X5),X2),X1),X20) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X25,X184,X5),X1),hAPP(X2,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__def) ).

fof(fact_scomp__apply,axiom,
    ! [X20,X1,X2,X5,X184,X25,X17] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X17,X25,X184,X5),X2),X1),X20) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X25,X184,X5),X1),hAPP(X2,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__apply) ).

fof(fact_Un__least,axiom,
    ! [X22,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__least) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [X22,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(X2,hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [X24,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => hAPP(X2,hAPP(c_Fun_Othe__inv__into(X5,X17,X19,X2),X24)) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool))),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool))),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool))),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool))),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_inj__on__def,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X63),X19))
             => ( hAPP(X2,X3) = hAPP(X2,X63)
               => X3 = X63 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_rtrancl__subset,axiom,
    ! [X36,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),c_Transitive__Closure_Ortrancl(X5,X37)))
       => c_Transitive__Closure_Ortrancl(X5,X36) = c_Transitive__Closure_Ortrancl(X5,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_eq__equiv__class,axiom,
    ! [X19,X21,X6,X78,X5] :
      ( hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(X5,X19,X78)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_SigmaD1,axiom,
    ! [X22,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).

fof(fact_setprod__zero__iff,axiom,
    ! [X2,X19,X5,X17] :
      ( ( class_Rings_Ocomm__semiring__1(X17)
        & class_Rings_Ono__zero__divisors(X17) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) = c_Groups_Ozero__class_Ozero(X17)
        <=> ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_card__image__le,axiom,
    ! [X2,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19))),hAPP(c_Finite__Set_Ocard(X5),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [X22,X19,X5,X17] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => hAPP(X22,X3) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [X22,X19,X5,X17] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => hAPP(X22,X3) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [X22,X19,X17,X5] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => hAPP(X22,X3) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [X22,X19,X17,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X19))
         => hAPP(X22,X3) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_setsum__SucD,axiom,
    ! [X89,X19,X2,X5] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) = hAPP(c_Nat_OSuc,X89)
     => ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__SucD) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),c_Big__Operators_Olattice__class_OInf__fin(X5,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)),c_Big__Operators_Olattice__class_OSup__fin(X5,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X19)),c_Big__Operators_Olinorder__class_OMax(X5,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),c_Big__Operators_Olinorder__class_OMin(X5,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_sorted_Osimps,axiom,
    ! [X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X6)
      <=> ( X6 = c_List_Olist_ONil(X5)
          | ? [X229,X3] :
              ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X229)
              & ! [X63] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X63),hAPP(c_List_Oset(X5),X229)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X63)) )
              & c_List_Olinorder__class_Osorted(X5,X229) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [X24,X20,X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X17),X24),X19))
         => ( hAPP(X202,X20) = hAPP(X202,X24)
          <=> X20 = X24 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_acyclicP__converse,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Predicate_Oconversep(X5,X5,X78))))
    <=> c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_Field__insert,axiom,
    ! [X78,X21,X6,X5] : hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OField(X5),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__insert) ).

fof(fact_start__le__sum,axiom,
    ! [X231,X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X231))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_start__le__sum) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [X21,X6,X279,X123,X17,X5] : c_Nitpick_Opair__box_Opair__box__size(X5,X17,X123,X279,c_Nitpick_Opair__box_OPairBox(X5,X17,X6,X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X123,X6)),hAPP(X279,X21))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).

fof(fact_card__partition,axiom,
    ! [X90,X62,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X62))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62)))
       => ( ! [X154] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X154),X62))
             => hAPP(c_Finite__Set_Ocard(X5),X154) = X90 )
         => ( ! [X155] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X155),X62))
               => ! [X156] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X156),X62))
                   => ( X155 != X156
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X155),X156) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),X62)) = hAPP(c_Finite__Set_Ocard(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__partition) ).

fof(fact_bij__is__surj,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__is__surj) ).

fof(fact_sorted__same,axiom,
    ! [X224,X1,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),hAPP(X1,X224))),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__same) ).

fof(fact_inj__comp,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(X25,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool)))
       => c_Fun_Oinj__on(X25,X17,hAPP(c_Fun_Ocomp(X5,X17,X25,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__comp) ).

fof(fact_set__update__subset__insert,axiom,
    ! [X20,X96,X224,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X20))),hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [X19,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X19) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [X19,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [X21,X2,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Set_Oinsert(X17),X21),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))))
    <=> hAPP(X2,X6) = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_inj__on__imageI2,axiom,
    ! [X19,X2,X213,X25,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,hAPP(c_Fun_Ocomp(X25,X17,X5,X213),X2),X19)
     => c_Fun_Oinj__on(X5,X25,X2,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_finite__Diff__insert,axiom,
    ! [X22,X6,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_insert__def,axiom,
    ! [X22,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X22) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__def) ).

fof(fact_eq__add__iff1,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),X79)),X23) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [X27,X21,X23,X79,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X79)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X79)),X27)
      <=> X23 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X6)),X79)),X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_Image__INT__eq,axiom,
    ! [X22,X25,X19,X78,X17,X5] :
      ( c_Relation_Osingle__valued(X5,X17,hAPP(c_Relation_Oconverse(X17,X5),X78))
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X25,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(X17,X5,X78),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Relation_OImage(X17,X5,X78)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_partition__filter2,axiom,
    ! [X224,X30,X5] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X30,X224)) = hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X30)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter2) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X36,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X19))
       => hAPP(c_Set_Oimage(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2)),hAPP(c_Set_Oimage(X5,X17,X2),X36)) = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_vimage__mono,axiom,
    ! [X2,X17,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17,X5,X2),X19)),hAPP(c_Set_Ovimage(X17,X5,X2),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__mono) ).

fof(fact_image__mono,axiom,
    ! [X2,X17,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_UN__equiv__class,axiom,
    ! [X6,X2,X17,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X17,tc_HOL_Obool),X78,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X2) = hAPP(X2,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_comp__cong,axiom,
    ! [X183,X184,X25,X5,X17,X211,X212,X213,X20,X1,X2] :
      ( hAPP(X2,hAPP(X1,X20)) = hAPP(X213,hAPP(X212,X211))
     => hAPP(hAPP(c_Fun_Ocomp(X17,X5,X25,X2),X1),X20) = hAPP(hAPP(c_Fun_Ocomp(X184,X5,X183,X213),X212),X211) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).

fof(fact_inv__o__cancel,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X17,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__o__cancel) ).

fof(fact_bij__betw__imp__surj,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__imp__surj) ).

fof(fact_folding__one_Oremove,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X18,X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X18,X19) = hAPP(hAPP(X2,X20),hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_card_Ounion__inter,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__Int) ).

fof(fact_wf__same__fst,axiom,
    ! [X5,X37,X17,X30] :
      ( ! [X3] :
          ( hBOOL(hAPP(X30,X3))
         => c_Wellfounded_Owf(X17,hAPP(X37,X3)) )
     => c_Wellfounded_Owf(tc_prod(X5,X17),c_Recdef_Osame__fst(X5,X17,X30,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).

fof(fact_in__rel__def,axiom,
    ! [X24,X20,X37,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X17,X37),X20),X24))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_bij__betw__imp__inj__on,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => c_Fun_Oinj__on(X5,X17,X2,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).

fof(fact_bij__betw__def,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
    <=> ( c_Fun_Oinj__on(X5,X17,X2,X19)
        & hAPP(c_Set_Oimage(X5,X17,X2),X19) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__def) ).

fof(fact_Image__closed__trancl,axiom,
    ! [X40,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),X40)),X40))
     => hAPP(c_Relation_OImage(X5,X5,c_Transitive__Closure_Ortrancl(X5,X78)),X40) = X40 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_acc__downwards__aux,axiom,
    ! [X78,X6,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X6)),c_Transitive__Closure_Ortrancl(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),c_Wellfounded_Oacc(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_acc__downwards,axiom,
    ! [X21,X78,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X21),X6)),c_Transitive__Closure_Ortrancl(X5,X78)))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),c_Wellfounded_Oacc(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = X19 )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = X19 )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [X22,X19,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = X19 )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Min_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,X19) = X20 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oremove) ).

fof(fact_type__definition_ORep,axiom,
    ! [X20,X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X203,X20)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [X24,X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X24),X19))
       => hAPP(X203,hAPP(X202,X24)) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_sorted__insort__key,axiom,
    ! [X224,X20,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X224)))
      <=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_mod__induct__0,axiom,
    ! [X96,X30,X133] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X133))
         => ( hBOOL(hAPP(X30,X88))
           => hBOOL(hAPP(X30,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X88),X133))) ) )
     => ( hBOOL(hAPP(X30,X96))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X133))
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__induct__0) ).

fof(fact_bijI,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))
       => c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bijI) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [X59,X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X61),X59))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X59))),X59)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [X59,X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X61),X59))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X61,X59))),X59)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [X89,X51,X102,X96,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X96))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X96),X95)),X102)),X51) = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [X89,X51,X102,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X95))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X102)),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X102)),X89)
      <=> X51 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X96)),X102)),X89) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [X62,X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X62),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [X22,X19,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19)),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [X19,X111,X17,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [X22,X62,X17,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [X22,X62,X17,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [X19,X111,X17,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X111),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [X22,X62,X17,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_union__comp__emptyR,axiom,
    ! [X62,X22,X19,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X19),X62) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X22),X62)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_BIJ,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
       => ( ? [X68] : c_Fun_Obij__betw(X5,X17,X68,X19,X22)
        <=> hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Finite__Set_Ocard(X17),X22) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BIJ) ).

fof(fact_type__definition_ORep__range,axiom,
    ! [X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => hAPP(c_Set_Oimage(X5,X17,X203),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_singleton__quotient,axiom,
    ! [X78,X20,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X78) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__quotient) ).

fof(fact_congruentD,axiom,
    ! [X26,X24,X2,X78,X17,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X17,X78,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X26)),X78))
       => hAPP(X2,X24) = hAPP(X2,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),c_Transitive__Closure_Ortrancl(X5,X146)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X78)),c_Transitive__Closure_Ortrancl(X5,X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [X37,X89,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Ortrancl(X5,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_acc__downward,axiom,
    ! [X6,X78,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Wellfounded_Oacc(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),X78))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X78))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = X20 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => hAPP(c_Set_Oimage(X17,X5,X202),X19) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_inj__on__mapI,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),X19)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X17),hAPP(c_List_Omap(X5,X17),X2),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_inv__image__comp,axiom,
    ! [X40,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X17,X2),X40)) = X40 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_image__inv__f__f,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_update__zip,axiom,
    ! [X233,X98,X221,X222,X161,X56] : hAPP(hAPP(c_List_Olist__update(tc_prod(X56,X161),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)),X98),X233) = hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),hAPP(c_Product__Type_Ofst(X56,X161),X233))),hAPP(hAPP(c_List_Olist__update(X161,X221),X98),hAPP(c_Product__Type_Osnd(X56,X161),X233))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__zip) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [X90] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X90)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [X90] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X90)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_O__assoc,axiom,
    ! [X110,X36,X37,X184,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),hAPP(hAPP(c_Relation_Orel__comp(X5,X184,X25),X37),X36)),X110) = hAPP(hAPP(c_Relation_Orel__comp(X5,X184,X17),X37),hAPP(hAPP(c_Relation_Orel__comp(X184,X25,X17),X36),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).

fof(fact_setprod_Oremove,axiom,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_setsum__diff1_H,axiom,
    ! [X2,X6,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_setsum_Oremove,axiom,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_Pow__INT__eq,axiom,
    ! [X22,X19,X17,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X17),c_Set_OPow(X5)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_q__pos__lemma,axiom,
    ! [X135,X136,X137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X136)),X135)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X135),X137))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X136)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_bij__betw__finite,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__finite) ).

fof(fact_bij__betw__empty1,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X19)
     => X19 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).

fof(fact_bij__betw__empty2,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))
     => X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [X76,X89,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89)),X76) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X89)),X76)),hAPP(X76,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__le__eq__Un0) ).

fof(fact_card__Diff__subset__Int,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__subset__Int) ).

fof(fact_pair__leq__def,axiom,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leq__def) ).

fof(fact_INT__Un,axiom,
    ! [X76,X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)),X76) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X76)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X22),X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Un) ).

fof(fact_UN__Un,axiom,
    ! [X76,X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)),X76) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X76)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X22),X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_INT__lower,axiom,
    ! [X22,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22)),hAPP(X22,X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__lower) ).

fof(fact_rtrancl__mono,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X78)),c_Transitive__Closure_Ortrancl(X5,X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_Image__UN,axiom,
    ! [X22,X19,X25,X78,X5,X17] : hAPP(c_Relation_OImage(X17,X5,X78),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Relation_OImage(X17,X5,X78)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__UN) ).

fof(fact_vimage__INT,axiom,
    ! [X22,X19,X25,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Set_Ovimage(X5,X17,X2)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__INT) ).

fof(fact_vimage__UN,axiom,
    ! [X22,X19,X25,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Set_Ovimage(X5,X17,X2)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__UN) ).

fof(fact_image__UN,axiom,
    ! [X22,X19,X25,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X25),c_Set_Oimage(X17,X5,X2)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__UN) ).

fof(fact_add__frac__eq,axiom,
    ! [X126,X55,X58,X57,X56] :
      ( class_Fields_Ofield(X56)
     => ( X57 != c_Groups_Ozero__class_Ozero(X56)
       => ( X58 != c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X126),X58)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X126),X57))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

fof(fact_diff__frac__eq,axiom,
    ! [X126,X55,X58,X57,X56] :
      ( class_Fields_Ofield(X56)
     => ( X57 != c_Groups_Ozero__class_Ozero(X56)
       => ( X58 != c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X126),X58)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X126),X57))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_Compl__eq,axiom,
    ! [X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq) ).

fof(fact_list__all2__lengthD,axiom,
    ! [X223,X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,X223)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_split__pos__lemma,axiom,
    ! [X89,X30,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X89),X90)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X89,X90)))
      <=> ! [X88,X120] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X90))
              & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
           => hBOOL(hAPP(hAPP(X30,X88),X120)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X19,X2,X17,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
     => c_Fun_Oinj__on(X5,X17,c_Hilbert__Choice_Oinv__into(X17,X5,X19,X2),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_UN__o,axiom,
    ! [X2,X1,X25,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Fun_Ocomp(X25,tc_fun(X5,tc_HOL_Obool),X17,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X25,X2),X19)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__o) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [X20,X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [X20,X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_f__inv__into__f,axiom,
    ! [X19,X2,X17,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X5,X19,X2),X24)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_split__neg__lemma,axiom,
    ! [X89,X30,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X89),X90)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X89,X90)))
      <=> ! [X88,X120] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X120))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
           => hBOOL(hAPP(hAPP(X30,X88),X120)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zip__same__conv__map,axiom,
    ! [X224,X5] : hAPP(hAPP(c_List_Ozip(X5,X5),X224),X224) = hAPP(hAPP(c_List_Omap(X5,tc_prod(X5,X5)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [X22,X19] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
    ! [X22,X19] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_surj__iff,axiom,
    ! [X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> hAPP(c_Fun_Ocomp(X17,X5,X5,X2),c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2)) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff) ).

fof(fact_power__Suc__less,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Oone__class_Oone(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [X24,X20,X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => ( hAPP(X203,X20) = hAPP(X203,X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [X22,X19,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))))
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [X22,X19,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))))
     => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [X20,X19,X202,X203,X17,X5] :
      ( c_Typedef_Otype__definition(X5,X17,X203,X202,X19)
     => hAPP(X202,hAPP(X203,X20)) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_bij__betw__same__card,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Obij__betw(X5,X17,X2,X19,X22)
     => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Finite__Set_Ocard(X17),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61))),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61))),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X61),X60)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_vimage__insert,axiom,
    ! [X22,X6,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Set_Oinsert(X17),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__insert) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [X24,X20,X2,X17,X5] :
      ( c_Fun_Ofun__upd(X5,X17,X2,X20,X24) = X2
    <=> hAPP(X2,X20) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_list__all2__Nil,axiom,
    ! [X223,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,c_List_Olist_ONil(X5),X223)
    <=> X223 = c_List_Olist_ONil(X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_list__all2__Nil2,axiom,
    ! [X224,X30,X17,X5] :
      ( c_List_Olist__all2(X5,X17,X30,X224,c_List_Olist_ONil(X17))
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_bij__betw__id__iff,axiom,
    ! [X22,X19,X5] :
      ( c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X19,X22)
    <=> X19 = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).

fof(fact_DomainI,axiom,
    ! [X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).

fof(fact_RangeI,axiom,
    ! [X78,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78))
     => hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(c_Relation_ORange(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [X224,X5,X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),X51))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X51),X224))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X89),X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [X224,X5,X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X51),X224))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X89),X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_list__all2__eq,axiom,
    ! [X5,X223,X224] :
      ( X224 = X223
    <=> c_List_Olist__all2(X5,X5,c_fequal,X224,X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__eq) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [X61,X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),hAPP(c_Nat_OSuc,X92))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [X21,X6,X19,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X21)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X21),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [X21,X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X21),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_Domain__mono,axiom,
    ! [X146,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X78),X146))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X17),X78)),hAPP(c_Relation_ODomain(X5,X17),X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X17,X5,c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_less__half__sum,axiom,
    ! [X61,X60,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_combine__common__factor,axiom,
    ! [X59,X61,X85,X60,X56] :
      ( class_Rings_Osemiring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X85)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X85)),X59)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X85)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId__on(X5,X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_sort__foldl__insort,axiom,
    ! [X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X224) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5))),c_List_Olist_ONil(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_Range__Collect__split,axiom,
    ! [X30,X5,X17] : hAPP(c_Relation_ORange(X17,X5),hAPP(c_Set_OCollect(tc_prod(X17,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X17,X5,tc_HOL_Obool),X30))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X17)),hAPP(c_COMBC(X17,X5,tc_HOL_Obool),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_inj__on__imp__bij__betw,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => c_Fun_Obij__betw(X5,X17,X2,X19,hAPP(c_Set_Oimage(X5,X17,X2),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imp__bij__betw) ).

fof(fact_equiv__type,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__type) ).

fof(fact_map__comp__map,axiom,
    ! [X1,X2,X5,X17,X25] : hAPP(c_Fun_Ocomp(tc_List_Olist(X25),tc_List_Olist(X17),tc_List_Olist(X5),hAPP(c_List_Omap(X25,X17),X2)),hAPP(c_List_Omap(X5,X25),X1)) = hAPP(c_List_Omap(X5,X17),hAPP(c_Fun_Ocomp(X25,X17,X5,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__map) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [X1,X2,X5,X17,X25] : hAPP(c_Fun_Ocomp(tc_List_Olist(X25),tc_List_Olist(X17),tc_List_Olist(X5),hAPP(c_List_Omap(X25,X17),X2)),hAPP(c_List_Omap(X5,X25),X1)) = hAPP(c_List_Omap(X5,X17),hAPP(c_Fun_Ocomp(X25,X17,X5,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_refl__onD1,axiom,
    ! [X24,X20,X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
       => hBOOL(hAPP(hAPP(c_member(X5),X20),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD2,axiom,
    ! [X24,X20,X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),X78))
       => hBOOL(hAPP(hAPP(c_member(X5),X24),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).

fof(fact_listrel_ONil,axiom,
    ! [X78,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).

fof(fact_Int__Union2,axiom,
    ! [X19,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22)),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union2) ).

fof(fact_Id__on__iff,axiom,
    ! [X19,X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Relation_OId__on(X5,X19)))
    <=> ( X20 = X24
        & hBOOL(hAPP(hAPP(c_member(X5),X20),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X22,X19,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X22,X19,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X22,X19,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_SigmaI,axiom,
    ! [X22,X21,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).

fof(fact_foldl__assoc,axiom,
    ! [X228,X24,X20,X5] :
      ( class_Groups_Osemigroup__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X24)),X228) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X24),X228)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__assoc) ).

fof(fact_rel__pow__0__I,axiom,
    ! [X37,X20,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X20)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X37))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_quotient__disj,axiom,
    ! [X43,X40,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X43),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
         => ( X40 = X43
            | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X40),X43) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__disj) ).

fof(fact_pick__same,axiom,
    ! [X224,X5,X106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => hAPP(c_Random_Opick(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X224)),hAPP(c_Code__Numeral_Oof__nat,X106)) = hAPP(hAPP(c_List_Onth(X5),X224),X106) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__same) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X90,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X19),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X19)))))
     => X19 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [X102,X106,X105,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OgreaterThanLessThan(X5,X105,X106,X102)))
    <=> ( hBOOL(hAPP(hAPP(X105,X106),X96))
        & hBOOL(hAPP(hAPP(X105,X96),X102)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [X102,X106,X104,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OatLeastAtMost(X5,X104,X106,X102)))
    <=> ( hBOOL(hAPP(hAPP(X104,X106),X96))
        & hBOOL(hAPP(hAPP(X104,X96),X102)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [X19,X5] : c_List_Oset__Cons(X5,X19,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X5,tc_List_Olist(X5),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_INT__insert__distrib,axiom,
    ! [X22,X6,X17,X19,X102,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X102),X19))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X17),X6)),X22)) = hAPP(hAPP(c_Set_Oinsert(X17),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_UN__insert__distrib,axiom,
    ! [X22,X6,X17,X19,X102,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X102),X19))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X17),X6)),X22)) = hAPP(hAPP(c_Set_Oinsert(X17),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
    <=> ? [X130,X68] : X19 = hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X68),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X130))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [X89,X2,X5,X19] :
      ( X19 = hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X89)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_take__hd__drop,axiom,
    ! [X222,X56,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X92),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222))),c_List_Olist_ONil(X56))) = hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_OSuc,X92)),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__hd__drop) ).

fof(fact_Diff__insert2,axiom,
    ! [X22,X6,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [X78,X224,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),X224)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_Inter__subset,axiom,
    ! [X22,X19,X5] :
      ( ! [X152] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X152),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X152),X22)) )
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__subset) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [X61,X60,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X59)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61),X59))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_Int__greatest,axiom,
    ! [X22,X19,X62,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X62),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X62),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).

fof(fact_max__Suc2,axiom,
    ! [X89,X51] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X89),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X89)),X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc2) ).

fof(fact_rel__pow__add,axiom,
    ! [X37,X89,X51,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89)),X37) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X51),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__add) ).

fof(fact_Union__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__mono) ).

fof(fact_Inter__anti__mono,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X22),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_min__Suc2,axiom,
    ! [X89,X51] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X89)),X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc2) ).

fof(fact_card_Oremove,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oremove) ).

fof(fact_zip__update,axiom,
    ! [X57,X221,X55,X98,X222,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),hAPP(hAPP(c_List_Olist__update(X161,X221),X98),X57)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X56,X161),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)),X98),hAPP(hAPP(c_Product__Type_OPair(X56,X161),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__update) ).

fof(fact_image__Int,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int) ).

fof(fact_image__set__diff,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X17,X2),X19)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__set__diff) ).

fof(fact_the__inv__into__onto,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => hAPP(c_Set_Oimage(X17,X5,c_Fun_Othe__inv__into(X5,X17,X19,X2)),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_pair__box_Orecs,axiom,
    ! [X21,X6,X28,X5,X25,X17] : c_Nitpick_Opair__box_Opair__box__rec(X17,X25,X5,X28,c_Nitpick_Opair__box_OPairBox(X17,X25,X6,X21)) = hAPP(hAPP(X28,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [X21,X6,X28,X5,X25,X17] : c_Nitpick_Opair__box_Opair__box__case(X17,X25,X5,X28,c_Nitpick_Opair__box_OPairBox(X17,X25,X6,X21)) = hAPP(hAPP(X28,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_setprod__dvd__setprod__subset,axiom,
    ! [X2,X19,X22,X5,X17] :
      ( ( class_Groups_Ocomm__monoid__mult(X17)
        & class_Rings_Odvd(X17) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [X223,X224,X30,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),c_List_OtakeWhile(X5,X30,X224)),X223) = c_List_OtakeWhile(tc_prod(X5,X17),hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,tc_prod(X5,X17),X30),c_Product__Type_Ofst(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),X94))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_Diff__Int2,axiom,
    ! [X22,X62,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X62)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X62)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [X19,X62,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X19)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X62)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [X19,X62,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X19)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X62),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_Un__Diff,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X62)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff) ).

fof(fact_aset_I3_J,axiom,
    ! [X19,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X63] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),X19))
                 => X15 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X63),X3) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X64) = X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I3_J) ).

fof(fact_bset_I3_J,axiom,
    ! [X22,X15,X64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X64))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X22))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X64)))
             => ! [X63] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X63),X22))
                 => X15 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X3) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),X64) = X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I3_J) ).

fof(fact_take__add,axiom,
    ! [X222,X56,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X222) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222)),hAPP(hAPP(c_List_Otake(X56),X94),hAPP(hAPP(c_List_Odrop(X56),X98),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__add) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
           => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X5),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X22)),hAPP(X18,X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_takeWhile__not__last,axiom,
    ! [X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
       => c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),c_List_Olast(X5,X224))),X224) = c_List_Obutlast(X5,X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_Compl__INT,axiom,
    ! [X22,X19,X17,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [X22,X19,X17,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UN) ).

fof(fact_fold1Set__sing,axiom,
    ! [X21,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X21))
    <=> X6 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_folding_Ounion,axiom,
    ! [X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion) ).

fof(fact_split__div_H,axiom,
    ! [X89,X51,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X51),X89)))
    <=> ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        | ? [X144] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),X144)),X51))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X144))))
            & hBOOL(hAPP(X30,X144)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_o__eq__elim,axiom,
    ! [X27,X23,X184,X21,X6,X5,X17,X25] :
      ( hAPP(c_Fun_Ocomp(X25,X17,X5,X6),X21) = hAPP(c_Fun_Ocomp(X184,X17,X5,X23),X27)
     => ! [X209] : hAPP(X6,hAPP(X21,X209)) = hAPP(X23,hAPP(X27,X209)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [X75,X27,X23,X184,X21,X6,X5,X17,X25] :
      ( hAPP(c_Fun_Ocomp(X25,X17,X5,X6),X21) = hAPP(c_Fun_Ocomp(X184,X17,X5,X23),X27)
     => hAPP(X6,hAPP(X21,X75)) = hAPP(X23,hAPP(X27,X75)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).

fof(fact_insort__left__comm,axiom,
    ! [X224,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X24),X224)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X24),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__left__comm) ).

fof(fact_o__eq__id__dest,axiom,
    ! [X75,X23,X21,X6,X5,X17,X25] :
      ( hAPP(c_Fun_Ocomp(X25,X17,X5,X6),X21) = hAPP(c_Fun_Ocomp(X17,X17,X5,c_Fun_Oid(X17)),X23)
     => hAPP(X6,hAPP(X21,X75)) = hAPP(X23,X75) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_distinct__sort,axiom,
    ! [X224,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osort__key(X5,X17,X2,X224)))
      <=> hBOOL(hAPP(c_List_Odistinct(X5),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sort) ).

fof(fact_equiv__class__self,axiom,
    ! [X6,X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__self) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [X19,X6,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_INF__subset,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X22),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X19),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__subset) ).

fof(fact_SUP__subset,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X19),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X22),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__subset) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [X22,X6,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X17),X6)),X22)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X17),X6)),X22)) = hAPP(hAPP(c_Set_Oinsert(X17),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [X22,X6,X17,X5,X62] :
      ( ( X62 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X17),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Set_Oinsert(X17),X6),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) )
      & ( X62 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X17),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X17),X6)),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_setsum__right__distrib,axiom,
    ! [X19,X2,X17,X78,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),hAPP(c_Groups_Otimes__class_Otimes(X5),X78)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_mlex__less,axiom,
    ! [X37,X5,X24,X20,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X24)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Wellfounded_Omlex__prod(X5,X2,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X25,X5,X17] : hAPP(c_Set_Oimage(X17,X5,hAPP(hAPP(c_COMBB(X25,X5,X17),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X25,X5,X2),hAPP(c_Set_Oimage(X17,X25,X1),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ! [X88,X120] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X120))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_List_Onth(X56),X222),X88)),hAPP(hAPP(c_List_Onth(X56),X222),X120))) ) )
       => c_List_Olinorder__class_Osorted(X56,X222) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X224)
      <=> ! [X120] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => ! [X88] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X120))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_List_Onth(X5),X224),X88)),hAPP(hAPP(c_List_Onth(X5),X224),X120))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_INT__D,axiom,
    ! [X6,X22,X19,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ( hBOOL(hAPP(hAPP(c_member(X17),X6),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(X22,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__D) ).

fof(fact_foldl__absorb0,axiom,
    ! [X228,X20,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X228)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X20),X228) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_list__update__swap,axiom,
    ! [X234,X55,X222,X56,X235,X98] :
      ( X98 != X235
     => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X235),X234) = hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X235),X234)),X98),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).

fof(fact_rel__pow__commute,axiom,
    ! [X89,X37,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_card__insert,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X60)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X61))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_divide__left__mono,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X60)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X61))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

fof(fact_mono__Field,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X78)),hAPP(c_Relation_OField(X5),X146))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Field) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X20)),hAPP(X18,X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X2,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [X22,X6,X62,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Set_Oinsert(X5),X6)),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [X22,X62,X17,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X17),hAPP(c_Set_Oinsert(X5),X6)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [X93,X94,X103,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X103)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X103)),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [X223,X30,X224,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),X224),c_List_OtakeWhile(X17,X30,X223)) = c_List_OtakeWhile(tc_prod(X5,X17),hAPP(c_Fun_Ocomp(X17,tc_HOL_Obool,tc_prod(X5,X17),X30),c_Product__Type_Osnd(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [X2,X20,X5,X17,X96] :
      ( ( X96 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X17,X5,X20,X2),X96) = c_Lazy__Sequence_Ohit__bound(X5) )
      & ( X96 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X17,X5,X20,X2),X96) = c_Lazy__Sequence_Ohb__bind(X17,X5,hAPP(X20,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_inj__fun,axiom,
    ! [X25,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,tc_fun(X25,X17),hAPP(hAPP(c_COMBB(X17,tc_fun(X25,X17),X5),c_COMBK(X17,X25)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).

fof(fact_Int__eq__Inter,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X22),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_Un__eq__Union,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X22),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__eq__Union) ).

fof(fact_divide__strict__left__mono__neg,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X60)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X61))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X60)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X59),X61))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [X2,X20,X5,X17,X96] :
      ( ( X96 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X17,X5,X20,X2),X96) = c_Lazy__Sequence_Oempty(X5) )
      & ( X96 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X17,X5,X20,X2),X96) = hAPP(c_Lazy__Sequence_Obind(X17,X5,hAPP(X20,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_nth__zip,axiom,
    ! [X221,X161,X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X221)))
       => hAPP(hAPP(c_List_Onth(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)),X98) = hAPP(hAPP(c_Product__Type_OPair(X56,X161),hAPP(hAPP(c_List_Onth(X56),X222),X98)),hAPP(hAPP(c_List_Onth(X161),X221),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__zip) ).

fof(fact_mod__mult2__eq,axiom,
    ! [X59,X61,X60] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X59)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X60),X61),X59))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_list__update__length,axiom,
    ! [X57,X221,X55,X222,X56] : hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X221))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X57) = hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X57),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__length) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [X78,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,c_Transitive__Closure_Ortrancl(X5,X78))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [X36,X37,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X37)),c_Transitive__Closure_Ortrancl(X5,X36))) = c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_div__dvd__div,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Divides_Osemiring__div(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X23))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X21),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X23),X6)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X21),X23)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__dvd__div) ).

fof(fact_unity__coeff__ex,axiom,
    ! [X106,X30,X5] :
      ( ( class_Rings_Odvd(X5)
        & class_Rings_Osemiring__0(X5) )
     => ( ? [X3] : hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X106),X3)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),c_Groups_Ozero__class_Ozero(X5))))
            & hBOOL(hAPP(X30,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [X228,X17,X5] : hAPP(hAPP(c_List_Ozip(X5,X17),hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X5),c_Product__Type_Ofst(X5,X17)),X228)),hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X17),c_Product__Type_Osnd(X5,X17)),X228)) = X228,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [X16,X1,X22,X19,X2,X17,X5,X25] :
      ( class_Groups_Ocomm__monoid__mult(X25)
     => ( c_Fun_Oinj__on(X5,X17,X2,X19)
       => ( X22 = hAPP(c_Set_Oimage(X5,X17,X2),X19)
         => ( X1 = hAPP(c_Fun_Ocomp(X17,X25,X5,X16),X2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X25),X16),X22) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X25),X1),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X57)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X51),X89)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [X20,X24,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X24)),hAPP(X2,X20)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X20)),hAPP(X2,X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [X62,X112,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X111),X112)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X62)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X112),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [X62,X112,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X111),X112)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X62)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X112),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [X62,X112,X111,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X111),X112)),X62) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X111),X62)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X112),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [X223,X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X224))))
        | hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X223)))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X224),X223))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_acc__subset,axiom,
    ! [X188,X189,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X189),X188))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oacc(X5,X188)),c_Wellfounded_Oacc(X5,X189))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).

fof(fact_insort__key__left__comm,axiom,
    ! [X224,X17,X24,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(X2,X20) != hAPP(X2,X24)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X24),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X224)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X24),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X24,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),X24)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [X60,X61] :
      ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [X2,X22,X25,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(X25,tc_fun(X5,tc_HOL_Obool),X17),X22),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X25,X2),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [X2,X22,X25,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(X25,tc_fun(X5,tc_HOL_Obool),X17),X22),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X25,X2),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [X22,X19,X2,X25,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25,X17,X2),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(X17,tc_fun(X5,tc_HOL_Obool),X25),X22),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [X22,X19,X2,X25,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25,X17,X2),X19)),X22) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(X17,tc_fun(X5,tc_HOL_Obool),X25),X22),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_divmod__nat__rel,axiom,
    ! [X92,X86] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_Compl__anti__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_Oimage(X5,X5,X2),X19)))
       => c_Fun_Oinj__on(X5,X5,X2,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [X19,X17,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X19))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [X19,X17,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [X224,X78,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X78)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X78))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [X6,X21,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [X6,X21,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_accp__subset,axiom,
    ! [X188,X189,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X189),X188))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oaccp(X5,X188)),c_Wellfounded_Oaccp(X5,X189))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
         => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X18,X22)) = hAPP(X18,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_insort__insert__triv,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X20,X224) = X224 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_split__div__lemma,axiom,
    ! [X51,X145,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),X145)),X51))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X145)))) )
      <=> X145 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X51),X89) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).

fof(fact_setsum__diff,axiom,
    ! [X2,X22,X19,X5,X17] :
      ( class_Groups_Oab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff) ).

fof(fact_id__take__nth__drop,axiom,
    ! [X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => X222 = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(hAPP(c_List_Onth(X56),X222),X98)),hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_OSuc,X98)),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_less__than__iff,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__iff) ).

fof(fact_image__image,axiom,
    ! [X19,X1,X25,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Oimage(X25,X17,X1),X19)) = hAPP(c_Set_Oimage(X25,X5,hAPP(hAPP(c_COMBB(X17,X5,X25),X2),X1)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).

fof(fact_map__inj__on,axiom,
    ! [X223,X224,X2,X5,X17] :
      ( hAPP(hAPP(c_List_Omap(X17,X5),X2),X224) = hAPP(hAPP(c_List_Omap(X17,X5),X2),X223)
     => ( c_Fun_Oinj__on(X17,X5,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),hAPP(c_List_Oset(X17),X224)),hAPP(c_List_Oset(X17),X223)))
       => X224 = X223 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [X223,X224,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(c_List_Oset(X5),X223)))
     => ( hAPP(hAPP(c_List_Omap(X5,X17),X2),X224) = hAPP(hAPP(c_List_Omap(X5,X17),X2),X223)
      <=> X224 = X223 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_zdiff__int__split,axiom,
    ! [X24,X20,X30] :
      ( hBOOL(hAPP(X30,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X24))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X20))
         => hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24))
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_listsp__infI,axiom,
    ! [X22,X106,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X19),X106))
     => ( hBOOL(hAPP(c_List_Olistsp(X5,X22),X106))
       => hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X106)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).

fof(fact_ex__bij__betw__nat__finite__1,axiom,
    ! [X76,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
     => ? [X285] : c_Fun_Obij__betw(tc_Nat_Onat,X5,X285,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X76)),X76) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite__1) ).

fof(fact_Image__Int__eq,axiom,
    ! [X22,X19,X37,X17,X5] :
      ( c_Relation_Osingle__valued(X5,X17,hAPP(c_Relation_Oconverse(X17,X5),X37))
     => hAPP(c_Relation_OImage(X17,X5,X37),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X37),X19)),hAPP(c_Relation_OImage(X17,X5,X37),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_frac__less2,axiom,
    ! [X58,X126,X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X126))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X126),X58))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X57),X126))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_frac__less,axiom,
    ! [X58,X126,X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X126))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X126),X58))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X57),X126))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_mult__strict__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_frac__le,axiom,
    ! [X58,X126,X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X126))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X126),X58))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X57),X126))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_mult__mono_H,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Oordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Oordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),X73))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [X2,X6,X19,X5,X17] :
      ( class_Rings_Oring(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_geometric__sum,axiom,
    ! [X89,X20,X5] :
      ( class_Fields_Ofield(X5)
     => ( X20 != c_Groups_Oone__class_Oone(X5)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_Power_Opower__class_Opower(X5),X20)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X20),X89)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X20),c_Groups_Oone__class_Oone(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_geometric__sum) ).

fof(fact_listsum__abs,axiom,
    ! [X224,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),X224))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X5,X5),c_Groups_Oabs__class_Oabs(X5)),X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__abs) ).

fof(fact_ex__bij__betw__nat__finite,axiom,
    ! [X76,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
     => ? [X285] : c_Fun_Obij__betw(tc_Nat_Onat,X5,X285,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X76)),X76) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite) ).

fof(fact_ex__bij__betw__finite__nat,axiom,
    ! [X76,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
     => ? [X285] : c_Fun_Obij__betw(X5,tc_Nat_Onat,X285,X76,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X76))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__finite__nat) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X95,X96,X90] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X90)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [X2,X133,X89,X51,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),X133))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X89),X133))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X133)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [X2,X133,X89,X51,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),X133))
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X133))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X89),X133)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Rings_Olinordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [X61,X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Rings_Olinordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_setsum__diff__nat,axiom,
    ! [X2,X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19)),X20))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X20)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_fold1__below__iff,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19)),X20))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X20)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_INF1__D,axiom,
    ! [X6,X21,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(hAPP(X22,X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__D) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [X24,X20,X21,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X20)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [X92,X86,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [X24,X20,X21,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X20)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [X92,X86,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_select,axiom,
    ! [X146,X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X5,X224),X146))),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [X19,X20,X17,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X19))) = hAPP(c_Finite__Set_Ocard(X17),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_splitD,axiom,
    ! [X21,X6,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)))
     => hBOOL(hAPP(hAPP(X2,X6),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).

fof(fact_swap__inj__on,axiom,
    ! [X19,X17,X5] : c_Fun_Oinj__on(tc_prod(X5,X17),tc_prod(X17,X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_prod(X17,X5)),hAPP(c_COMBC(X17,X5,tc_prod(X17,X5)),c_Product__Type_OPair(X17,X5))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__inj__on) ).

fof(fact_setprod__pos__nat,axiom,
    ! [X2,X36,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [X2,X36,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X36)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos__nat__iff) ).

fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [X89,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X51),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_Int__lower1,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).

fof(fact_Diff__subset,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).

fof(fact_listsum__map__remove1,axiom,
    ! [X2,X224,X20,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X2,X20)),hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),c_List_Oremove1(X5,X20,X224)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_Int__Un__distrib,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [X22,X19,X62,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),X19)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X62),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_Un__Int__distrib,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_Diff__Int,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Un) ).

fof(fact_prod_Orecs,axiom,
    ! [X21,X6,X28,X5,X25,X17] : c_Product__Type_Oprod_Oprod__rec(X17,X25,X5,X28,hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)) = hAPP(hAPP(X28,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [X96,X2,X20,X5,X17] : hAPP(c_New__DSequence_Oneg__bind(X17,X5,X20,X2),X96) = c_Lazy__Sequence_Ohb__bind(X17,X5,hAPP(X20,X96),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X96)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X89,X51,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X51)),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [X95,X96,X90] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X96,X95)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X90)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_Int__Collect,axiom,
    ! [X30,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OCollect(X5),X30))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
        & hBOOL(hAPP(X30,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X27)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [X22,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_wf__Un,axiom,
    ! [X146,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( c_Wellfounded_Owf(X5,X146)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X78)),hAPP(c_Relation_ORange(X5,X5),X146)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Un) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [X224,X24,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X24),hAPP(c_List_Oset(X5),X224)) = hAPP(c_List_Ofoldl(X17,X5,hAPP(c_COMBC(X5,X17,X17),X2),X24),c_List_Oremdups(X5,X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_converse__meet,axiom,
    ! [X146,X78,X5,X17] : c_Predicate_Oconversep(X17,X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_fun(X5,tc_HOL_Obool))),X78),X146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),c_Predicate_Oconversep(X17,X5,X78)),c_Predicate_Oconversep(X17,X5,X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__meet) ).

fof(fact_converse__join,axiom,
    ! [X146,X78,X5,X17] : c_Predicate_Oconversep(X17,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_fun(X5,tc_HOL_Obool))),X78),X146)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),c_Predicate_Oconversep(X17,X5,X78)),c_Predicate_Oconversep(X17,X5,X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__join) ).

fof(fact_less__diff__iff,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X51))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X89))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X90)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),X90)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).

fof(fact_le__diff__iff,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X51))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X89))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X90)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),X90)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X21,X23,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_insert__subset,axiom,
    ! [X22,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [X2,X19,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X19)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [X2,X19,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X19)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [X1,X22,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X22)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [X19,X2,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [X19,X2,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [X78,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X78)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [X102,X106] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X106)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),X106))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X106),X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_drop__append,axiom,
    ! [X221,X222,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222)),hAPP(hAPP(c_List_Odrop(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__append) ).

fof(fact_take__append,axiom,
    ! [X221,X222,X92,X56] : hAPP(hAPP(c_List_Otake(X56),X92),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X92),X222)),hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__append) ).

fof(fact_set__remove1__subset,axiom,
    ! [X224,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X20,X224))),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_set__sublist__subset,axiom,
    ! [X111,X224,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X111))),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => c_Fun_Oinj__on(X17,X5,c_Fun_Othe__inv__into(X5,X17,X19,X2),hAPP(c_Set_Oimage(X5,X17,X2),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_Domain__Collect__split,axiom,
    ! [X30,X17,X5] : hAPP(c_Relation_ODomain(X5,X17),hAPP(c_Set_OCollect(tc_prod(X5,X17)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X30))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X17)),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [X224,X24,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X24),hAPP(c_List_Oset(X5),X224)) = hAPP(c_List_Ofoldl(X17,X5,hAPP(c_COMBC(X5,X17,X17),X2),X24),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_setsum__negf,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Ouminus__class_Ouminus(X5)),X2)),X19) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__negf) ).

fof(fact_abs__setprod,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Fields_Olinordered__field(X5)
     => hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(hAPP(c_COMBB(X5,X5,X17),c_Groups_Oabs__class_Oabs(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setprod) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [X30,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) )
    <=> ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_insert__mono,axiom,
    ! [X6,X64,X62,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X62),X64))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X62)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X64))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(fact_sorted__append,axiom,
    ! [X223,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Oappend(X5),X224),X223))
      <=> ( c_List_Olinorder__class_Osorted(X5,X224)
          & c_List_Olinorder__class_Osorted(X5,X223)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
             => ! [X63] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X63),hAPP(c_List_Oset(X5),X223)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X63)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__append) ).

fof(fact_power__less__power__Suc,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_double__diff,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X62),X19)) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).

fof(fact_Pow__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)),hAPP(c_Set_OPow(X5),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__mono) ).

fof(fact_K__record__comp,axiom,
    ! [X20,X2,X23,X25,X5,X17] : hAPP(hAPP(c_Fun_Ocomp(X17,X5,X25,hAPP(c_COMBK(X5,X17),X23)),X2),X20) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_K__record__comp) ).

fof(fact_set__drop__subset,axiom,
    ! [X224,X89,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X89),X224))),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset) ).

fof(fact_set__take__subset,axiom,
    ! [X224,X89,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X89),X224))),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [X6,X21,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57)),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [X6,X21,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57)),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_takeWhile__nth,axiom,
    ! [X224,X30,X5,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OtakeWhile(X5,X30,X224)),X95) = hAPP(hAPP(c_List_Onth(X5),X224),X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_of__int__setprod,axiom,
    ! [X19,X2,X17,X5] :
      ( ( class_Groups_Ocomm__monoid__mult(X5)
        & class_Rings_Oring__1(X5) )
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,tc_Int_Oint),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X17),c_Int_Oring__1__class_Oof__int(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__setprod) ).

fof(fact_of__nat__setprod,axiom,
    ! [X19,X2,X17,X5] :
      ( ( class_Groups_Ocomm__monoid__mult(X5)
        & class_Rings_Osemiring__1(X5) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,tc_Nat_Onat),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X17),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_converse__Int,axiom,
    ! [X146,X78,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X78),X146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X17,X5),X78)),hAPP(c_Relation_Oconverse(X17,X5),X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__Un,axiom,
    ! [X146,X78,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X78),X146)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X17,X5),X78)),hAPP(c_Relation_Oconverse(X17,X5),X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Un) ).

fof(fact_length__takeWhile__le,axiom,
    ! [X224,X30,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_funpow__add,axiom,
    ! [X2,X89,X51,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(hAPP(c_Nat_Ocompow(X5,X5),X51),X2)),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X89),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__add) ).

fof(fact_of__int__setsum,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Rings_Oring__1(X5)
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,tc_Int_Oint),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X17),c_Int_Oring__1__class_Oof__int(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__setsum) ).

fof(fact_of__nat__setsum,axiom,
    ! [X19,X2,X17,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,tc_Nat_Onat),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X17),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_inj__singleton,axiom,
    ! [X5] : c_Fun_Oinj__on(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__singleton) ).

fof(fact_finite__cartesian__product,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_card__psubset,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_finite__surj,axiom,
    ! [X2,X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),X22),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).

fof(fact_bij__id,axiom,
    ! [X5] : c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__id) ).

fof(fact_inj__on__Int,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( c_Fun_Oinj__on(X5,X17,X2,X22)
       => c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Int) ).

fof(fact_nth__drop,axiom,
    ! [X222,X56,X98,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X98)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222)),X98) = hAPP(hAPP(c_List_Onth(X56),X222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [X94,X98,X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,hAPP(c_List_Orev(X56),X222))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_List_Onth(X56),X222),X94)),hAPP(hAPP(c_List_Onth(X56),X222),X98))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_zip__append,axiom,
    ! [X243,X221,X241,X161,X222,X56] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X241)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X221) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X243)
       => hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),hAPP(hAPP(c_List_Oappend(X161),X241),X243)) = hAPP(hAPP(c_List_Oappend(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X241)),hAPP(hAPP(c_List_Ozip(X56,X161),X221),X243)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append) ).

fof(fact_list__size__map,axiom,
    ! [X224,X1,X17,X2,X5] : c_List_Olist_Olist__size(X5,X2,hAPP(hAPP(c_List_Omap(X17,X5),X1),X224)) = c_List_Olist_Olist__size(X17,hAPP(c_Fun_Ocomp(X5,tc_Nat_Onat,X17,X2),X1),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__map) ).

fof(fact_refl__onD,axiom,
    ! [X6,X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).

fof(fact_UN__upper,axiom,
    ! [X22,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool)),hAPP(X22,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__upper) ).

fof(fact_take__Cons__number__of,axiom,
    ! [X222,X55,X56,X122] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = c_List_Olist_ONil(X56) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_predicate2D,axiom,
    ! [X24,X20,X29,X30,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X30),X29))
     => ( hBOOL(hAPP(hAPP(X30,X20),X24))
       => hBOOL(hAPP(hAPP(X29,X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X29,X17,X5,X24,X20,X30] :
      ( hBOOL(hAPP(hAPP(X30,X20),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X30),X29))
       => hBOOL(hAPP(hAPP(X29,X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_fold1__antimono,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X22)),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__antimono) ).

fof(fact_Un__iff,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
        | hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__iff) ).

fof(fact_field__le__epsilon,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( ! [X273] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X273))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X57),X273))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_foldl__Cons,axiom,
    ! [X224,X20,X6,X2,X17,X5] : hAPP(c_List_Ofoldl(X5,X17,X2,X6),hAPP(hAPP(c_List_Olist_OCons(X17),X20),X224)) = hAPP(c_List_Ofoldl(X5,X17,X2,hAPP(hAPP(X2,X6),X20)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Cons) ).

fof(fact_length__transpose__sorted,axiom,
    ! [X224,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X224)))
     => ( ( X224 = c_List_Olist_ONil(tc_List_Olist(X5))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X224)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X224 != c_List_Olist_ONil(tc_List_Olist(X5))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X224),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__transpose__sorted) ).

fof(fact_power__strict__mono,axiom,
    ! [X92,X61,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

fof(fact_power__strict__decreasing,axiom,
    ! [X60,X109,X92,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X109))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Oone__class_Oone(X56)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X109)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__decreasing,axiom,
    ! [X60,X109,X92,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X109))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Oone__class_Oone(X56)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X109)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(fact_Image__Un,axiom,
    ! [X22,X19,X37,X5,X17] : hAPP(c_Relation_OImage(X17,X5,X37),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17,X5,X37),X19)),hAPP(c_Relation_OImage(X17,X5,X37),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Un) ).

fof(fact_vimage__Int,axiom,
    ! [X22,X19,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X19)),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__Un,axiom,
    ! [X22,X19,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X19)),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Un) ).

fof(fact_vimage__Diff,axiom,
    ! [X22,X19,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X19)),hAPP(c_Set_Ovimage(X5,X17,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Diff) ).

fof(fact_image__Un,axiom,
    ! [X22,X19,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17,X5,X2),X19)),hAPP(c_Set_Oimage(X17,X5,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Un) ).

fof(fact_append__in__lists__conv,axiom,
    ! [X19,X223,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X224),X223)),c_List_Olists(X5,X19)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_List_Olists(X5,X19)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X223),c_List_Olists(X5,X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Powp__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X5,X19)),c_Predicate_OPowp(X5,X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__mono) ).

fof(fact_distinct__product,axiom,
    ! [X221,X161,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => ( hBOOL(hAPP(c_List_Odistinct(X161),X221))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(X56,X161)),c_Enum_Oproduct(X56,X161,X222,X221))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__product) ).

fof(fact_finite__Plus,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(fact_Id__on__eqI,axiom,
    ! [X19,X5,X21,X6] :
      ( X6 = X21
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Relation_OId__on(X5,X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [X30,X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X24),c_Int_OInteg))
     => ( ! [X3] : hBOOL(hAPP(X30,hAPP(c_Int_ORep__Integ,X3)))
       => hBOOL(hAPP(X30,X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_list__update__append1,axiom,
    ! [X55,X221,X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X98),X55) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append1) ).

fof(fact_nat__mult__dvd__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

fof(fact_dvd__mult__cancel,axiom,
    ! [X92,X86,X93] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X93))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [X92,X86,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X92)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [X89,X90,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),X90)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_power__dvd__imp__le,axiom,
    ! [X92,X86,X98] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X92)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X98))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_wfE__pf,axiom,
    ! [X19,X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Relation_OImage(X5,X5,X37),X19)))
       => X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfE__pf) ).

fof(fact_int__setprod,axiom,
    ! [X19,X2,X5] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setprod) ).

fof(fact_int__setsum,axiom,
    ! [X19,X2,X5] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setsum) ).

fof(fact_override__on__emptyset,axiom,
    ! [X1,X2,X17,X5] : c_Fun_Ooverride__on(X5,X17,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__emptyset) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [X24,X20,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X20)),hAPP(X2,X24)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X24)),hAPP(X2,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_hoare__derivs_OSkip,axiom,
    ! [X30,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X30),c_Com_Ocom_OSKIP),X30)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).

fof(fact_hoare__derivs_Oequations_I7_J,axiom,
    ! [X33,X34,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X34,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X33),c_Com_Ocom_OSKIP),X33)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

fof(fact_set__update__memI,axiom,
    ! [X20,X224,X5,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X224),X89),X20)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__memI) ).

fof(fact_UN__I,axiom,
    ! [X22,X21,X17,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6)))
       => hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__I) ).

fof(fact_unique__quotient,axiom,
    ! [X135,X136,X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X136),X135)))
       => ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X107 = X136 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [X135,X136,X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X136),X135)))
       => ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X119 = X135 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__remainder) ).

fof(fact_finite__imageD,axiom,
    ! [X19,X2,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X17,X5,X2),X19)))
     => ( c_Fun_Oinj__on(X17,X5,X2,X19)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_dvd__mult__cancel__left,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Oidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X21)))
      <=> ( X23 = c_Groups_Ozero__class_Ozero(X5)
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).

fof(fact_dvd__mult__cancel__right,axiom,
    ! [X21,X23,X6,X5] :
      ( class_Rings_Oidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X23)))
      <=> ( X23 = c_Groups_Ozero__class_Ozero(X5)
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).

fof(fact_single__valued__subset,axiom,
    ! [X146,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X78),X146))
     => ( c_Relation_Osingle__valued(X5,X17,X146)
       => c_Relation_Osingle__valued(X5,X17,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X21,X23,X6,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X23)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X61)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X21,X23,X6,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X23)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X61)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_sorted__nth__mono,axiom,
    ! [X94,X98,X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X222)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_List_Onth(X56),X222),X98)),hAPP(hAPP(c_List_Onth(X56),X222),X94))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [X37,X89,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [X57,X55,X58,X56] :
      ( class_Fields_Ofield(X56)
     => ( X58 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X57),X58)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X55)),X57)),X58) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [X57,X55,X58,X56] :
      ( class_Fields_Ofield(X56)
     => ( X58 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X57),X58)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X55)),X57)),X58) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_filter__insort,axiom,
    ! [X20,X30,X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))
       => ( hBOOL(hAPP(X30,X20))
         => hAPP(c_List_Ofilter(X17,X30),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X224)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(c_List_Ofilter(X17,X30),X224)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort) ).

fof(fact_subset__singletonD,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X19 = hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__singletonD) ).

fof(fact_DiffE,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
         => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).

fof(fact_fun__upd__triv,axiom,
    ! [X20,X2,X17,X5] : c_Fun_Ofun__upd(X5,X17,X2,X20,hAPP(X2,X20)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_fun__upd__idem,axiom,
    ! [X5,X17,X24,X20,X2] :
      ( hAPP(X2,X20) = X24
     => c_Fun_Ofun__upd(X17,X5,X2,X20,X24) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X2,X20)) = hAPP(X18,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_OSuc,X98)),X222) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(hAPP(c_List_Onth(X56),X222),X98)),c_List_Olist_ONil(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_comp__funpow,axiom,
    ! [X2,X89,X17,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X5,X17),tc_fun(X5,X17)),X89),c_Fun_Ocomp(X17,X17,X5,X2)) = c_Fun_Ocomp(X17,X17,X5,hAPP(hAPP(c_Nat_Ocompow(X17,X17),X89),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__funpow) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [X96,X2,X20,X5,X17] : hAPP(c_New__DSequence_Opos__bind(X17,X5,X20,X2),X96) = hAPP(c_Lazy__Sequence_Obind(X17,X5,hAPP(X20,X96)),hAPP(hAPP(c_COMBC(X17,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X96)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_curry__conv,axiom,
    ! [X21,X6,X2,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Ocurry(X17,X25,X5,X2),X6),X21) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).

fof(fact_curry__def,axiom,
    ! [X24,X20,X23,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Ocurry(X17,X25,X5,X23),X20),X24) = hAPP(X23,hAPP(hAPP(c_Product__Type_OPair(X17,X25),X20),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__def) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hAPP(c_Set_Oimage(X5,X17,X2),X19) = hAPP(c_Set_Oimage(X5,X17,X2),X22)
      <=> X19 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_refl__on__Int,axiom,
    ! [X146,X22,X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( c_Relation_Orefl__on(X5,X22,X146)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__on__Un,axiom,
    ! [X146,X22,X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( c_Relation_Orefl__on(X5,X22,X146)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Un) ).

fof(fact_lazy__sequence_Orecs_I1_J,axiom,
    ! [X149,X28,X17,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X17,X28,X149,c_Lazy__Sequence_Olazy__sequence_OEmpty(X17)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => c_Fun_Oinj__on(X5,X17,c_Hilbert__Choice_Oinv__into(X17,X5,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_bij__betw__id,axiom,
    ! [X19,X5] : c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X19,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__id) ).

fof(fact_Domain__insert,axiom,
    ! [X78,X21,X6,X17,X5] : hAPP(c_Relation_ODomain(X5,X17),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),X78)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Relation_ODomain(X5,X17),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).

fof(fact_Range__insert,axiom,
    ! [X78,X21,X6,X5,X17] : hAPP(c_Relation_ORange(X17,X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X6),X21)),X78)) = hAPP(hAPP(c_Set_Oinsert(X5),X21),hAPP(c_Relation_ORange(X17,X5),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).

fof(fact_psubset__trans,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_subset__trans,axiom,
    ! [X62,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X62)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X19,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20),X19))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_Pair__scomp,axiom,
    ! [X2,X20,X17,X25,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X25,X5,X17),hAPP(c_Product__Type_OPair(X25,X5),X20)),X2) = hAPP(X2,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__scomp) ).

fof(fact_mod__div__equality,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),X61)),c_Divides_Odiv__class_Omod(X56,X60,X61)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__decomp,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),X61)),c_Divides_Odiv__class_Omod(X56,X60,X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_sorted__sort__key,axiom,
    ! [X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Olinorder__class_Osort__key(X17,X5,X2,X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_UN__singleton,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__singleton) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [X60,X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X60) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),X60),hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_OSuc,X98)),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_distinct__set__sublists,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),c_List_Oset(X5)),c_Enum_Osublists(X5,X224)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_Pow__insert,axiom,
    ! [X19,X6,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)),hAPP(c_Set_Oimage(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oinsert(X5),X6)),hAPP(c_Set_OPow(X5),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [X18,X16,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X17,X16),X18)))
     => ( hAPP(c_Set_Oimage(X5,X17,X16),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X18)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageD) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [X19,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),c_List_Olists(X5,X19)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_List_Olists(X5,X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_range,axiom,
    ! [X101,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X93))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X93),X101))),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range) ).

fof(fact_IntD1,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).

fof(fact_Int__iff,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
        & hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).

fof(fact_DiffD1,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).

fof(fact_IntD2,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).

fof(fact_Diff__insert,axiom,
    ! [X22,X6,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).

fof(fact_fold1__Un,axiom,
    ! [X22,X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X2,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_scomp__Pair,axiom,
    ! [X20,X25,X17,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X17,X25,tc_prod(X17,X25)),X20),c_Product__Type_OPair(X17,X25)) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__Pair) ).

fof(fact_Pow__def,axiom,
    ! [X19,X5] : hAPP(c_Set_OPow(X5),X19) = hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__def) ).

fof(fact_rev__foldl__cons,axiom,
    ! [X224,X5] : hAPP(c_List_Orev(X5),X224) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_gauss__sum,axiom,
    ! [X89,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),c_Nat_Osemiring__1__class_Oof__nat(X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X89))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)),c_Groups_Oone__class_Oone(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gauss__sum) ).

fof(fact_length__n__lists__elem,axiom,
    ! [X224,X89,X223,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X223),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X89,X224))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223) = X89 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_antisym__subset,axiom,
    ! [X146,X78,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
     => ( c_Relation_Oantisym(X5,X146)
       => c_Relation_Oantisym(X5,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__subset) ).

fof(fact_acyclic__subset,axiom,
    ! [X78,X146,X5] :
      ( c_Wellfounded_Oacyclic(X5,X146)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146))
       => c_Wellfounded_Oacyclic(X5,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__subset,axiom,
    ! [X133,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X133),X78))
       => c_Wellfounded_Owf(X5,X133) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__subset) ).

fof(fact_in__set__remove1,axiom,
    ! [X224,X5,X21,X6] :
      ( X6 != X21
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X21,X224))))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__remove1) ).

fof(fact_Int__assoc,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).

fof(fact_Un__assoc,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__assoc) ).

fof(fact_Int__Diff,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Diff) ).

fof(fact_le__add__diff,axiom,
    ! [X86,X92,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(fact_set__takeWhileD,axiom,
    ! [X224,X30,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_OtakeWhile(X5,X30,X224))))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
        & hBOOL(hAPP(X30,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_in__set__sublistD,axiom,
    ! [X111,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X111))))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_filter__is__subset,axiom,
    ! [X224,X30,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X30),X224))),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__is__subset) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( ( X6 != X21
          & X23 != X27 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X27)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X26,X20,X24,X84,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X84),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X84),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X24))
      <=> ( X84 = X20
          | X24 = X26 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_reflp__def,axiom,
    ! [X78,X5] :
      ( c_Predicate_Oreflp(X5,X78)
    <=> c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflp__def) ).

fof(fact_le__diff__conv2,axiom,
    ! [X96,X95,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90)),X95)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_THE__default__def,axiom,
    ! [X27,X5,X30] :
      ( ( ? [X3] :
            ( hBOOL(hAPP(X30,X3))
            & ! [X38] :
                ( hBOOL(hAPP(X30,X38))
               => X38 = X3 ) )
       => c_FunDef_OTHE__default(X5,X27,X30) = c_HOL_OThe(X5,X30) )
      & ( ~ ? [X3] :
              ( hBOOL(hAPP(X30,X3))
              & ! [X38] :
                  ( hBOOL(hAPP(X30,X38))
                 => X38 = X3 ) )
       => c_FunDef_OTHE__default(X5,X27,X30) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_THE__default__def) ).

fof(fact_vimageD,axiom,
    ! [X19,X2,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X17,X2),X19)))
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X6)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [X22,X2,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X17,X2),X22)))
    <=> hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X6)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).

fof(fact_drop__Cons,axiom,
    ! [X224,X20,X89,X5] : hAPP(hAPP(c_List_Odrop(X5),X89),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Odrop(X5)),X224),X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),c_Groups_Oone__class_Oone(X56)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X57)),X55)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),c_Groups_Oone__class_Oone(X56)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X55)),X55)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_Union__disjoint,axiom,
    ! [X19,X62,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X62))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__disjoint) ).

fof(fact_zdiv__mono2,axiom,
    ! [X61,X137,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X137),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X137))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_Domain__Un__eq,axiom,
    ! [X22,X19,X17,X5] : hAPP(c_Relation_ODomain(X5,X17),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X17),X19)),hAPP(c_Relation_ODomain(X5,X17),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_Range__Un__eq,axiom,
    ! [X22,X19,X5,X17] : hAPP(c_Relation_ORange(X17,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X17,X5),X19)),hAPP(c_Relation_ORange(X17,X5),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_map__update,axiom,
    ! [X24,X90,X224,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Olist__update(X17,X224),X90),X24)) = hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),X90),hAPP(X2,X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__update) ).

fof(fact_set__ConsD,axiom,
    ! [X224,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))))
     => ( X24 = X20
        | hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_List_Oset(X5),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__ConsD) ).

fof(fact_code__numeral__decr,axiom,
    ! [X93] :
      ( X93 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X93)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_in__set__dropD,axiom,
    ! [X224,X89,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X89),X224))))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__dropD) ).

fof(fact_in__set__takeD,axiom,
    ! [X224,X89,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X89),X224))))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__takeD) ).

fof(fact_power__Suc__less__one,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Oone__class_Oone(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92))),c_Groups_Oone__class_Oone(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [X61,X137,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X137),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X137)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_Id__onE,axiom,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X23),c_Relation_OId__on(X5,X19)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => X23 != hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).

fof(fact_inv__f__f,axiom,
    ! [X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X20)) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_the__inv__f__f,axiom,
    ! [X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X20)) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),hAPP(hAPP(X2,X20),X26)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_inv__f__eq,axiom,
    ! [X24,X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X20) = X24
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X24) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_wfP__subset,axiom,
    ! [X133,X78,X5] :
      ( c_Wellfounded_OwfP(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X133),X78))
       => c_Wellfounded_OwfP(X5,X133) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__subset) ).

fof(fact_pred__equals__eq,axiom,
    ! [X36,X37,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X37) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36)
    <=> X37 = X36 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_mult__less__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [X89,X90,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),X90)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [X224,X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => c_List_Olinorder__class_Osort__key(X5,X17,X2,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),c_List_Olinorder__class_Osort__key(X5,X17,X2,X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I2_J) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Olinordered__comm__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_divide__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_power__mono,axiom,
    ! [X92,X61,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Oordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Oordered__comm__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Oordered__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [X221,X57,X222,X55,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),hAPP(hAPP(c_List_Olist_OCons(X161),X57),X221)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X56,X161)),hAPP(hAPP(c_Product__Type_OPair(X56,X161),X55),X57)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X21)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X21)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [X19,X20] :
      ( c_Nat__Transfer_Ois__nat(X20)
     => ( c_Nat__Transfer_Onat__set(X19)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X20),X19))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X20)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_Max__eqI,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X38] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X38),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X20)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
           => c_Big__Operators_Olinorder__class_OMax(X5,X19) = X20 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__eqI) ).

fof(fact_nat__mult__dvd__cancel__disj,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)))
    <=> ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(fact_list__all__length,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__all(X5,X30,X224)
    <=> ! [X130] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X130))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__length) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_subset__inj__on,axiom,
    ! [X19,X22,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X22)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => c_Fun_Oinj__on(X5,X17,X2,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_length__filter__le,axiom,
    ! [X224,X30,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X30),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__le) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [X78,X6,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),c_Transitive__Closure_Ortrancl(X5,X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_inv__into__f__f,axiom,
    ! [X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),hAPP(X2,X20)) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Fun_Othe__inv__into(X5,X17,X19,X2),hAPP(X2,X20)) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X24,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => ( hAPP(X2,X20) = X24
         => hAPP(c_Hilbert__Choice_Oinv__into(X5,X17,X19,X2),X24) = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [X24,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hAPP(X2,X20) = X24
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Fun_Othe__inv__into(X5,X17,X19,X2),X24) = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_finite__INT,axiom,
    ! [X19,X17,X111,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X111))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(X19,X3))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__INT) ).

fof(fact_power__strict__increasing,axiom,
    ! [X60,X109,X92,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X109))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X109))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__increasing,axiom,
    ! [X60,X109,X92,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X109))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Oone__class_Oone(X56)),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X109))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Rings_Olinordered__ring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Rings_Olinordered__ring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Rings_Oordered__ring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Rings_Oordered__ring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_card__Diff__singleton,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_finite__Diff2,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff2) ).

fof(fact_listsum__update__nat,axiom,
    ! [X92,X232,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X232)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X232),X93),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X232)),X92)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X232),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_o__def,axiom,
    ! [X20,X1,X2,X25,X5,X17] : hAPP(hAPP(c_Fun_Ocomp(X17,X5,X25,X2),X1),X20) = hAPP(X2,hAPP(X1,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).

fof(fact_o__apply,axiom,
    ! [X20,X1,X2,X25,X5,X17] : hAPP(hAPP(c_Fun_Ocomp(X17,X5,X25,X2),X1),X20) = hAPP(X2,hAPP(X1,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).

fof(fact_mult__dvd__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X59),X73))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X59),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_inf__mono,axiom,
    ! [X73,X61,X59,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X59),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).

fof(fact_sup__mono,axiom,
    ! [X73,X61,X59,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X59),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__mono) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [X73,X61,X59,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X59),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [X73,X61,X59,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X59),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_add__mono,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Groups_Oordered__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X59),X73))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X73))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X59,X61,X122,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Rings_Osemiring(X161) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X161),X61),X59)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [X59,X61,X122,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Rings_Oring(X161) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X161),X61),X59)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_div__mult__div__if__dvd,axiom,
    ! [X126,X58,X55,X57,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X58),X126))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X55),X57)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X126),X58)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).

fof(fact_fold__inf__insert,axiom,
    ! [X6,X21,X19,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [X6,X21,X19,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X21),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [X6,X21,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X21),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [X6,X21,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X21),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_finite__vimageI,axiom,
    ! [X16,X17,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( c_Fun_Oinj__on(X17,X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_Ovimage(X17,X5,X16),X18))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageI) ).

fof(fact_INF__leI,axiom,
    ! [X76,X19,X96,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X19),X76)),hAPP(X76,X96))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__leI) ).

fof(fact_add__number__of__diff2,axiom,
    ! [X126,X59,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X59),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)))),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),X89))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_SUP1__I,axiom,
    ! [X17,X21,X22,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => ( hBOOL(hAPP(hAPP(X22,X6),X21))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__I) ).

fof(fact_Sup__le__iff,axiom,
    ! [X21,X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OSup__class_OSup(X5,X19)),X21))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [X20,X26,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [X231,X51] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_List_Oset(tc_Nat_Onat),X231)))
           => X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).

fof(fact_one__less__mult,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X86))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).

fof(fact_one__le__mult__iff,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X51))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_mod__mult__self4,axiom,
    ! [X86,X92,X93] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)),X86)),X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X86),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_Union__Un__distrib,axiom,
    ! [X22,X19,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [X22,X19,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_split__mod,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X89,X90)))
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X30,X89)) )
        & ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X88,X120] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X90))
             => ( X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X88)),X120)
               => hBOOL(hAPP(X30,X120)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).

fof(fact_in__lists__conv__set,axiom,
    ! [X19,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_List_Olists(X5,X19)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [X226,X6,X123,X5] : c_List_Olist_Olist__size(X5,X123,hAPP(hAPP(c_List_Olist_OCons(X5),X6),X226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X123,X6)),c_List_Olist_Olist__size(X5,X123,X226))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [X224,X20,X5] : c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X20)),X224)) = c_Random_Oselect__weight(X5,X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [X259,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X259)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X259)) = c_List_Otranspose(X5,X259) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_card__seteq,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X22)),hAPP(c_Finite__Set_Ocard(X5),X19)))
         => X19 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_Inter__lower,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__lower) ).

fof(fact_converse__rel__comp,axiom,
    ! [X146,X78,X25,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(hAPP(c_Relation_Orel__comp(X17,X25,X5),X78),X146)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),hAPP(c_Relation_Oconverse(X25,X5),X146)),hAPP(c_Relation_Oconverse(X17,X25),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_min__less__iff__disj,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),X24)),X26))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X26))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__le__iff__disj,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),X24)),X26))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X26))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_split__div,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X89),X90)))
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X88,X120] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X90))
             => ( X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X88)),X120)
               => hBOOL(hAPP(X30,X88)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X22)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X22)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_subset__Pow__Union,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X19),hAPP(c_Set_OPow(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_IntI,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).

fof(fact_conjI__realizer,axiom,
    ! [X17,X5,X145,X29,X133,X30] :
      ( hBOOL(hAPP(X30,X133))
     => ( hBOOL(hAPP(X29,X145))
       => ( hBOOL(hAPP(X30,hAPP(c_Product__Type_Ofst(X5,X17),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X133),X145))))
          & hBOOL(hAPP(X29,hAPP(c_Product__Type_Osnd(X5,X17),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X133),X145)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conjI__realizer) ).

fof(fact_INFI__apply,axiom,
    ! [X20,X2,X19,X25,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X25,X5)),X19),X2),X20) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,X5),X19),hAPP(hAPP(c_COMBC(X17,X25,X5),X2),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__apply) ).

fof(fact_SUPR__apply,axiom,
    ! [X20,X2,X19,X25,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X25,X5)),X19),X2),X20) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X5),X19),hAPP(hAPP(c_COMBC(X17,X25,X5),X2),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__apply) ).

fof(fact_finite__Un,axiom,
    ! [X4,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X18),X4)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Un) ).

fof(fact_Un__Diff__Int,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_listsp__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X19)),c_List_Olistsp(X5,X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).

fof(fact_lists__mono,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olists(X5,X19)),c_List_Olists(X5,X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_symp__def,axiom,
    ! [X78,X5] :
      ( c_Predicate_Osymp(X5,X78)
    <=> c_Relation_Osym(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symp__def) ).

fof(fact_transp__def,axiom,
    ! [X78,X5] :
      ( c_Predicate_Otransp(X5,X78)
    <=> c_Relation_Otrans(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transp__def) ).

fof(fact_wfP__def,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_OwfP(X5,X78)
    <=> c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__def) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [X6,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X21)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_Times__eq__cancel2,axiom,
    ! [X22,X19,X17,X62,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X62))
     => ( hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X62)) = hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X22),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X62))
      <=> X19 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_wfI__pf,axiom,
    ! [X37,X5] :
      ( ! [X50] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X50),hAPP(c_Relation_OImage(X5,X5,X37),X50)))
         => X50 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(X5,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfI__pf) ).

fof(fact_prod__caseI,axiom,
    ! [X17,X5,X21,X6,X28] :
      ( hBOOL(hAPP(hAPP(X28,X6),X21))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X28),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).

fof(fact_splitI,axiom,
    ! [X17,X5,X21,X6,X2] :
      ( hBOOL(hAPP(hAPP(X2,X6),X21))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [X6,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X21)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_less__diff__conv,axiom,
    ! [X90,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X90)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90)),X95)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(fact_le__diff__conv,axiom,
    ! [X96,X90,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X90)),X96))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(fact_card__Diff__subset,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [X20,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X17,X2,X18)
     => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X20)),hAPP(X2,X20)) = hAPP(X2,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_Field__Un,axiom,
    ! [X146,X78,X5] : hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X78)),hAPP(c_Relation_OField(X5),X146)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Un) ).

fof(fact_product__list__set,axiom,
    ! [X223,X224,X17,X5] : hAPP(c_List_Oset(tc_prod(X5,X17)),c_Enum_Oproduct(X5,X17,X224,X223)) = hAPP(hAPP(c_Product__Type_OSigma(X5,X17),hAPP(c_List_Oset(X5),X224)),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),hAPP(c_List_Oset(X17),X223))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product__list__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [X228,X223,X17,X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
     => ( hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223) = X228
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X5),c_Product__Type_Ofst(X5,X17)),X228) = X224
          & hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X17),c_Product__Type_Osnd(X5,X17)),X228) = X223 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_inf1D1,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => hBOOL(hAPP(X19,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).

fof(fact_inf1D2,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => hBOOL(hAPP(X22,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [X71,X33,X72,X34,X78,X5] :
      ( c_List_Olistrelp(X5,X78,hAPP(hAPP(c_List_Olist_OCons(X5),X34),X72),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X71))
    <=> ( hBOOL(hAPP(hAPP(X78,X34),X33))
        & c_List_Olistrelp(X5,X78,X72,X71) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [X223,X224,X5,X24,X20,X78] :
      ( hBOOL(hAPP(hAPP(X78,X20),X24))
     => ( c_List_Olistrelp(X5,X78,X224,X223)
       => c_List_Olistrelp(X5,X78,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X24),c_Int_OInteg))
     => ~ ! [X3] : X24 != hAPP(c_Int_ORep__Integ,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_InterI,axiom,
    ! [X19,X62,X5] :
      ( ! [X152] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X152),X62))
         => hBOOL(hAPP(hAPP(c_member(X5),X19),X152)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X62))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterI) ).

fof(fact_lists_Osimps,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X6),c_List_Olists(X5,X19)))
    <=> ( X6 = c_List_Olist_ONil(X5)
        | ? [X49,X253] :
            ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X49),X253)
            & hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X253),c_List_Olists(X5,X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).

fof(fact_in__set__replicate,axiom,
    ! [X24,X89,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X24))))
    <=> ( X20 = X24
        & X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__replicate) ).

fof(fact_folding__one_Ounion__disjoint,axiom,
    ! [X22,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_mod__mult__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__add__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).

fof(fact_mod__diff__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_power__gt1__lemma,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_inj__on__diff__nat,axiom,
    ! [X90,X41] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X3)) )
     => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X90),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_InterD,axiom,
    ! [X40,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X62)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),X62))
       => hBOOL(hAPP(hAPP(c_member(X5),X19),X40)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterD) ).

fof(fact_InterE,axiom,
    ! [X40,X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X62)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),X62))
       => hBOOL(hAPP(hAPP(c_member(X5),X19),X40)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterE) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg__trivial) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X17)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X17),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X17),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X94))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X93))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__mono2,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X94))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_zdiv__mono1,axiom,
    ! [X61,X140,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),X140))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X140),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__le__mono2,axiom,
    ! [X93,X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X93),X92)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X93),X86))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).

fof(fact_inj__map,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X17),hAPP(c_List_Omap(X5,X17),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__map) ).

fof(fact_inj__mapD,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X17),hAPP(c_List_Omap(X5,X17),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__mapD) ).

fof(fact_subset__insertI2,axiom,
    ! [X21,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [X222,X55,X92,X56] : hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X92,X55)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X92,X55)),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_INT__insert,axiom,
    ! [X22,X19,X6,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17),X6),X19)),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(X22,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert) ).

fof(fact_UN__insert,axiom,
    ! [X22,X19,X6,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17),X6),X19)),X22) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(X22,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert) ).

fof(fact_below__fold1__iff,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X19)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [X224,X20,X2,X5,X17] : c_List_Omaps(X17,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X17),X20),X224)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(X2,X20)),c_List_Omaps(X17,X5,X2,X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [X61,X140,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),X140))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X140),X61)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_nth__mem,axiom,
    ! [X224,X5,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_List_Onth(X5),X224),X89)),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__mem) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X86))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X86))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X86))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [X57,X55,X58,X56] :
      ( class_Fields_Ofield(X56)
     => ( X58 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X58)),X57) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57))),X58) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => ( X57 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),X58) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57))),X57) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [X57,X55,X58,X56] :
      ( class_Fields_Ofield(X56)
     => ( X58 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X58)),X57) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57))),X58) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_in__set__conv__nth,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
          & hAPP(hAPP(c_List_Onth(X5),X224),X88) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X58,X131,X126,X132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X132),X126))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X58))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),X131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X58))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_add__less__mono,axiom,
    ! [X91,X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X91))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X91))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_diff__less__mono,axiom,
    ! [X59,X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),X61))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X59),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X60),X59)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__less__mono2,axiom,
    ! [X91,X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X91))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X91),X92)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X91),X86))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_mult__le__mono,axiom,
    ! [X91,X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X91))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X91))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

fof(fact_add__le__mono,axiom,
    ! [X91,X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X91))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X91))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X80,X81,X82,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [X89,X51,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X51)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_atMost__subset__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X20)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X20)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X20)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X20)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_divide__neg__pos,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__cancel__semiring(X56)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__cancel__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__cancel__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__cancel__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_set__subset__Cons,axiom,
    ! [X20,X224,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__subset__Cons) ).

fof(fact__06,axiom,
    ! [X254,X20,X2,X5,X17] : c_Lazy__Sequence_Omap(X17,X5,X2,c_Lazy__Sequence_Olazy__sequence_OInsert(X17,X20,X254)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X5,hAPP(X2,X20),c_Lazy__Sequence_Omap(X17,X5,X2,X254)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__06) ).

fof(fact_transpose__map__map,axiom,
    ! [X224,X2,X17,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X17),tc_List_Olist(X5)),hAPP(c_List_Omap(X17,X5),X2)),X224)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X17),tc_List_Olist(X5)),hAPP(c_List_Omap(X17,X5),X2)),c_List_Otranspose(X17,X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__map__map) ).

fof(fact_dvd__mult__left,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X59))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X59)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).

fof(fact_dvd__mult__right,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X59))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X61),X59)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).

fof(fact_max__less__iff__conj,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),X24)),X26))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X26))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_le__sup__iff,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),X24)),X26))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X26))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__sup__iff) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),X24)),X26))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X26))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [X95,X96,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => ( hAPP(hAPP(c_List_Onth(X5),X224),X96) = hAPP(hAPP(c_List_Onth(X5),X224),X95)
          <=> X96 = X95 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__conv__nth,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
    <=> ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => ! [X120] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
             => ( X88 != X120
               => hAPP(hAPP(c_List_Onth(X5),X224),X88) != hAPP(hAPP(c_List_Onth(X5),X224),X120) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_distinct__map,axiom,
    ! [X224,X2,X17,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X17),X224))
        & c_Fun_Oinj__on(X17,X5,X2,hAPP(c_List_Oset(X17),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__map) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_inj__on__diff,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [X278,X6,X123,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X123),c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X123,X6)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X123),X278))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
    ! [X20,X26,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),hAPP(hAPP(X2,X20),X26)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_insert__Diff,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X17)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X17),tc_HOL_Obool))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X17),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_setsum__head__Suc,axiom,
    ! [X2,X89,X51,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X51)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X51),X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_vimageI2,axiom,
    ! [X17,X19,X6,X2,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X6)),X19))
     => hBOOL(hAPP(hAPP(c_member(X17),X6),hAPP(c_Set_Ovimage(X17,X5,X2),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).

fof(fact_sorted__insort,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),X224))
      <=> c_List_Olinorder__class_Osorted(X5,X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [X2,X89,X51,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X51)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X51)),X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_set__eq__subset,axiom,
    ! [X5,X22,X19] :
      ( X19 = X22
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
       => X19 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_rev__nth,axiom,
    ! [X222,X56,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Onth(X56),hAPP(c_List_Orev(X56),X222)),X92) = hAPP(hAPP(c_List_Onth(X56),X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),hAPP(c_Nat_OSuc,X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__nth) ).

fof(fact_INT__absorb,axiom,
    ! [X19,X17,X111,X90,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X90),X111))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool)),hAPP(X19,X90)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__absorb) ).

fof(fact_UN__absorb,axiom,
    ! [X19,X17,X111,X90,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X90),X111))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,tc_HOL_Obool)),hAPP(X19,X90)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X111),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__absorb) ).

fof(fact_list__update__overwrite,axiom,
    ! [X57,X55,X98,X222,X56] : hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X98),X57) = hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X57),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_negative__zless,axiom,
    ! [X86,X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X92)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).

fof(fact_add__neg__neg,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),c_Groups_Ozero__class_Ozero(X56))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_Nats__mult,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Nat_Osemiring__1__class_ONats(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__mult) ).

fof(fact_Ints__mult,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__mult) ).

fof(fact_Nats__add,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Nat_Osemiring__1__class_ONats(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__add) ).

fof(fact_Ints__add,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).

fof(fact_Ints__diff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__diff) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [X224,X2,X5] : c_List_Olist_Olist__size(X5,X2,X224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X5,tc_Nat_Onat),X2),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(X5,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_listsum__triv,axiom,
    ! [X224,X78,X17,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(c_COMBK(X5,X17),X78)),X224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X224))),X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__triv) ).

fof(fact_power__minus,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56))),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

fof(fact_rangeI,axiom,
    ! [X17,X20,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X122,X61,X60,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Rings_Osemiring(X161) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X161),X60),X61)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),X60),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),X61),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [X122,X61,X60,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Rings_Oring(X161) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X161),X60),X61)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),X60),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X161),X61),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),c_Big__Operators_Olattice__class_OInf__fin(X5,X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)),c_Big__Operators_Olattice__class_OSup__fin(X5,X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),c_Big__Operators_Olinorder__class_OMin(X5,X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X19)),c_Big__Operators_Olinorder__class_OMax(X5,X22)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__right__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__ab__semigroup__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_fold1__Un2,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un2) ).

fof(fact_rev__drop,axiom,
    ! [X222,X98,X56] : hAPP(c_List_Orev(X56),hAPP(hAPP(c_List_Odrop(X56),X98),X222)) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X98)),hAPP(c_List_Orev(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [X222,X98,X56] : hAPP(c_List_Orev(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222)) = hAPP(hAPP(c_List_Odrop(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X98)),hAPP(c_List_Orev(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__take) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X106),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_pdivmod__def,axiom,
    ! [X91,X93] : c_Divides_Opdivmod(X93,X91) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X91))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X91))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__def) ).

fof(fact_Union__upper,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__upper) ).

fof(fact_fold__image__def,axiom,
    ! [X1,X2,X17,X5] : hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1) = c_Finite__Set_Ofold(X17,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X17),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__def) ).

fof(fact_max__Suc1,axiom,
    ! [X51,X89] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X89),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X89)),X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc1) ).

fof(fact_Field__Union,axiom,
    ! [X37,X5] : hAPP(c_Relation_OField(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X37)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Relation_OField(X5)),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Union) ).

fof(fact_Diff__partition,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__partition) ).

fof(fact_inj__mapI,axiom,
    ! [X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X17),hAPP(c_List_Omap(X5,X17),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__mapI) ).

fof(fact_Compl__Int,axiom,
    ! [X22,X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Int) ).

fof(fact_Compl__Un,axiom,
    ! [X22,X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Un) ).

fof(fact_peek__and__def,axiom,
    ! [X146,X158,X133,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X30,X133),X158),X146))
    <=> ( hBOOL(hAPP(hAPP(X30,X158),X146))
        & hBOOL(hAPP(X133,X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_peek__and__def) ).

fof(fact_conversep__iff,axiom,
    ! [X21,X6,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X17,X78),X6),X21))
    <=> hBOOL(hAPP(hAPP(X78,X21),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).

fof(fact_conversep_Oequations,axiom,
    ! [X34,X33,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X17,X78),X33),X34))
    <=> hBOOL(hAPP(hAPP(X78,X34),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversepD,axiom,
    ! [X21,X6,X78,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X17,X78),X6),X21))
     => hBOOL(hAPP(hAPP(X78,X21),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).

fof(fact_vimage__code,axiom,
    ! [X20,X19,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X5,X17,X2),X19),X20))
    <=> hBOOL(hAPP(X19,hAPP(X2,X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).

fof(fact_Inf__less__iff,axiom,
    ! [X6,X36,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Complete__Lattice_OInf__class_OInf(X5,X36)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_mult__number__of__left,axiom,
    ! [X58,X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)),X58)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X126))),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_add__number__of__left,axiom,
    ! [X58,X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X126))),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_add__number__of__diff1,axiom,
    ! [X59,X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)),X59)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X126))),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X106),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_nth__map,axiom,
    ! [X2,X17,X224,X5,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => hAPP(hAPP(c_List_Onth(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)),X89) = hAPP(X2,hAPP(hAPP(c_List_Onth(X5),X224),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X20),X24)))
     => ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X20,X24) = X20 )
        & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X20,X24) = c_Nitpick_Onat__gcd(X24,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_UnionI,axiom,
    ! [X19,X62,X40,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),X62))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X19),X40))
       => hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionI) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X60,X61,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X230,X262] : X224 = hAPP(hAPP(c_List_Oappend(X5),X230),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X262)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_sym__Int__converse,axiom,
    ! [X78,X5] : c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(c_Relation_Oconverse(X5,X5),X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Int__converse) ).

fof(fact_sym__Un__converse,axiom,
    ! [X78,X5] : c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),hAPP(c_Relation_Oconverse(X5,X5),X78))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Un__converse) ).

fof(fact_card__Un__disjoint,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_min__Suc1,axiom,
    ! [X51,X89] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X89)),X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = c_List_Oremove1(X5,X20,c_List_Olinorder__class_Osorted__list__of__set(X5,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X17)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X17),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_filter__sort,axiom,
    ! [X224,X2,X30,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(c_List_Ofilter(X5,X30),c_List_Olinorder__class_Osort__key(X5,X17,X2,X224)) = c_List_Olinorder__class_Osort__key(X5,X17,X2,hAPP(c_List_Ofilter(X5,X30),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__sort) ).

fof(fact_Pow__iff,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OPow(X5),X22)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__iff) ).

fof(fact_PowD,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OPow(X5),X22)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowD) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [X89,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20)),X89)))
    <=> ( X20 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

fof(fact_ivl__disj__un_I22_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X51,X102)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X51,X102)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X51,X102)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X51)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X51,X102)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_Un__upper1,axiom,
    ! [X22,X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [X19,X22,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper2) ).

fof(fact_r__into__rtrancl,axiom,
    ! [X78,X133,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),X78))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X133),c_Transitive__Closure_Ortrancl(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_card__Plus,axiom,
    ! [X22,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22))
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X17),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X22,X17,X19,X5] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X17),X22)) )
      & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X22)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X17)),c_Sum__Type_OPlus(X5,X17,X19,X22)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_sup__least,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__least) ).

fof(fact_le__supI,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),X55))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_Int__left__commute,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Un__left__commute,axiom,
    ! [X62,X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [X19,X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_Diff__idemp,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)),X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).

fof(fact_imageI,axiom,
    ! [X2,X17,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X20)),hAPP(c_Set_Oimage(X5,X17,X2),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [X13,X15,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => c_Finite__Set_Ofun__left__comm(X25,X17,hAPP(hAPP(c_COMBB(X5,tc_fun(X17,X17),X25),X2),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
    ! [X1,X25,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => c_Finite__Set_Ofun__left__comm__idem(X25,X17,hAPP(hAPP(c_COMBB(X5,tc_fun(X17,X17),X25),X2),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).

fof(fact_Int__insert__left__if1,axiom,
    ! [X22,X62,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X22,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X5,X17,X2),X19) = hAPP(c_Set_Oimage(X5,X17,X2),X22)
      <=> X19 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [X75,X23,X21,X6,X5,X17,X25] :
      ( hAPP(c_Fun_Ocomp(X25,X17,X5,X6),X21) = X23
     => hAPP(X6,hAPP(X21,X75)) = hAPP(X23,X75) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_negative__zless__0,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X92)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless__0) ).

fof(fact_nth__drop_H,axiom,
    ! [X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(hAPP(c_List_Onth(X56),X222),X98)),hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_OSuc,X98)),X222)) = hAPP(hAPP(c_List_Odrop(X56),X98),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop_H) ).

fof(fact_image__vimage__eq,axiom,
    ! [X19,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Ovimage(X17,X5,X2),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X51,X102)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [X19] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_psubset__card__mono,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_card__mono,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_UnI1,axiom,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [X19,X22,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI2) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(X5,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
       => c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_abs__less__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),X21))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

fof(fact_abs__le__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),X21))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

fof(fact_abs__leI,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

fof(fact_lists__accI,axiom,
    ! [X78,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X51)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X51),X102)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_div__mult__self2,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__mult__self1,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61))),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).

fof(fact_add__num__frac,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => ( X57 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),X57))),X57) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

fof(fact_setprod__reindex__id,axiom,
    ! [X22,X2,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( c_Fun_Oinj__on(X5,X17,X2,X22)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X22) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X17),c_Fun_Oid(X17)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_setsum__reindex__id,axiom,
    ! [X22,X2,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( c_Fun_Oinj__on(X5,X17,X2,X22)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X22) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X17),c_Fun_Oid(X17)),hAPP(c_Set_Oimage(X5,X17,X2),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_wf__comp__self,axiom,
    ! [X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
    <=> c_Wellfounded_Owf(X5,hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).

fof(fact_less__by__empty,axiom,
    ! [X22,X5,X19] :
      ( X19 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).

fof(fact_distinct__append,axiom,
    ! [X223,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Oappend(X5),X224),X223)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
        & hBOOL(hAPP(c_List_Odistinct(X5),X223))
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(c_List_Oset(X5),X223)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__append) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_min__max_OSup__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_setsum__head,axiom,
    ! [X30,X89,X51,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X30),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X30,X51)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X30),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X51,X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [X2,X89,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(c_Nat_OSuc,X89)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,X2),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X89),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_list__size__estimation,axiom,
    ! [X2,X24,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(X2,X20)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_List_Olist_Olist__size(X5,X2,X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation) ).

fof(fact_list__size__estimation_H,axiom,
    ! [X2,X24,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(X2,X20)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),c_List_Olist_Olist__size(X5,X2,X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [X232,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X232)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X232),X93)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X232))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_le__div__geq,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).

fof(fact_lists__accD,axiom,
    ! [X78,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X78))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X224),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [X89,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,hAPP(hAPP(c_COMBC(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_Groups_Oone__class_Oone(X5)),X89,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_impossible__Cons,axiom,
    ! [X55,X221,X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X221)))
     => X222 != hAPP(hAPP(c_List_Olist_OCons(X56),X55),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).

fof(fact_PowI,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OPow(X5),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowI) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [X89,X6,X115,X116,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X116,X115),X6),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(X115,X6),hAPP(hAPP(c_Power_Opower_Opower(X5,X116,X115),X6),X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_Min__antimono,axiom,
    ! [X41,X76,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X76),X41))
       => ( X76 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X41)),c_Big__Operators_Olinorder__class_OMin(X5,X76))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__antimono) ).

fof(fact_Max__mono,axiom,
    ! [X41,X76,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X76),X41))
       => ( X76 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X41))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMax(X5,X76)),c_Big__Operators_Olinorder__class_OMax(X5,X41))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__mono) ).

fof(fact_less__bin__lemma,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),X106)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_singletonE,axiom,
    ! [X6,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => X21 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).

fof(fact_singleton__iff,axiom,
    ! [X6,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
    <=> X21 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).

fof(fact_range__eqI,axiom,
    ! [X17,X5,X20,X2,X21] :
      ( X21 = hAPP(X2,X20)
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_snd__image__times,axiom,
    ! [X22,X17,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X17),X17,c_Product__Type_Osnd(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X17),X17,c_Product__Type_Osnd(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__image__times) ).

fof(fact_fst__image__times,axiom,
    ! [X19,X17,X5,X22] :
      ( ( X22 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X17,X5),X17,c_Product__Type_Ofst(X17,X5)),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X22))) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X17,X5),X17,c_Product__Type_Ofst(X17,X5)),hAPP(hAPP(c_Product__Type_OSigma(X17,X5),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),X22))) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__image__times) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X23),hAPP(hAPP(c_Set_Oinsert(X5),X27),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> ( ( X6 = X23
          & X21 = X27 )
        | ( X6 = X27
          & X21 = X23 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_nth__list__update,axiom,
    ! [X55,X94,X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => ( ( X98 = X94
         => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X94) = X55 )
        & ( X98 != X94
         => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X94) = hAPP(hAPP(c_List_Onth(X56),X222),X94) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update) ).

fof(fact_add__lessD1,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X93))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__leD1,axiom,
    ! [X92,X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X92,X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_diff__Suc__less,axiom,
    ! [X98,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_OSuc,X98))),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X51)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X51,X102)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [X90,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X95))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X90))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_insert__Diff__single,axiom,
    ! [X19,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X5),X6),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_card__insert__le,axiom,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_zadd__int__left,axiom,
    ! [X58,X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92))),X58),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).

fof(fact_less__Sup__iff,axiom,
    ! [X36,X6,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Complete__Lattice_OSup__class_OSup(X5,X36)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X36))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Sup__iff) ).

fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
    ! [X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X19))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20)),hAPP(c_Int_Onat,X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20)),hAPP(c_Int_Onat,X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)),hAPP(hAPP(c_Set_Oinsert(X5),X102),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_Min__eqI,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ! [X38] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X38),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X38)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
           => c_Big__Operators_Olinorder__class_OMin(X5,X19) = X20 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__eqI) ).

fof(fact_map__append,axiom,
    ! [X223,X224,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Oappend(X17),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),hAPP(hAPP(c_List_Omap(X17,X5),X2),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__append) ).

fof(fact_finite__Union,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X19))
     => ( ! [X153] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X153),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X153)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Union) ).

fof(fact_int__div__less__self,axiom,
    ! [X93,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X55),X93)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).

fof(fact_div__less__dividend,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),X86)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).

fof(fact_diff__less,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X86)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).

fof(fact_insert__inter__insert,axiom,
    ! [X22,X19,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_dvd__mod__iff,axiom,
    ! [X51,X89,X90,X5] :
      ( class_Divides_Osemiring__div(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X90),X89))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X90),c_Divides_Odiv__class_Omod(X5,X51,X89)))
        <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X90),X51)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).

fof(fact_dvd__mod__imp__dvd,axiom,
    ! [X92,X86,X93,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),c_Divides_Odiv__class_Omod(X56,X86,X92)))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),X92))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),X86)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Divides_Odiv__class_Omod(X56,X60,X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),X61)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X21)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_all__interval__int__def,axiom,
    ! [X95,X96,X30] :
      ( c_List_Oall__interval__int(X30,X96,X95)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__int__def) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_zadd__left__mono,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X98)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X94))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_div__le__mono,axiom,
    ! [X93,X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X93)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X92),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).

fof(fact_mult__le__mono1,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X94))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_add__le__mono1,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_diff__le__mono,axiom,
    ! [X91,X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X91)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X91))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [X91,X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X91),X92)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X91),X86))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X20),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [X86,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93))),X86) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_mod__div__equality2,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61))),c_Divides_Odiv__class_Omod(X56,X60,X61)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [X57,X98,X222,X55,X56] : hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),hAPP(c_Nat_OSuc,X98)),X57) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_pair__box_Oinject,axiom,
    ! [X181,X182,X21,X6,X17,X5] :
      ( c_Nitpick_Opair__box_OPairBox(X5,X17,X6,X21) = c_Nitpick_Opair__box_OPairBox(X5,X17,X182,X181)
    <=> ( X6 = X182
        & X21 = X181 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_vimageI,axiom,
    ! [X17,X22,X5,X21,X6,X2] :
      ( hAPP(X2,X6) = X21
     => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X22))
       => hBOOL(hAPP(hAPP(c_member(X17),X6),hAPP(c_Set_Ovimage(X17,X5,X2),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).

fof(fact_image__eqI,axiom,
    ! [X5,X19,X17,X20,X2,X21] :
      ( X21 = hAPP(X2,X20)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Set_Oimage(X17,X5,X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X17,X2,X21,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( X21 = hAPP(X2,X20)
       => hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(c_Set_Oimage(X5,X17,X2),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__on__iff,axiom,
    ! [X24,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
         => ( hAPP(X2,X20) = hAPP(X2,X24)
          <=> X20 = X24 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__on__contraD,axiom,
    ! [X24,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( X20 != X24
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
           => hAPP(X2,X20) != hAPP(X2,X24) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_inj__onD,axiom,
    ! [X24,X20,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( hAPP(X2,X20) = hAPP(X2,X24)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X19))
           => X20 = X24 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [X21,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X21)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X6))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_list__ex__length,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex(X5,X30,X224)
    <=> ? [X130] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
          & hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X130))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__length) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [X22,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(X2,hAPP(X18,X22)),hAPP(X18,X19)) = hAPP(X18,X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_part__equivp__def,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X37,X3),X3))
        & ! [X3,X38] :
            ( hBOOL(hAPP(hAPP(X37,X3),X38))
          <=> ( hBOOL(hAPP(hAPP(X37,X3),X3))
              & hBOOL(hAPP(hAPP(X37,X38),X38))
              & hAPP(X37,X3) = hAPP(X37,X38) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__def) ).

fof(fact_comp__equivI,axiom,
    ! [X19,X78,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X78)),X78) = X78
     => ( hAPP(c_Relation_ODomain(X5,X5),X78) = X19
       => c_Equiv__Relations_Oequiv(X5,X19,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__equivI) ).

fof(fact_zip__replicate,axiom,
    ! [X57,X94,X55,X98,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),c_List_Oreplicate(X56,X98,X55)),c_List_Oreplicate(X161,X94,X57)) = c_List_Oreplicate(tc_prod(X56,X161),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),X94),hAPP(hAPP(c_Product__Type_OPair(X56,X161),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__replicate) ).

fof(fact_com_Osize_I13_J,axiom,
    ! [X47,X48,X52] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X52,X48,X47)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X48)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X47))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I13_J) ).

fof(fact_le__funD,axiom,
    ! [X20,X1,X2,X5,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X20)),hAPP(X1,X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_le__funE,axiom,
    ! [X20,X1,X2,X5,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X2,X20)),hAPP(X1,X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_map__injective,axiom,
    ! [X223,X224,X2,X5,X17] :
      ( hAPP(hAPP(c_List_Omap(X17,X5),X2),X224) = hAPP(hAPP(c_List_Omap(X17,X5),X2),X223)
     => ( c_Fun_Oinj__on(X17,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
       => X224 = X223 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__injective) ).

fof(fact_inj__map__eq__map,axiom,
    ! [X223,X224,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(X5,X17),X2),X224) = hAPP(hAPP(c_List_Omap(X5,X17),X2),X223)
      <=> X224 = X223 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_nth__list__update__eq,axiom,
    ! [X55,X222,X56,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X98) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [X89,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89))),hAPP(X2,hAPP(c_Nat_OSuc,X89))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_sym__Int,axiom,
    ! [X146,X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => ( c_Relation_Osym(X5,X146)
       => c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Int) ).

fof(fact_sym__Un,axiom,
    ! [X146,X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => ( c_Relation_Osym(X5,X146)
       => c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Un) ).

fof(fact_trans__Int,axiom,
    ! [X146,X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => ( c_Relation_Otrans(X5,X146)
       => c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X51))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),X102))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X51)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X51),X102)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_butlast__conv__take,axiom,
    ! [X222,X56] : c_List_Obutlast(X56,X222) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_fold1__belowI,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X19)),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__belowI) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19)),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_sorted_OCons,axiom,
    ! [X20,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X3)) )
       => ( c_List_Olinorder__class_Osorted(X5,X224)
         => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_OCons) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [X34,X33,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X33),X34))
      <=> ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X34)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X3)) )
          & c_List_Olinorder__class_Osorted(X5,X34) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__Cons,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))
      <=> ( c_List_Olinorder__class_Osorted(X5,X224)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__Cons) ).

fof(fact_int__power__div__base,axiom,
    ! [X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X86))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X86)),X93) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power__div__base) ).

fof(fact_divide__pos__pos,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_mult__pos__pos,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__semiring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_less__1__mult,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X86))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X92))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X86),X92))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__cancel__semiring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__ring(X56)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56))) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hAPP(c_Finite__Set_Ocard(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = hAPP(c_Finite__Set_Ocard(X5),X19)
       => c_Fun_Oinj__on(X5,X17,X2,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X17,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( c_Fun_Oinj__on(X5,X17,X2,X19)
      <=> hAPP(c_Finite__Set_Ocard(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = hAPP(c_Finite__Set_Ocard(X5),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [X22,X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [X61,X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
             => X60 = X61 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_card__cartesian__product,axiom,
    ! [X22,X19,X17,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),hAPP(c_Finite__Set_Ocard(X17),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [X22,X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [X5,X223,X224] :
      ( X224 = X223
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X223)
        & ! [X88] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => hAPP(hAPP(c_List_Onth(X5),X224),X88) = hAPP(hAPP(c_List_Onth(X5),X223),X88) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [X146,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(X18,X19),X146) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X146),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_weaken,axiom,
    ! [X13,X66,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X66)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X66))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_weaken) ).

fof(fact_thin,axiom,
    ! [X4,X13,X14,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X14,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X14),X4))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_thin) ).

fof(fact_le__SUPI,axiom,
    ! [X76,X19,X96,X5,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17),hAPP(X76,X96)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X19),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SUPI) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__add__left__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),c_Divides_Odiv__class_Omod(X56,X60,X59)),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
        & X19 != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
        | X19 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_finite__UnI,axiom,
    ! [X4,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X18),X4))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnI) ).

fof(fact_Pow__Int__eq,axiom,
    ! [X22,X19,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)),hAPP(c_Set_OPow(X5),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_finite__maxlen,axiom,
    ! [X76,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),X76))
     => ? [X130] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),X76))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X3)),X130)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__maxlen) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Oplus__class_Oplus(X17)),X1),c_Groups_Ozero__class_Ozero(X17)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_append__replicate__commute,axiom,
    ! [X93,X55,X92,X56] : hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X92,X55)),c_List_Oreplicate(X56,X93,X55)) = hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X93,X55)),c_List_Oreplicate(X56,X92,X55)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__replicate__commute) ).

fof(fact_mod__pos__neg,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_ex__nat__less,axiom,
    ! [X30,X89] :
      ( ? [X99] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X89))
          & hBOOL(hAPP(X30,X99)) )
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X89)))
          & hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [X222,X55,X56,X122] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Odrop(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [X20,X30] :
      ( ! [X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg))
         => hBOOL(hAPP(X30,hAPP(c_Int_OAbs__Integ,X38))) )
     => hBOOL(hAPP(X30,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_wf__Int1,axiom,
    ! [X157,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X78),X157)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [X157,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X157),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int2) ).

fof(fact_div__pos__neg,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg) ).

fof(fact_fold1__set,axiom,
    ! [X224,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X224 != c_List_Olist_ONil(X5)
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_List_Oset(X5),X224)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Ohd(X5),X224)),hAPP(c_List_Otl(X5),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__set) ).

fof(fact_drop__zip,axiom,
    ! [X221,X222,X92,X161,X56] : hAPP(hAPP(c_List_Odrop(tc_prod(X56,X161)),X92),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)) = hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Odrop(X56),X92),X222)),hAPP(hAPP(c_List_Odrop(X161),X92),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__zip) ).

fof(fact_take__zip,axiom,
    ! [X221,X222,X92,X161,X56] : hAPP(hAPP(c_List_Otake(tc_prod(X56,X161)),X92),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)) = hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(hAPP(c_List_Otake(X56),X92),X222)),hAPP(hAPP(c_List_Otake(X161),X92),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__zip) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102)),hAPP(hAPP(c_Set_Oinsert(X5),X102),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_mod__neg__neg,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [X146,X25,X78,X17,X5] :
      ( c_Relation_Osingle__valued(X5,X17,X78)
     => ( c_Relation_Osingle__valued(X17,X25,X146)
       => c_Relation_Osingle__valued(X5,X25,hAPP(hAPP(c_Relation_Orel__comp(X5,X17,X25),X78),X146)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_sorted__transpose,axiom,
    ! [X224,X5] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X224)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__transpose) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X23,X27)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X6,X21)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X23,X27)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_set__rev__mp,axiom,
    ! [X22,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X20),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_psubsetD,axiom,
    ! [X23,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_in__mono,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X20),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_set__mp,axiom,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X20),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_subsetD,axiom,
    ! [X23,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_nth__append__length,axiom,
    ! [X221,X55,X222,X56] : hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X221))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length) ).

fof(fact_div__neg__neg,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X41,X90] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X90),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_times__divide__times__eq,axiom,
    ! [X126,X58,X57,X55,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X58),X126)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X80,X81,X82,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X82),X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X73,X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X73)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X80,X81,X82,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X82),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_sorted__map__remove1,axiom,
    ! [X20,X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Oremove1(X17,X20,X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_Domain__Union,axiom,
    ! [X36,X17,X5] : hAPP(c_Relation_ODomain(X5,X17),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),X36)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X5,X17),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X36),c_Relation_ODomain(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Union) ).

fof(fact_Range__Union,axiom,
    ! [X36,X5,X17] : hAPP(c_Relation_ORange(X17,X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),X36)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X17,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X36),c_Relation_ORange(X17,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Union) ).

fof(fact_all__nat__less,axiom,
    ! [X30,X89] :
      ( ! [X99] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X89))
         => hBOOL(hAPP(X30,X99)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X89)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).

fof(fact_Ints__power,axiom,
    ! [X89,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X89)),c_Int_Oring__1__class_OInts(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__power) ).

fof(fact_Collect__mem__eq,axiom,
    ! [X19,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_nat__one__le__power,axiom,
    ! [X92,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_all__interval__nat__def,axiom,
    ! [X95,X96,X30] :
      ( c_List_Oall__interval__nat(X30,X96,X95)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__nat__def) ).

fof(fact_one__less__power,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

fof(fact_divide__neg__neg,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__neg__neg,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__ring__strict(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X57,X55,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__ring(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [X89,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))),hAPP(X2,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [X91,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_Divides_OposDivAlg(X93,X91) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X91)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [X96,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_lex__def,axiom,
    ! [X78,X5] : c_List_Olex(X5,X78) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lex__def) ).

fof(fact_less__max__iff__disj,axiom,
    ! [X24,X20,X26,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),X24)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),X20))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_le__max__iff__disj,axiom,
    ! [X24,X20,X26,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),X24)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X26),X20))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X26),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_select__weigth__select,axiom,
    ! [X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X224)) = c_Random_Oselect(X5,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__select) ).

fof(fact_finite__Inter,axiom,
    ! [X76,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X76))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X76))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Inter) ).

fof(fact_abs__eq__mult,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oordered__ring__abs(X56)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),c_Groups_Ozero__class_Ozero(X56))) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_butlast__take,axiom,
    ! [X222,X56,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => c_List_Obutlast(X56,hAPP(hAPP(c_List_Otake(X56),X92),X222)) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__take) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [X90,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X90),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X90)) = hAPP(hAPP(c_Set_Oinsert(X5),X90),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => ! [X63] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X63),X22))
             => X3 != X63 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_insort__remove1,axiom,
    ! [X224,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X224)))
       => ( c_List_Olinorder__class_Osorted(X5,X224)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X6),c_List_Oremove1(X5,X6,X224)) = X224 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__remove1) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [X91,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_Divides_OnegDivAlg(X93,X91) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X91)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X22)),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X22)),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X22)),c_Big__Operators_Olinorder__class_OMax(X5,X19)) = c_Big__Operators_Olinorder__class_OMax(X5,X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X22)),c_Big__Operators_Olinorder__class_OMin(X5,X19)) = c_Big__Operators_Olinorder__class_OMin(X5,X19) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_zpower__zmod,axiom,
    ! [X57,X86,X55] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X86)),X57),X86) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X57),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [X57,X86,X55] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X86)),X57),X86) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X57),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_le__Inf__iff,axiom,
    ! [X19,X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),c_Complete__Lattice_OInf__class_OInf(X5,X19)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_take__Cons_H,axiom,
    ! [X222,X55,X56,X92] :
      ( ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X56),X92),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = c_List_Olist_ONil(X56) )
      & ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X56),X92),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons_H) ).

fof(fact_inf1I,axiom,
    ! [X5,X22,X20,X19] :
      ( hBOOL(hAPP(X19,X20))
     => ( hBOOL(hAPP(X22,X20))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).

fof(fact_list__ex__iff__raw,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex(X5,X30,X224)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).

fof(fact_Bex__set__list__ex,axiom,
    ! [X30,X224,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(X30,X3)) )
    <=> c_List_Olist__ex(X5,X30,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).

fof(fact_list__ex__iff,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex(X5,X30,X224)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff) ).

fof(fact_Rep__Integ,axiom,
    ! [X20] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X20)),c_Int_OInteg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [X22,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(X2,hAPP(X18,X19)),hAPP(X18,X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [X224,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X19),X224))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X19,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_pos__add__strict,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__increasing,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X59))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X60,X61,X59,X56] :
      ( class_Groups_Oordered__comm__monoid__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X59))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [X61,X60] : X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_less__infI1,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [X60,X55,X61,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [X60,X55,X61,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_le__infI1,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [X60,X55,X61,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [X61,X55,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [X60,X55,X61,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_listrel__Nil,axiom,
    ! [X78,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X78)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil) ).

fof(fact_setprod__eq__1__iff,axiom,
    ! [X2,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X18) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X18))
           => hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__eq__1__iff) ).

fof(fact_setsum__eq__0__iff,axiom,
    ! [X2,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X18))
           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).

fof(fact_Babs__def,axiom,
    ! [X51,X17,X133,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X133))
     => hAPP(c_Quotient_OBabs(X5,X17,X133,X51),X20) = hAPP(X51,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Babs__def) ).

fof(fact_nat__diff__split,axiom,
    ! [X21,X6,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X21)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X21))
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X121] :
            ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X121)
           => hBOOL(hAPP(X30,X121)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(fact_dvd__div__mult,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X61),X60)),X59) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)),X60) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult) ).

fof(fact_finite__compl,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__compl) ).

fof(fact_less__nat__number__of,axiom,
    ! [X167,X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X75),X167))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X167)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X75),X167)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_Un__insert__left,axiom,
    ! [X62,X22,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__left) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [X20,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X2,X20)),hAPP(X2,X20)) = hAPP(X2,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_com_Osize_I12_J,axiom,
    ! [X138,X139] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X139,X138)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X139)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X138))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I12_J) ).

fof(fact_derivs__insertD,axiom,
    ! [X13,X15,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),X13))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_derivs__insertD) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = X119 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_snd__def,axiom,
    ! [X133,X5,X17] : hAPP(c_Product__Type_Osnd(X17,X5),X133) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X5,X5),hAPP(c_COMBK(tc_fun(X5,X5),X17),c_COMBI(X5))),X133),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__def) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [X6,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X6)),X6) != c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_finite__Int,axiom,
    ! [X4,X18,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X18),X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Int) ).

fof(fact_finite__Diff,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff) ).

fof(fact_sorted__many__eq,axiom,
    ! [X228,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X228)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X24),X228)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_sorted__many,axiom,
    ! [X237,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( c_List_Olinorder__class_Osorted(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X57),X237))
         => c_List_Olinorder__class_Osorted(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Olist_OCons(X56),X57),X237))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many) ).

fof(fact_mod__eq,axiom,
    ! [X119,X107,X92,X86] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X107),X119)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = X119 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).

fof(fact_pos__mod__conj,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_pos__mod__bound,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_mod__less__divisor,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X93)),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_mod__le__divisor,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_length__remdups__leq,axiom,
    ! [X222,X56] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),c_List_Oremdups(X56,X222))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_card__length,axiom,
    ! [X224,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__length) ).

fof(fact_image__Pow__surj,axiom,
    ! [X22,X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),X19) = X22
     => hAPP(c_Set_Oimage(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X17,X5,X2)),hAPP(c_Set_OPow(X17),X19)) = hAPP(c_Set_OPow(X5),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_Set_Ovimage(X17,X5,X2),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [X119,X107,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = X107 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_minus__less__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X21))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_abs__le__D2,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

fof(fact_minus__le__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X21))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_neg__mod__conj,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_neg__mod__sign,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__sign) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [X30,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(c_Set_OCollect(X17),X30)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X17,tc_HOL_Obool,X5),X30),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_div__eq,axiom,
    ! [X119,X107,X92,X86] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X107),X119)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = X107 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).

fof(fact_card__image,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => hAPP(c_Finite__Set_Ocard(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = hAPP(c_Finite__Set_Ocard(X5),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_take__drop,axiom,
    ! [X222,X86,X92,X56] : hAPP(hAPP(c_List_Otake(X56),X92),hAPP(hAPP(c_List_Odrop(X56),X86),X222)) = hAPP(hAPP(c_List_Odrop(X56),X86),hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__drop) ).

fof(fact_sorted__filter,axiom,
    ! [X30,X224,X2,X17,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Ofilter(X17,X30),X224))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__filter) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [X57,X92,X55] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X55,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,X92)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X55))
       => ? [X144] : X55 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X144)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [X224,X30,X5] :
      ( c_List_OtakeWhile(X5,X30,X224) = X224
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_Ball__set__list__all,axiom,
    ! [X30,X224,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) )
    <=> c_List_Olist__all(X5,X30,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__all(X5,X30,X224)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__all__iff,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__all(X5,X30,X224)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff) ).

fof(fact_add__gr__0,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X51))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_asm,axiom,
    ! [X4,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X4))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_asm) ).

fof(fact_mod__mult__cong,axiom,
    ! [X137,X61,X140,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( c_Divides_Odiv__class_Omod(X56,X60,X59) = c_Divides_Odiv__class_Omod(X56,X140,X59)
       => ( c_Divides_Odiv__class_Omod(X56,X61,X59) = c_Divides_Odiv__class_Omod(X56,X137,X59)
         => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X140),X137),X59) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_mod__add__cong,axiom,
    ! [X137,X61,X140,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( c_Divides_Odiv__class_Omod(X56,X60,X59) = c_Divides_Odiv__class_Omod(X56,X140,X59)
       => ( c_Divides_Odiv__class_Omod(X56,X61,X59) = c_Divides_Odiv__class_Omod(X56,X137,X59)
         => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X140),X137),X59) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).

fof(fact_mod__diff__cong,axiom,
    ! [X137,X61,X140,X59,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => ( c_Divides_Odiv__class_Omod(X56,X60,X59) = c_Divides_Odiv__class_Omod(X56,X140,X59)
       => ( c_Divides_Odiv__class_Omod(X56,X61,X59) = c_Divides_Odiv__class_Omod(X56,X137,X59)
         => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X140),X137),X59) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_dvd__mod,axiom,
    ! [X92,X86,X93,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),X86))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),X92))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X93),c_Divides_Odiv__class_Omod(X56,X86,X92))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod) ).

fof(fact_power__diff,axiom,
    ! [X86,X92,X60,X56] :
      ( class_Fields_Ofield(X56)
     => ( X60 != c_Groups_Ozero__class_Ozero(X56)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [X185,X61,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)),X185))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(c_Divides_OnegateSnd,X185))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_insert__Diff1,axiom,
    ! [X19,X22,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [X92,X86,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X86))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X93)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X93)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [X224,X30,X5] : c_List_OtakeWhile(X5,X30,X224) = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [X30,X89] :
      ( ? [X99] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X89))
          & hBOOL(hAPP(X30,X99)) )
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)))
          & hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_Suc__diff__diff,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92)),hAPP(c_Nat_OSuc,X93)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_power__inject__base,axiom,
    ! [X61,X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),hAPP(c_Nat_OSuc,X92))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X61))
           => X60 = X61 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).

fof(fact_bex__reg__eqv,axiom,
    ! [X30,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Quotient_ORespects(X5,X37)))
            & hBOOL(hAPP(X30,X3)) )
      <=> ? [X77] : hBOOL(hAPP(X30,X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__reg__eqv) ).

fof(fact_int__zle__neg,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51))))
    <=> ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__zle__neg) ).

fof(fact_wf,axiom,
    ! [X5] :
      ( class_Orderings_Owellorder(X5)
     => c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf) ).

fof(fact_min__less__iff__conj,axiom,
    ! [X24,X20,X26,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),X24)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),X20))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X26),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_inf__greatest,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).

fof(fact_le__infI,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).

fof(fact_le__inf__iff,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X24),X26)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [X26,X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X26)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_self__quotient__aux2,axiom,
    ! [X107,X119,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X107))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_filter__id__conv,axiom,
    ! [X224,X30,X5] :
      ( hAPP(c_List_Ofilter(X5,X30),X224) = X224
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__id__conv) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X57))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_nth__append__length__plus,axiom,
    ! [X92,X221,X222,X56] : hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92)) = hAPP(hAPP(c_List_Onth(X56),X221),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [X226,X6,X149,X28,X17,X5] : hAPP(c_List_Olist_Olist__case(X5,X17,X28,X149),hAPP(hAPP(c_List_Olist_OCons(X17),X6),X226)) = hAPP(hAPP(X149,X6),X226),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_sup1I1,axiom,
    ! [X22,X5,X20,X19] :
      ( hBOOL(hAPP(X19,X20))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [X19,X5,X20,X22] :
      ( hBOOL(hAPP(X22,X20))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I2) ).

fof(fact_zero__le__power__abs,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [X86,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),hAPP(c_Nat_OSuc,X94)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_subset__empty,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).

fof(fact_wfP__acyclicP,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_OwfP(X5,X78)
     => c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_rel__comp__empty1,axiom,
    ! [X37,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X25),tc_HOL_Obool))),X37) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [X60,X61] :
      ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60)),X61) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60)),X61) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).

fof(fact_neg__less__iff__less,axiom,
    ! [X6,X21,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X6,X21,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_all__nat__less__eq,axiom,
    ! [X30,X89] :
      ( ! [X99] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X89))
         => hBOOL(hAPP(X30,X99)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)))
         => hBOOL(hAPP(X30,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_power__gt1,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).

fof(fact__05,axiom,
    ! [X2,X254,X5,X17] : hAPP(c_Lazy__Sequence_Obind(X17,X5,X254),X2) = c_Lazy__Sequence_Oflat(X5,c_Lazy__Sequence_Omap(X17,tc_Lazy__Sequence_Olazy__sequence(X5),X2,X254)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__05) ).

fof(fact_self__quotient__aux1,axiom,
    ! [X107,X119,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X107))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X107)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_conversep_Ointros,axiom,
    ! [X17,X5,X21,X6,X78] :
      ( hBOOL(hAPP(hAPP(X78,X6),X21))
     => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X17,X78),X21),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_less__number__of,axiom,
    ! [X24,X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_le__number__of,axiom,
    ! [X24,X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_list__update__beyond,axiom,
    ! [X55,X98,X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X98))
     => hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__beyond) ).

fof(fact_le__cube,axiom,
    ! [X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X86)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

fof(fact_in__set__butlastD,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X224))))
     => hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_insert__image,axiom,
    ! [X2,X17,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hAPP(hAPP(c_Set_Oinsert(X17),hAPP(X2,X20)),hAPP(c_Set_Oimage(X5,X17,X2),X19)) = hAPP(c_Set_Oimage(X5,X17,X2),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_self__quotient,axiom,
    ! [X119,X107,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X60),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X60 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X107 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient) ).

fof(fact_self__remainder,axiom,
    ! [X119,X107,X60] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X60),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)))
     => ( X60 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X119 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__remainder) ).

fof(fact_wf__exp,axiom,
    ! [X37,X89,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37))
     => c_Wellfounded_Owf(X5,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__exp) ).

fof(fact_of__int__less__iff,axiom,
    ! [X26,X84,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X84)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__nat__less__iff,axiom,
    ! [X89,X51,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X51)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_of__int__le__iff,axiom,
    ! [X26,X84,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X84)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_of__nat__le__iff,axiom,
    ! [X89,X51,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X51)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_nonzero__power__divide,axiom,
    ! [X92,X60,X61,X56] :
      ( class_Fields_Ofield(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)),X92) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X58,X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),c_Groups_Oone__class_Oone(tc_Int_Oint))),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),c_Big__Operators_Olattice__class_OInf__fin(X5,X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [X22,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)),c_Big__Operators_Olattice__class_OSup__fin(X5,X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Min__Un,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),c_Big__Operators_Olinorder__class_OMin(X5,X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__Un) ).

fof(fact_Max__Un,axiom,
    ! [X22,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
           => ( X22 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X19)),c_Big__Operators_Olinorder__class_OMax(X5,X22)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__Un) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [X221,X57,X222,X55,X56] : c_List_Osplice(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X57),X221)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Olist_OCons(X56),X57),c_List_Osplice(X56,X222,X221))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,X20) = hAPP(c_Code__Numeral_Oof__nat,X24)
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_nat__mono__iff,axiom,
    ! [X84,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X84)),hAPP(c_Int_Onat,X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X84)),hAPP(c_Int_Onat,X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [X26,X84] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X84)),hAPP(c_Int_Onat,X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_funpow__swap1,axiom,
    ! [X20,X89,X5,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X89),X2),X20)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X89),X2),hAPP(X2,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X61,X86,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_add__divide__distrib,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_diff__divide__distrib,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X59)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Lattices_Odistrib__lattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)),X55) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X55)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X58),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_power__divide,axiom,
    ! [X92,X61,X60,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)),X92) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

fof(fact_power__mult__distrib,axiom,
    ! [X92,X61,X60,X56] :
      ( class_Groups_Ocomm__monoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X61),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [X107,X57,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X57)),X107) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X107)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Lattices_Odistrib__lattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)),X55) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X55)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X58),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58)),X55) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X55)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X58),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [X55,X58,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)),X55) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X55)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X58),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_max__add__distrib__left,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_min__add__distrib__left,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Groups_Oordered__ab__group__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),X58)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Groups_Oordered__ab__group__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),X58)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_set__insort,axiom,
    ! [X224,X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X51))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X55),X57))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X57))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),X57))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_dvd__div__div__eq__mult,axiom,
    ! [X27,X21,X23,X6,X5] :
      ( class_Divides_Osemiring__div(X5)
     => ( X6 != c_Groups_Ozero__class_Ozero(X5)
       => ( X23 != c_Groups_Ozero__class_Ozero(X5)
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21))
           => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X23),X27))
             => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X21),X6) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X27),X23)
              <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X27) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X106),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X106)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X106) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_finite__converse,axiom,
    ! [X78,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),hAPP(c_Relation_Oconverse(X17,X5),X78)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X17,X5)),X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__converse) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_set__remove1__eq,axiom,
    ! [X20,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X20,X224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remove1__eq) ).

fof(fact_Int__Union,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union) ).

fof(fact_Un__Inter,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X22)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X22),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Inter) ).

fof(fact_length__insort,axiom,
    ! [X224,X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__insort) ).

fof(fact_nat__less__iff,axiom,
    ! [X51,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X84)),X51))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__iff) ).

fof(fact_remove1__insort,axiom,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Oremove1(X5,X20,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),X224)) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__insort) ).

fof(fact_Powp__def,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,X19),X22))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X22))
         => hBOOL(hAPP(X19,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).

fof(fact_split__curry,axiom,
    ! [X2,X25,X17,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),c_Product__Type_Ocurry(X5,X17,X25,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).

fof(fact_eq__number__of__eq,axiom,
    ! [X24,X20,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X20) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [X228,X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = X228
    <=> ( X224 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),X228)
        & X223 = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),X228) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [X60,X61] :
      ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

fof(fact_singleton__conv,axiom,
    ! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv) ).

fof(fact_insert__is__Un,axiom,
    ! [X19,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__is__Un) ).

fof(fact_nat__of__induct,axiom,
    ! [X30,X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( ! [X3] : hBOOL(hAPP(X30,hAPP(c_Code__Numeral_Onat__of,X3)))
       => hBOOL(hAPP(X30,X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__induct) ).

fof(fact_less__imp__diff__less,axiom,
    ! [X92,X93,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),X93))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X92)),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_add__diff__assoc2,axiom,
    ! [X98,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93)),X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X98)),X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [X98,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X98)),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_Int__absorb2,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).

fof(fact_Un__absorb1,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb1) ).

fof(fact_subset__Un__eq,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb2,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X30,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_drop__all,axiom,
    ! [X92,X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92))
     => hAPP(hAPP(c_List_Odrop(X56),X92),X222) = c_List_Olist_ONil(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [X224,X89,X5] :
      ( hAPP(hAPP(c_List_Odrop(X5),X89),X224) = c_List_Olist_ONil(X5)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_insert__iff,axiom,
    ! [X19,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),X19)))
    <=> ( X6 = X21
        | hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X19,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),X19)))
     => ( X6 != X21
       => hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_take__all,axiom,
    ! [X92,X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92))
     => hAPP(hAPP(c_List_Otake(X56),X92),X222) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__all) ).

fof(fact_ivl__diff,axiom,
    ! [X51,X89,X96,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X96),X89))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X96),X51)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X96),X89)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X89),X51) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__diff) ).

fof(fact_accp_Oequations,axiom,
    ! [X6,X78,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X78,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).

fof(fact_accp_Osimps,axiom,
    ! [X6,X78,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X78,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).

fof(fact_Times__empty,axiom,
    ! [X22,X19,X17,X5] :
      ( hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X22)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool))
    <=> ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X22 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__empty) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X102)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X106) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X102)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X106) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X102)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X106) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_Sup__set__fold,axiom,
    ! [X224,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_List_Oset(X5),X224)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Obot__class_Obot(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [X224,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_List_Oset(X5),X224)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Otop__class_Otop(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X106,X102)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),X106)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_finite__imageI,axiom,
    ! [X16,X17,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_Oimage(X5,X17,X16),X18))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_Sup__binary,axiom,
    ! [X21,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__binary) ).

fof(fact_Inf__binary,axiom,
    ! [X21,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__binary) ).

fof(fact_div__mult__swap,axiom,
    ! [X60,X61,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X59),X61))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X61),X59)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X59) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__swap) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [X90,X105,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OlessThan(X5,X105,X90)))
    <=> hBOOL(hAPP(hAPP(X105,X96),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [X90,X104,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OatMost(X5,X104,X90)))
    <=> hBOOL(hAPP(hAPP(X104,X96),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [X90,X105,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OgreaterThan(X5,X105,X90)))
    <=> hBOOL(hAPP(hAPP(X105,X90),X96)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [X90,X104,X96,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X96),c_SetInterval_Oord_OatLeast(X5,X104,X90)))
    <=> hBOOL(hAPP(hAPP(X104,X90),X96)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_partition__set,axiom,
    ! [X255,X256,X224,X30,X5] :
      ( c_List_Opartition(X5,X30,X224) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X256),X255)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X256)),hAPP(c_List_Oset(X5),X255)) = hAPP(c_List_Oset(X5),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__set) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [X222,X55,X56,X122] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = X55 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(hAPP(c_List_Onth(X56),X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).

fof(fact_r__comp__rtrancl__eq,axiom,
    ! [X78,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X78),c_Transitive__Closure_Ortrancl(X5,X78)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X78)),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(help_c__COMBS__1,axiom,
    ! [X37,X29,X30,X5,X25,X17] : hAPP(hAPP(hAPP(c_COMBS(X17,X25,X5),X30),X29),X37) = hAPP(hAPP(X30,X37),hAPP(X29,X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60))),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_Un__insert__right,axiom,
    ! [X22,X6,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24)) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
          & X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_union__fold__insert,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),X22),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__fold__insert) ).

fof(fact_eq__special_I3_J,axiom,
    ! [X20,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X20) = c_Groups_Ozero__class_Ozero(X5)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).

fof(fact_eq__special_I1_J,axiom,
    ! [X24,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_trans__lex__prod,axiom,
    ! [X188,X17,X189,X5] :
      ( c_Relation_Otrans(X5,X189)
     => ( c_Relation_Otrans(X17,X188)
       => c_Relation_Otrans(tc_prod(X5,X17),c_Wellfounded_Olex__prod(X5,X17,X189,X188)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).

fof(fact_wf__lex__prod,axiom,
    ! [X204,X17,X205,X5] :
      ( c_Wellfounded_Owf(X5,X205)
     => ( c_Wellfounded_Owf(X17,X204)
       => c_Wellfounded_Owf(tc_prod(X5,X17),c_Wellfounded_Olex__prod(X5,X17,X205,X204)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_distinct__zipI1,axiom,
    ! [X221,X161,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_distinct__zipI2,axiom,
    ! [X222,X161,X221,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X221))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X161,X56)),hAPP(hAPP(c_List_Ozip(X161,X56),X222),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_vimage__Union,axiom,
    ! [X19,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X19),c_Set_Ovimage(X5,X17,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Union) ).

fof(fact_image__Union,axiom,
    ! [X36,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17,tc_HOL_Obool),X36)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X36),c_Set_Oimage(X17,X5,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Union) ).

fof(fact_Pow__bottom,axiom,
    ! [X22,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),hAPP(c_Set_OPow(X5),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__bottom) ).

fof(fact_listsum__0,axiom,
    ! [X224,X17,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X17,X5),hAPP(c_COMBK(X5,X17),c_Groups_Ozero__class_Ozero(X5))),X224)) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__0) ).

fof(fact_Int__left__absorb,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Un__left__absorb,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_rotate1__length01,axiom,
    ! [X222,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(X56),X222) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__length01) ).

fof(fact_fold__image__empty,axiom,
    ! [X26,X1,X2,X17,X5] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1),X26),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__empty) ).

fof(fact_mult__eq__if,axiom,
    ! [X92,X86] :
      ( ( X86 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X86 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).

fof(fact_listsp__inf__eq,axiom,
    ! [X22,X19,X5] : c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X19)),c_List_Olistsp(X5,X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_triple_Orecs,axiom,
    ! [X10,X11,X12,X28,X5,X17] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X17,X5,X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17),X12),X11),X10)) = hAPP(hAPP(hAPP(X28,X12),X11),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Orecs) ).

fof(fact_triple_Osimps_I2_J,axiom,
    ! [X10,X11,X12,X28,X5,X17] : c_Hoare__Mirabelle_Otriple_Otriple__case(X17,X5,X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17),X12),X11),X10)) = hAPP(hAPP(hAPP(X28,X12),X11),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).

fof(fact_RangeP_Oequations,axiom,
    ! [X33,X78,X17,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X17,X78),X33))
    <=> ? [X49] : hBOOL(hAPP(hAPP(X78,X49),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [X131,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X131))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [X61,X60,X161,X56] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X56,X161)),c_Nitpick_Opair__box_OPairBox(X56,X161,X60,X61)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osize_I2_J) ).

fof(fact_butlast__list__update,axiom,
    ! [X55,X222,X56,X93] :
      ( ( X93 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X93),X55)) = c_List_Obutlast(X56,X222) )
      & ( X93 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X93),X55)) = hAPP(hAPP(c_List_Olist__update(X56,c_List_Obutlast(X56,X222)),X93),X55) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__list__update) ).

fof(fact_image__insert,axiom,
    ! [X22,X6,X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),hAPP(hAPP(c_Set_Oinsert(X17),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),hAPP(X2,X6)),hAPP(c_Set_Oimage(X17,X5,X2),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).

fof(fact_finite__subset,axiom,
    ! [X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X19,X22,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_length__sort,axiom,
    ! [X224,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Olinorder__class_Osort__key(X5,X17,X2,X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sort) ).

fof(fact_zip__rev,axiom,
    ! [X221,X161,X222,X56] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X221)
     => hAPP(hAPP(c_List_Ozip(X56,X161),hAPP(c_List_Orev(X56),X222)),hAPP(c_List_Orev(X161),X221)) = hAPP(c_List_Orev(tc_prod(X56,X161)),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__rev) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [X89,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20),X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
        | X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X23)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [X27,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X27)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [X57,X222,X55,X56] : hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = hAPP(hAPP(c_List_Olist_OCons(X56),X57),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).

fof(help_c__COMBC__1,axiom,
    ! [X37,X29,X30,X5,X25,X17] : hAPP(hAPP(hAPP(c_COMBC(X17,X25,X5),X30),X29),X37) = hAPP(hAPP(X30,X37),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBB__1,axiom,
    ! [X37,X29,X30,X25,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X25),X30),X29),X37) = hAPP(X30,hAPP(X29,X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_vimage__Compl,axiom,
    ! [X19,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X17,X2),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Compl) ).

fof(fact_mod__mult__self3,axiom,
    ! [X86,X92,X93] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)),X86),X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),hAPP(c_Int_Onat,X57)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),hAPP(c_Int_Onat,X57)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),hAPP(c_Int_Onat,X57)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_nat__add__distrib,axiom,
    ! [X131,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),X131)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X58)),hAPP(c_Int_Onat,X131)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_finite__nonempty__imp__fold1Set,axiom,
    ! [X2,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ? [X77] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,X19),X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nonempty__imp__fold1Set) ).

fof(fact_length__zip,axiom,
    ! [X221,X222,X161,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X56,X161))),hAPP(hAPP(c_List_Ozip(X56,X161),X222),X221)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X161)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__zip) ).

fof(fact_Union__image__eq,axiom,
    ! [X19,X22,X17,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__image__eq) ).

fof(fact_Inter__image__eq,axiom,
    ! [X19,X22,X17,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [X22,X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X17,tc_fun(X5,tc_HOL_Obool),X22),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [X96,X89,X134,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X134,hAPP(c_Nat_OSuc,X89),X96) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X134,X89,hAPP(X134,X96)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X55),hAPP(c_Int_Onat,X57)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__mod__distrib,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X57)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X55),hAPP(c_Int_Onat,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X92)),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_zero__less__power,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_zero__le__power,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(fact_one__le__power,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Oone__class_Oone(X56)),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(fact_image__constant,axiom,
    ! [X23,X17,X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hAPP(c_Set_Oimage(X5,X17,hAPP(c_COMBK(X17,X5),X23)),X19) = hAPP(hAPP(c_Set_Oinsert(X17),X23),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant) ).

fof(fact_zless__nat__conj,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X84)),hAPP(c_Int_Onat,X26)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_zless__add1__eq,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26))
        | X84 = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_neg__less__nonneg,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X6))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_minus__le__self__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X6))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_append__in__listsp__conv,axiom,
    ! [X223,X224,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X19),hAPP(hAPP(c_List_Oappend(X5),X224),X223)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X19),X224))
        & hBOOL(hAPP(c_List_Olistsp(X5,X19),X223)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_funpow__mult,axiom,
    ! [X2,X51,X89,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),X89),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X51),X2)) = hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__mult) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_zless__int,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X106,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X106)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_zle__int,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__int) ).

fof(fact_zero__less__diff,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),X51)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(fact_zle__diff1__eq,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_minus__number__of__mult,axiom,
    ! [X58,X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126))),X58) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126))),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X86,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X86)),X86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Oone__class_Oone(X56))),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_list__update__same__conv,axiom,
    ! [X20,X224,X5,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => ( hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X20) = X224
      <=> hAPP(hAPP(c_List_Onth(X5),X224),X96) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_negative__zle,axiom,
    ! [X86,X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [X92,X55] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X55)),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_min__diff,axiom,
    ! [X92,X98,X86] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X98)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X86),X92)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [X126,X128,X129] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X129),X128)),X126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X129),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [X126,X128,X129] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X129),X128)),X126) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X129),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_add__mult__distrib,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_diff__mult__distrib,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X93) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_nth_Osimps,axiom,
    ! [X89,X224,X20,X5] : hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)),X89) = c_Nat_Onat_Onat__case(X5,X20,hAPP(c_List_Onth(X5),X224),X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth_Osimps) ).

fof(fact_replicate__length__filter,axiom,
    ! [X224,X20,X5] : c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X20)),X224)),X20) = hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X20)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__length__filter) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [X22,X19,X17,X5] :
      ( c_Sum__Type_OPlus(X5,X17,X19,X22) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X5,X17),tc_HOL_Obool))
    <=> ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X22 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_set__sort,axiom,
    ! [X224,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osort__key(X5,X17,X2,X224)) = hAPP(c_List_Oset(X5),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sort) ).

fof(fact_replicate__append__same,axiom,
    ! [X55,X98,X56] : hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X98,X55)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56))) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Oreplicate(X56,X98,X55)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__append__same) ).

fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
    ! [X23,X21,X6] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    <=> ( X6 = X21
        & X21 = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).

fof(fact_Union__insert,axiom,
    ! [X22,X6,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__insert) ).

fof(fact_Inter__insert,axiom,
    ! [X22,X6,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X6),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__insert) ).

fof(fact_wf__no__loop,axiom,
    ! [X37,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X37),X37) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => c_Wellfounded_Owf(X5,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__loop) ).

fof(fact_add__eq__if,axiom,
    ! [X92,X86] :
      ( ( X86 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92) = X92 )
      & ( X86 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).

fof(fact_setsum__constant,axiom,
    ! [X19,X24,X17,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(c_COMBK(X5,X17),X24)),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X17),X19))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__constant) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [X26,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).

fof(fact_of__int__le__0__iff,axiom,
    ! [X26,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).

fof(fact_zmod__simps_I2_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_mod__add__right__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61),X59) = c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),c_Divides_Odiv__class_Omod(X56,X61,X59)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_predicate1D,axiom,
    ! [X20,X29,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X30),X29))
     => ( hBOOL(hAPP(X30,X20))
       => hBOOL(hAPP(X29,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X29,X5,X20,X30] :
      ( hBOOL(hAPP(X30,X20))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X30),X29))
       => hBOOL(hAPP(X29,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_nat__diff__distrib,axiom,
    ! [X58,X131] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X58))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X58),X131)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X58)),hAPP(c_Int_Onat,X131)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [X33,X34,X19,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X19),hAPP(hAPP(c_List_Olist_OCons(X5),X34),X33)))
    <=> ( hBOOL(hAPP(X19,X34))
        & hBOOL(hAPP(c_List_Olistsp(X5,X19),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X102)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X106) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X20)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_map__fst__zip,axiom,
    ! [X223,X17,X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X5),c_Product__Type_Ofst(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223)) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [X223,X17,X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X223)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X17),X17),c_Product__Type_Osnd(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223)) = X223 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__snd__zip) ).

fof(fact_div__add__self1,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X60)),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),c_Groups_Oone__class_Oone(X56)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61)),c_Groups_Oone__class_Oone(X56)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).

fof(fact_mod__mult__mult2,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Divides_Odiv__class_Omod(X56,X60,X61)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [X58,X126] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X58))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X126))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X58))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [X92,X86,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X93))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [X61,X60,X59] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X59)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_split__def,axiom,
    ! [X133,X23,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X23),X133) = hAPP(hAPP(X23,hAPP(c_Product__Type_Ofst(X17,X25),X133)),hAPP(c_Product__Type_Osnd(X17,X25),X133)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__def) ).

fof(fact_split__beta,axiom,
    ! [X26,X30,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X30),X26) = hAPP(hAPP(X30,hAPP(c_Product__Type_Ofst(X17,X25),X26)),hAPP(c_Product__Type_Osnd(X17,X25),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__beta) ).

fof(fact_prod__case__beta,axiom,
    ! [X133,X2,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2),X133) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X17,X25),X133)),hAPP(c_Product__Type_Osnd(X17,X25),X133)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__case__beta) ).

fof(fact_sorted__sort,axiom,
    ! [X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort) ).

fof(fact_append1__eq__conv,axiom,
    ! [X24,X223,X20,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5))) = hAPP(hAPP(c_List_Oappend(X5),X223),hAPP(hAPP(c_List_Olist_OCons(X5),X24),c_List_Olist_ONil(X5)))
    <=> ( X224 = X223
        & X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [X92,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = hAPP(hAPP(c_List_Onth(X56),X222),X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_abs__add__abs,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_inf__le1,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le2,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_expand__Suc,axiom,
    ! [X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).

fof(fact_ivl__disj__un_I9_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X106)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X106)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X106)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_minus__dvd__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)),X24))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_abs__le__D1,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Odistrib__lattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Odistrib__lattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X57),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X81,X82,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),X81) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X81)),X82) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_id__o,axiom,
    ! [X1,X5,X17] : hAPP(c_Fun_Ocomp(X17,X17,X5,c_Fun_Oid(X17)),X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__o) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [X89,X37,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X37)
     => c_Relation_Osingle__valued(X5,X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [X265,X266,X20,X5] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X5),X20),X266),X265) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X5),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_DomainP_Oequations,axiom,
    ! [X34,X78,X17,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X17,X78),X34))
    <=> ? [X77] : hBOOL(hAPP(hAPP(X78,X34),X77)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_inj__eq,axiom,
    ! [X24,X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X20) = hAPP(X2,X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X24,X20,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X20) = hAPP(X2,X24)
       => X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_replicate__add,axiom,
    ! [X55,X86,X92,X56] : c_List_Oreplicate(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86),X55) = hAPP(hAPP(c_List_Oappend(X56),c_List_Oreplicate(X56,X92,X55)),c_List_Oreplicate(X56,X86,X55)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__add) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

fof(fact_foldl__Nil,axiom,
    ! [X6,X2,X17,X5] : hAPP(c_List_Ofoldl(X5,X17,X2,X6),c_List_Olist_ONil(X17)) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Nil) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [X149,X28,X17,X5] : hAPP(c_List_Olist_Olist__case(X5,X17,X28,X149),c_List_Olist_ONil(X17)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_o__id,axiom,
    ! [X2,X17,X5] : hAPP(c_Fun_Ocomp(X5,X17,X5,X2),c_Fun_Oid(X5)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__id) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X20))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X24))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X24) = c_Groups_Ozero__class_Ozero(X5)
          <=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
              & X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_diff__add__assoc,axiom,
    ! [X98,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_add__diff__assoc,axiom,
    ! [X98,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_diff__diff__right,axiom,
    ! [X98,X94,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X94))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X94),X93)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X93)),X94) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(fact_compl__mono,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_one__less__nat__eq,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X26)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [X92,X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_greaterThan__Suc,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X90)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [X107,X108,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X108)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X107)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X108),X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_power__add,axiom,
    ! [X92,X86,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X86)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X73,X59,X61,X60,X119,X56] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X56)
     => ( X119 != c_Groups_Ozero__class_Ozero(X56)
       => ( ( X60 = X61
            & X59 != X73 )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X119),X59)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X119),X73)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_some__eq__trivial,axiom,
    ! [X20,X5] : c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X20)) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).

fof(fact_the__eq__trivial,axiom,
    ! [X6,X5] : c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__eq__trivial) ).

fof(fact_diff__less__Suc,axiom,
    ! [X92,X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),hAPP(c_Nat_OSuc,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_less__add__Suc1,axiom,
    ! [X86,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X86)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X86,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X98)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_ivl__disj__int_I10_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X51)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X51)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_empty__subsetI,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).

fof(fact_equiv__comp__eq,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X78)),X78) = X78 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X55,X57))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_subset__insertI,axiom,
    ! [X6,X22,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [X59,X61,X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X59)),X59) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X61),X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [X86,X57,X55] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),c_Divides_Odiv__class_Omod(tc_Int_Oint,X57,X86)),X86) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X57),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [X59,X61,X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X61),X59) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X59)),X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X102))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X106)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X102) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).

fof(fact_finite__option__UNIV,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [X27,X23,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X6)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [X27,X23,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X21),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [X26,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Int_Onat,X26)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),hAPP(c_Int_Onat,X57)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X55,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_drop__take,axiom,
    ! [X222,X86,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(hAPP(c_List_Otake(X56),X86),X222)) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),hAPP(hAPP(c_List_Odrop(X56),X92),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__take) ).

fof(fact_rel__comp__empty2,axiom,
    ! [X37,X17,X25,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X37),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25,X17),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_curry__split,axiom,
    ! [X2,X25,X17,X5] : c_Product__Type_Ocurry(X5,X17,X25,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X25),X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_mod__mult__distrib,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),X93) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_dvd__mult2,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).

fof(fact_dvd__mult,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X59))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).

fof(fact_less__supI1,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [X60,X61,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI2) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [X60,X61,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_le__supI1,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [X60,X61,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI2) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [X61,X60,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [X60,X61,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_negative__zle__0,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).

fof(fact_transpose__empty,axiom,
    ! [X224,X5] :
      ( c_List_Otranspose(X5,X224) = c_List_Olist_ONil(tc_List_Olist(X5))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X224)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__empty) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [X90,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X5)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_UN__empty2,axiom,
    ! [X19,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__empty2) ).

fof(fact_less__trans__Suc,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X98)),X93)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_pos__mod__sign,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [X95,X96] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X96,X95) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X95),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__upto) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [X224,X20,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Olist_OCons(X17),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),hAPP(X2,X20)),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_power__one__over,axiom,
    ! [X92,X60,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),c_Groups_Oone__class_Oone(X56)),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),c_Groups_Oone__class_Oone(X56)),X60)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

fof(fact_le__imp__0__less,axiom,
    ! [X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_insertI2,axiom,
    ! [X21,X22,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X22))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_less__minus__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(fact_le__minus__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(fact_last__list__update,axiom,
    ! [X55,X93,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => ( ( X93 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X93),X55)) = X55 )
        & ( X93 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X56,hAPP(hAPP(c_List_Olist__update(X56,X222),X93),X55)) = c_List_Olast(X56,X222) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__list__update) ).

fof(fact_sgn__less,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Osgn__class_Osgn(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(fact_take__butlast,axiom,
    ! [X222,X56,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => hAPP(hAPP(c_List_Otake(X56),X92),c_List_Obutlast(X56,X222)) = hAPP(hAPP(c_List_Otake(X56),X92),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__butlast) ).

fof(fact_last__drop,axiom,
    ! [X222,X56,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
     => c_List_Olast(X56,hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = c_List_Olast(X56,X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__drop) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [X21,X6,X28,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X28),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)) = hAPP(hAPP(X28,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_split__conv,axiom,
    ! [X21,X6,X2,X5,X25,X17] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,X5),X2),hAPP(hAPP(c_Product__Type_OPair(X17,X25),X6),X21)) = hAPP(hAPP(X2,X6),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X27))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)
          <=> ( X6 = X23
              & X21 = X27 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X27))
           => X6 = X23 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X27)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X27))
           => X21 = X27 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_posDivAlg__correct,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),c_Divides_OposDivAlg(X60,X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_nth__list__update__neq,axiom,
    ! [X55,X222,X56,X94,X98] :
      ( X98 != X94
     => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)),X94) = hAPP(hAPP(c_List_Onth(X56),X222),X94) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X51)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X51),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_converse__inv__image,axiom,
    ! [X2,X37,X17,X5] : hAPP(c_Relation_Oconverse(X5,X5),hAPP(hAPP(c_Relation_Oinv__image(X17,X5),X37),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X17,X5),hAPP(c_Relation_Oconverse(X17,X17),X37)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_log_Osimps,axiom,
    ! [X98,X61] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X61),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),X61)) )
       => c_Random_Olog(X61,X98) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X61),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),X61)) )
       => c_Random_Olog(X61,X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X61,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X98),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_log_Osimps) ).

fof(fact_Ints__minus,axiom,
    ! [X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Int_Oring__1__class_OInts(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__minus) ).

fof(fact_bot__empty__eq,axiom,
    ! [X20,X5] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X20))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_abs__div__pos,axiom,
    ! [X55,X57,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X57))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X55)),X57) = hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_abs__mult__pos,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X57)),X55) = hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_Pow__empty,axiom,
    ! [X5] : hAPP(c_Set_OPow(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__empty) ).

fof(fact_setsum__shift__lb__Suc0__0,axiom,
    ! [X90,X2] :
      ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X90)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_inf__apply,axiom,
    ! [X20,X1,X2,X17,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,X5)),X2),X1),X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X20)),hAPP(X1,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).

fof(fact_inf__fun__def,axiom,
    ! [X20,X1,X2,X17,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,X5)),X2),X1),X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X20)),hAPP(X1,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).

fof(fact_sup__apply,axiom,
    ! [X20,X1,X2,X17,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,X5)),X2),X1),X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X20)),hAPP(X1,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__apply) ).

fof(fact_sup__fun__def,axiom,
    ! [X20,X1,X2,X17,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17,X5)),X2),X1),X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X20)),hAPP(X1,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__fun__def) ).

fof(fact_minus__apply,axiom,
    ! [X20,X22,X19,X17,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,X5)),X19),X22),X20) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X19,X20)),hAPP(X22,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(fact_fun__diff__def,axiom,
    ! [X20,X22,X19,X17,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17,X5)),X19),X22),X20) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X19,X20)),hAPP(X22,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).

fof(fact_negDivAlg__correct,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),c_Divides_OnegDivAlg(X60,X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_neg__mod__bound,axiom,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_folding_Oempty,axiom,
    ! [X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Fun_Oid(X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oempty) ).

fof(fact_less__code__numeral__def,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X89),X51))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X89)),hAPP(c_Code__Numeral_Onat__of,X51))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X89)),hAPP(c_Code__Numeral_Oof__nat,X51)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_Suc__less__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),hAPP(c_Nat_OSuc,X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Nat_OSuc,X92)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X89),X51))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X89)),hAPP(c_Code__Numeral_Onat__of,X51))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X89)),hAPP(c_Code__Numeral_Oof__nat,X51)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_Suc__le__mono,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),hAPP(c_Nat_OSuc,X51)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_nth__take,axiom,
    ! [X222,X56,X92,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X92))
     => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Otake(X56),X92),X222)),X98) = hAPP(hAPP(c_List_Onth(X56),X222),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take) ).

fof(fact_Diff__disjoint,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X22),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_rev__eq__Cons__iff,axiom,
    ! [X223,X24,X224,X5] :
      ( hAPP(c_List_Orev(X5),X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)
    <=> X224 = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Orev(X5),X223)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),c_List_Olist_ONil(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [X92,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_div__le__dividend,axiom,
    ! [X92,X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(fact_diff__le__self,axiom,
    ! [X92,X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [X102,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X102)),hAPP(hAPP(c_Set_Oinsert(X5),X102),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X102) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_Min__le,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__le) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [X58,X57,X55] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [X128,X129,X126] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X129),X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X129)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X128)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [X128,X129,X126] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X129),X128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X129)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X128)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_add__mult__distrib2,axiom,
    ! [X92,X86,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [X92,X86,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_diff__commute,axiom,
    ! [X93,X94,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X94)),X93) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X93)),X94),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_dvd__trans,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X61),X59))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X59)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).

fof(fact_order__less__trans,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X58),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__trans,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X58,X55,X57,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X58),X55)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [X61] :
      ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__0) ).

fof(fact_mod__pos__pos,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X60,X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X27)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X27)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_eq__diff__iff,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X51))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X89))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X90) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X89),X90)
        <=> X51 = X89 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_Sigma__empty2,axiom,
    ! [X19,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__empty2) ).

fof(fact_numeral__1__eq__Suc__0,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_remdups__map__remdups,axiom,
    ! [X224,X2,X17,X5] : c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Oremdups(X17,X224))) = c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X60,X86,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Oone__class_Oone(X56))),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_div__pos__pos,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X60,X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X51)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X51,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_of__int__0__less__iff,axiom,
    ! [X26,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [X89,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [X26,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_com_Osize_I5_J,axiom,
    ! [X47,X48,X52] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X52,X48,X47)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X48)),c_Com_Ocom_Ocom__size(X47))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I5_J) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_mod__neg__pos,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X60,X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_dvd__div__mult__self,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X61),X60)),X60) = X61 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).

fof(fact_of__nat__diff,axiom,
    ! [X86,X92,X56] :
      ( class_Rings_Oring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__diff) ).

fof(fact_div__neg__pos,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X60,X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos) ).

fof(fact_finite__insert,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [X22,X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X22),c_Complete__Lattice_OInf__class_OInf(X5,X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X22),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [X22,X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X22),c_Complete__Lattice_OSup__class_OSup(X5,X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X22),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Sup__fold__sup) ).

fof(fact_nat__numeral__1__eq__1,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).

fof(fact_one__code__numeral__code,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).

fof(fact_one__is__num__one,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).

fof(fact_Numeral1__eq1__nat,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).

fof(fact_Compl__disjoint2,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__partition2,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)),X19) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__partition2) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [X17,X5] : c_Sum__Type_OPlus(X5,X17,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [X24,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [X24,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_finite__Domain,axiom,
    ! [X78,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),X78))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_ODomain(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Domain) ).

fof(fact_finite__Range,axiom,
    ! [X78,X17,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X17)),X78))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Relation_ORange(X5,X17),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Range) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [X20,X19,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,X19),X20))
     => X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_Nitpick_Oint__gcd__def,axiom,
    ! [X57,X55] : hAPP(hAPP(c_Nitpick_Oint__gcd,X55),X57) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X55)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X57)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_drop__map,axiom,
    ! [X224,X2,X17,X89,X5] : hAPP(hAPP(c_List_Odrop(X5),X89),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Odrop(X17),X89),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__map) ).

fof(fact_take__map,axiom,
    ! [X224,X2,X17,X89,X5] : hAPP(hAPP(c_List_Otake(X5),X89),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(hAPP(c_List_Otake(X17),X89),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__map) ).

fof(fact_filter__append,axiom,
    ! [X223,X224,X30,X5] : hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Ofilter(X5,X30),X224)),hAPP(c_List_Ofilter(X5,X30),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__append) ).

fof(fact_wf__acc__iff,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [X36,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( X36 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMin(X5,X36)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [X36,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( X36 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMax(X5,X36)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_finite__UnionD,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnionD) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [X86,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X93))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),X93) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).

fof(fact_sgn__greater,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Osgn__class_Osgn(X5,X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(fact_dvd__neg__div,axiom,
    ! [X55,X57,X56] :
      ( class_Divides_Oring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X57),X55))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),X57) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__neg__div) ).

fof(fact_mod__mult__mult1,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),c_Divides_Odiv__class_Omod(X56,X60,X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_INT__constant,axiom,
    ! [X23,X17,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X23)) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X23)) = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__constant) ).

fof(fact_UN__constant,axiom,
    ! [X23,X17,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X23)) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_HOL_Obool)),X19),hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X5),X23)) = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__constant) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [X265,X266,X5] : c_Random__Sequence_Oempty(X5,X266,X265) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( ( X59 = c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)) = c_Groups_Ozero__class_Ozero(X56) )
        & ( X59 != c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_div__mult__mult1,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_nat__rec__Suc,axiom,
    ! [X114,X149,X28,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X28,X149),hAPP(c_Nat_OSuc,X114)) = hAPP(hAPP(X149,X114),hAPP(c_Nat_Onat_Onat__rec(X5,X28,X149),X114)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X58,X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add1,axiom,
    ! [X86,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X86))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X57,X58,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X86,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X94))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X58,X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X55),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X86,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X86))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X57,X58,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X55),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X86,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X94))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_mod__mult__self2,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)),X61) = c_Divides_Odiv__class_Omod(X56,X60,X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [X61,X59,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X59),X61)),X61) = c_Divides_Odiv__class_Omod(X56,X60,X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)))
    <=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X120] :
            ( X51 = hAPP(c_Nat_OSuc,X120)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X89)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_bex__UNIV,axiom,
    ! [X30,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(X30,X3)) )
    <=> ? [X77] : hBOOL(hAPP(X30,X77)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__UNIV) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Orotate1(X56),X222) = hAPP(hAPP(c_List_Oappend(X56),hAPP(c_List_Otl(X56),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(c_List_Ohd(X56),X222)),c_List_Olist_ONil(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [X95,X96,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X96,X95))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X2),c_List_Oupto(X96,X95))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [X106,X90,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X2),c_List_Oupto(X90,X106))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X90,X106))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_inf__assoc,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X58) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf_Oassoc,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)),X59) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)),X58) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_sup__assoc,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)),X58) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__assoc) ).

fof(fact_sup_Oassoc,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)),X59) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)),X58) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)),X59) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)),X59) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)),X58) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_power__commutes,axiom,
    ! [X92,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),X60) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X81,X82,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X82)),X81) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X82),X81)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oab__semigroup__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Oab__semigroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_times__divide__eq__right,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X80,X81,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X81)),X80) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X73,X59,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)),X73) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_last__conv__nth,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => c_List_Olast(X56,X222) = hAPP(hAPP(c_List_Onth(X56),X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__conv__nth) ).

fof(fact_Nats__number__of,axiom,
    ! [X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X84))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Nat_Osemiring__1__class_ONats(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__number__of) ).

fof(fact_card__Pow,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Pow) ).

fof(fact_atLeast__Suc,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X90)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X90),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__Suc) ).

fof(fact_Diff__Compl,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Compl) ).

fof(fact_Diff__eq,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__eq) ).

fof(fact_zero__less__two,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X106,X102)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_nth__replicate,axiom,
    ! [X55,X56,X92,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X92))
     => hAPP(hAPP(c_List_Onth(X56),c_List_Oreplicate(X56,X92,X55)),X98) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__replicate) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [X6,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_less__minus__self__iff,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_le__minus__self__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_Diff__triv,axiom,
    ! [X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__triv) ).

fof(fact_insort__not__Nil,axiom,
    ! [X224,X6,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X6),X224) != c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_setprod__constant,axiom,
    ! [X24,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(c_COMBK(X17,X5),X24)),X19) = hAPP(hAPP(c_Power_Opower__class_Opower(X17),X24),hAPP(c_Finite__Set_Ocard(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__constant) ).

fof(fact_fold1__insert__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [X102,X51,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X51)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X51),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_diff__Suc,axiom,
    ! [X89,X51] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc) ).

fof(fact_append__assoc,axiom,
    ! [X237,X221,X222,X56] : hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X237) = hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Oappend(X56),X221),X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).

fof(fact_append__Cons,axiom,
    ! [X221,X222,X55,X56] : hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),X221) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).

fof(fact_dvd__imp__le,axiom,
    ! [X92,X93] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

fof(fact_take__Suc,axiom,
    ! [X92,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_OSuc,X92)),X222) = hAPP(hAPP(c_List_Olist_OCons(X56),hAPP(c_List_Ohd(X56),X222)),hAPP(hAPP(c_List_Otake(X56),X92),hAPP(c_List_Otl(X56),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X102))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_nth__Cons_H,axiom,
    ! [X222,X55,X56,X92] :
      ( ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),X92) = X55 )
      & ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),X92) = hAPP(hAPP(c_List_Onth(X56),X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons_H) ).

fof(fact_image__constant__conv,axiom,
    ! [X23,X17,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X17,hAPP(c_COMBK(X17,X5),X23)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X17,hAPP(c_COMBK(X17,X5),X23)),X19) = hAPP(hAPP(c_Set_Oinsert(X17),X23),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant__conv) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [X2,X224,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(c_List_Oset(X5),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_power__mult,axiom,
    ! [X92,X86,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X86)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [X107,X108,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X108)),X107) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X108),X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_mod__minus__eq,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60),X61) = c_Divides_Odiv__class_Omod(X56,hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Divides_Odiv__class_Omod(X56,X60,X61)),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_tl__take,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Otake(X56),X92),X222)) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__take) ).

fof(fact_abs__power__minus,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X92)) = hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => X19 = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_drop__Cons_H,axiom,
    ! [X222,X55,X56,X92] :
      ( ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222) )
      & ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Odrop(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X222) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_neg__zminus__int,axiom,
    ! [X92] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X92))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_insert__code,axiom,
    ! [X20,X19,X24,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X24),X19),X20))
    <=> ( X24 = X20
        | hBOOL(hAPP(X19,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).

fof(fact_dvd__minus__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Rings_Ocomm__ring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).

fof(fact_lessThan__iff,axiom,
    ! [X90,X96,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X96),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [X90,X96,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X90),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_atMost__iff,axiom,
    ! [X90,X96,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(c_SetInterval_Oord__class_OatMost(X5),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X96),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__iff) ).

fof(fact_atLeast__iff,axiom,
    ! [X90,X96,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X90)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X90),X96)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__iff) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [X24,X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X20,X24)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(X2,X20),hAPP(X18,X19)) = hAPP(X18,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_Max__ge,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__ge) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [X224,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X224) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X224)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_zdiff__int,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int) ).

fof(fact_odd__nonzero,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X58)),X58) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_Field__def,axiom,
    ! [X78,X5] : hAPP(c_Relation_OField(X5),X78) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X78)),hAPP(c_Relation_ORange(X5,X5),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__def) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [X89,X51] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X86)),X92) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)),X92) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [X61,X60] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_subset__UNIV,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(fact_zle__trans,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X93)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_le__trans,axiom,
    ! [X93,X94,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X93))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X93)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_mod__mod__cancel,axiom,
    ! [X60,X61,X59,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X59),X61))
       => c_Divides_Odiv__class_Omod(X56,c_Divides_Odiv__class_Omod(X56,X60,X61),X59) = c_Divides_Odiv__class_Omod(X56,X60,X59) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X86,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X86),X86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Oone__class_Oone(X56))),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_less__add__eq__less,axiom,
    ! [X92,X86,X91,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X91))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X91) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X92)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_dvd__div__neg,axiom,
    ! [X55,X57,X56] :
      ( class_Divides_Oring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X57),X55))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X55),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__neg) ).

fof(fact_Suc__lessD,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X51,X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),X89))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__leD,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_drop__drop,axiom,
    ! [X222,X86,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(hAPP(c_List_Odrop(X56),X86),X222)) = hAPP(hAPP(c_List_Odrop(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__drop) ).

fof(fact_take__take,axiom,
    ! [X222,X86,X92,X56] : hAPP(hAPP(c_List_Otake(X56),X92),hAPP(hAPP(c_List_Otake(X56),X86),X222)) = hAPP(hAPP(c_List_Otake(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X92),X86)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__take) ).

fof(fact_Inf__lower,axiom,
    ! [X19,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OInf__class_OInf(X5,X19)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__lower) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [X30] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X30,X3)) )
    <=> ! [X3] : hBOOL(hAPP(X30,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_nat__div__distrib,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X55),X57)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),hAPP(c_Int_Onat,X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_nat__mult__distrib,axiom,
    ! [X131,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X58)),hAPP(c_Int_Onat,X131)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [X89,X51] :
      ( c_Nat__Transfer_Ois__nat(X51)
     => ( c_Nat__Transfer_Ois__nat(X89)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X51,X89) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X51),hAPP(c_Int_Onat,X89))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),c_List_Olist_ONil(tc_List_Olist(X5))))
     => c_List_Otranspose(X5,c_List_Olist_ONil(tc_List_Olist(X5))) = c_List_Olist_ONil(tc_List_Olist(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_mod__mult__distrib2,axiom,
    ! [X92,X86,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [X22,X19] :
      ( X19 = X22
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_set__append,axiom,
    ! [X223,X224,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(c_List_Oset(X5),X223)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__append) ).

fof(fact_Suc__mono,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Nat_OSuc,X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_power__inject__exp,axiom,
    ! [X89,X51,X6,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X6))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X51) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X89)
        <=> X51 = X89 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [X238,X19,X5] : c_List_Olistset(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_HOL_Obool)),X19),X238)) = c_List_Oset__Cons(X5,X19,c_List_Olistset(X5,X238)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_bex__empty,axiom,
    ! [X30,X5] :
      ~ ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(X30,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__empty) ).

fof(fact_Sup__fold__sup,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Complete__Lattice_OSup__class_OSup(X5,X19) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),c_Orderings_Obot__class_Obot(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_Inf__fold__inf,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Complete__Lattice_OInf__class_OInf(X5,X19) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),c_Orderings_Otop__class_Otop(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_power__eq__if,axiom,
    ! [X108,X86] :
      ( ( X86 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X108),X86) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X86 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X108),X86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X108),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).

fof(fact_image__uminus__atLeastAtMost,axiom,
    ! [X24,X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X20,X24)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [X24,X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X20,X24)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [X89] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [X86,X92] : c_Code__Numeral_Odiv__mod__code__numeral(X92,X86) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X92),X86)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X92,X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [X107,X108] : c_Divides_Odivmod__int(X108,X107) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X108),X107)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X108,X107)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_zminus__zmod,axiom,
    ! [X86,X55] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X86)),X86) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X55),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
       => ( hAPP(c_Int_Onat,X20) = hAPP(c_Int_Onat,X24)
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [X147,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
       => ( hAPP(c_Int_Onat,X26) = hAPP(c_Int_Onat,X147)
        <=> X26 = X147 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X26))
    <=> ? [X130] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X130))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_div__mod__equality_H,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)),X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_zero__less__int__conv,axiom,
    ! [X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [X75,X51] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75)
    <=> ( X51 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_finite__Pow__iff,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X19)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_DomainP_Ointros,axiom,
    ! [X17,X5,X21,X6,X78] :
      ( hBOOL(hAPP(hAPP(X78,X6),X21))
     => hBOOL(hAPP(c_Predicate_ODomainP(X5,X17,X78),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_RangeP_Ointros,axiom,
    ! [X17,X5,X21,X6,X78] :
      ( hBOOL(hAPP(hAPP(X78,X6),X21))
     => hBOOL(hAPP(c_Predicate_ORangeP(X5,X17,X78),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_length__splice,axiom,
    ! [X221,X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),c_List_Osplice(X56,X222,X221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__splice) ).

fof(fact_length__greater__0__conv,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
    <=> X224 != c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_ivl__disj__int_I8_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X51)))
      <=> X89 = X51 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [X89,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X89)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X89)) = hAPP(hAPP(c_Set_Oinsert(X5),X89),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).

fof(fact_length__append,axiom,
    ! [X221,X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__append) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => ( X19 = X22
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X22) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_triple_Oinject,axiom,
    ! [X7,X8,X9,X10,X11,X12,X5] :
      ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X9),X8),X7)
    <=> ( X12 = X9
        & X11 = X8
        & X10 = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).

fof(fact_setprod__zero,axiom,
    ! [X2,X19,X5,X17] :
      ( class_Rings_Ocomm__semiring__1(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) = c_Groups_Ozero__class_Ozero(X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [X92,X86,X93] :
      ( ( X93 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X93 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_Pow__top,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Set_OPow(X5),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__top) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [X222,X55,X56] : hAPP(c_List_Orev(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(c_List_Orev(X56),X222)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [X90,X96] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),X90)) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X96)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_Inf__le__Sup,axiom,
    ! [X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)),c_Big__Operators_Olattice__class_OSup__fin(X5,X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_map__replicate__const,axiom,
    ! [X271,X90,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),hAPP(c_COMBK(X5,X17),X90)),X271) = c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X271),X90),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__const) ).

fof(fact_part__equivp__transp,axiom,
    ! [X26,X24,X20,X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
     => ( hBOOL(hAPP(hAPP(X37,X20),X24))
       => ( hBOOL(hAPP(hAPP(X37,X24),X26))
         => hBOOL(hAPP(hAPP(X37,X20),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__transp) ).

fof(fact_transpE,axiom,
    ! [X26,X24,X20,X78,X5] :
      ( c_Predicate_Otransp(X5,X78)
     => ( hBOOL(hAPP(hAPP(X78,X20),X24))
       => ( hBOOL(hAPP(hAPP(X78,X24),X26))
         => hBOOL(hAPP(hAPP(X78,X20),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpE) ).

fof(fact_equivp__transp,axiom,
    ! [X26,X24,X20,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ( hBOOL(hAPP(hAPP(X37,X20),X24))
       => ( hBOOL(hAPP(hAPP(X37,X24),X26))
         => hBOOL(hAPP(hAPP(X37,X20),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(X18,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_mod__minus__cong,axiom,
    ! [X140,X61,X60,X56] :
      ( class_Divides_Oring__div(X56)
     => ( c_Divides_Odiv__class_Omod(X56,X60,X61) = c_Divides_Odiv__class_Omod(X56,X140,X61)
       => c_Divides_Odiv__class_Omod(X56,hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60),X61) = c_Divides_Odiv__class_Omod(X56,hAPP(c_Groups_Ouminus__class_Ouminus(X56),X140),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_sublists__powset,axiom,
    ! [X224,X5] : hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_Osublists(X5,X224))) = hAPP(c_Set_OPow(X5),hAPP(c_List_Oset(X5),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists__powset) ).

fof(fact_Union__def,axiom,
    ! [X36,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X36) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X36),c_COMBI(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__def) ).

fof(fact_Inter__def,axiom,
    ! [X36,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X36) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X36),c_COMBI(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__def) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

fof(fact_int__le__0__conv,axiom,
    ! [X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [X92,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X55)),X92) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_nat__power__eq,axiom,
    ! [X92,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X58),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X58)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq) ).

fof(fact_diff__cancel,axiom,
    ! [X92,X86,X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X86)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [X92,X93,X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X93)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(fact_zpower__zpower,axiom,
    ! [X58,X57,X55] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X57)),X58) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

fof(fact_zmult__assoc,axiom,
    ! [X127,X128,X129] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X129),X128)),X127) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X127)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

fof(fact_nat__mult__assoc,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_zadd__assoc,axiom,
    ! [X127,X128,X129] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X129),X128)),X127) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X127)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [X93,X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_diff__diff__left,axiom,
    ! [X93,X94,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X94)),X93) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(fact_div__mult2__eq,axiom,
    ! [X59,X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X59)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X60),X61)),X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_ball__empty,axiom,
    ! [X30,X5,X3] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => hBOOL(hAPP(X30,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__empty) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X106)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X106,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X106)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X106,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X106)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X106,X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_mod__neg__neg__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X60))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_set__map,axiom,
    ! [X224,X2,X17,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_List_Oset(X17),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__map) ).

fof(fact_append__take__drop__id,axiom,
    ! [X222,X92,X56] : hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Otake(X56),X92),X222)),hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [X92,X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X86),X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_com_Osize_I4_J,axiom,
    ! [X138,X139] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X139,X138)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X139)),c_Com_Ocom_Ocom__size(X138))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I4_J) ).

fof(fact_less__0__number__of,axiom,
    ! [X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X75)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_list__ex__append,axiom,
    ! [X223,X224,X30,X5] :
      ( c_List_Olist__ex(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223))
    <=> ( c_List_Olist__ex(X5,X30,X224)
        | c_List_Olist__ex(X5,X30,X223) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__append) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X60))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_take__Suc__Cons,axiom,
    ! [X222,X55,X92,X56] : hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_OSuc,X92)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),hAPP(hAPP(c_List_Otake(X56),X92),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_small__lazy__prod__def,axiom,
    ! [X73,X161,X56] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X56)
        & class_Lazy__Sequence_Osmall__lazy(X161) )
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X56,X161),X73) = c_Lazy__Sequence_Oproduct(X56,X161,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X56,X73),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X161,X73)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__prod__def) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [X223,X1,X25,X224,X2,X5,X17] :
      ( hAPP(hAPP(c_List_Omap(X17,X5),X2),X224) = hAPP(hAPP(c_List_Omap(X25,X5),X1),X223)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X25)),X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_length__sublists,axiom,
    ! [X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X56))),c_Enum_Osublists(X56,X222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublists) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [X19] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_fst__eqD,axiom,
    ! [X60,X57,X55,X161,X56] :
      ( hAPP(c_Product__Type_Ofst(X56,X161),hAPP(hAPP(c_Product__Type_OPair(X56,X161),X55),X57)) = X60
     => X55 = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eqD) ).

fof(fact_snd__eqD,axiom,
    ! [X60,X57,X55,X56,X161] :
      ( hAPP(c_Product__Type_Osnd(X161,X56),hAPP(hAPP(c_Product__Type_OPair(X161,X56),X55),X57)) = X60
     => X57 = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eqD) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_finite__Field,axiom,
    ! [X78,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_OField(X5),X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Field) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [X24,X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X20),X24)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_Suc__lessI,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => ( hAPP(c_Nat_OSuc,X86) != X92
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X41] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X41))
    <=> ? [X99] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X99)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X41] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X41))
    <=> ? [X99] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X99)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_diff__number__of__eq,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_distinct__n__lists,axiom,
    ! [X92,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X56)),c_Enum_On__lists(X56,X92,X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X26)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_last__snoc,axiom,
    ! [X55,X222,X56] : c_List_Olast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56)))) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).

fof(fact_butlast__snoc,axiom,
    ! [X55,X222,X56] : c_List_Obutlast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56)))) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [X37,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X37)),c_Transitive__Closure_Ortrancl(X5,X37)) = c_Transitive__Closure_Ortrancl(X5,X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_fst__def,axiom,
    ! [X133,X17,X5] : hAPP(c_Product__Type_Ofst(X5,X17),X133) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,X5),c_COMBK(X5,X17)),X133),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__def) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [X78,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78))
     => ( c_Wellfounded_Oacyclic(X5,X78)
       => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_order__eq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X20 = X24
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_order__antisym__conv,axiom,
    ! [X20,X24,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__antisym,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
         => X55 = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I5_J,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
         => X55 = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_le__mod__geq,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mod__geq) ).

fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
    ! [X21,X6] :
      ( X6 = X21
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).

fof(fact_in__set__insert,axiom,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => c_List_Oinsert(X5,X20,X224) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__insert) ).

fof(fact_Suc__diff__le,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_zero__le__square,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_less__add__one,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Oone__class_Oone(X56)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)))
      <=> X6 != c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_accp__downward,axiom,
    ! [X6,X21,X78,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X21))
     => ( hBOOL(hAPP(hAPP(X78,X6),X21))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).

fof(fact_hd__in__set,axiom,
    ! [X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_List_Ohd(X5),X224)),hAPP(c_List_Oset(X5),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__in__set) ).

fof(fact_dvd_OatLeastAtMost__singleton,axiom,
    ! [X6] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X6) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [X274,X60,X56] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X56)),c_Lazy__Sequence_Olazy__sequence_OInsert(X56,X60,X274)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X56)),X274)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
    ! [X107,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X107)),X55) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Nat_OSuc,X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_power__Suc2,axiom,
    ! [X92,X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(c_List_Oset(X5),X224)) = c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),c_List_Oremdups(X5,X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [X227,X60,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(hAPP(c_List_Olist_OCons(X56),X60),X227)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X227)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).

fof(fact_length__n__lists,axiom,
    ! [X222,X92,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X56))),c_Enum_On__lists(X56,X92,X222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [X30] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X30,X3)) )
    <=> ? [X3] : hBOOL(hAPP(X30,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_Suc__leI,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_Max_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,X19)) = c_Big__Operators_Olinorder__class_OMax(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,X19)) = c_Big__Operators_Olinorder__class_OMin(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Sup__upper,axiom,
    ! [X19,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),c_Complete__Lattice_OSup__class_OSup(X5,X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__upper) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [X224,X20,X30,X5] :
      ( c_List_Olist__ex(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))
    <=> ( hBOOL(hAPP(X30,X20))
        | c_List_Olist__ex(X5,X30,X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [X102,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X106)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X106),X102)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_card__gt__0__iff,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X19)))
    <=> ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [X92,X222,X55,X56] : hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_List_Onth(X56),X222),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_map__tl,axiom,
    ! [X224,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Otl(X17),X224)) = hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__tl) ).

fof(fact_rev__map,axiom,
    ! [X224,X2,X17,X5] : hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(hAPP(c_List_Omap(X17,X5),X2),hAPP(c_List_Orev(X17),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__map) ).

fof(fact_in__respects,axiom,
    ! [X37,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),c_Quotient_ORespects(X5,X37)))
    <=> hBOOL(hAPP(hAPP(X37,X20),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__respects) ).

fof(fact_dvd__mult__div__cancel,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X61),X60)) = X61 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).

fof(fact_ex__nat,axiom,
    ! [X30] :
      ( ? [X77] : hBOOL(hAPP(X30,X77))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X30,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X19)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_list__all__append,axiom,
    ! [X223,X224,X30,X5] :
      ( c_List_Olist__all(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223))
    <=> ( c_List_Olist__all(X5,X30,X224)
        & c_List_Olist__all(X5,X30,X223) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__append) ).

fof(fact_Suc__pred,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X92 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

fof(fact_singleton__inject,axiom,
    ! [X21,X6,X5] :
      ( hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
     => X6 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).

fof(fact_of__nat__inverse,axiom,
    ! [X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X24)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [X84,X23,X21,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23) )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [X23,X21,X84,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23) = X21 )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_le__Suc__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
        | X51 = hAPP(c_Nat_OSuc,X89) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_append__butlast__last__id,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(hAPP(c_List_Oappend(X56),c_List_Obutlast(X56,X222)),hAPP(hAPP(c_List_Olist_OCons(X56),c_List_Olast(X56,X222)),c_List_Olist_ONil(X56))) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_pair__collapse,axiom,
    ! [X108,X161,X56] : hAPP(hAPP(c_Product__Type_OPair(X56,X161),hAPP(c_Product__Type_Ofst(X56,X161),X108)),hAPP(c_Product__Type_Osnd(X56,X161),X108)) = X108,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__collapse) ).

fof(fact_surjective__pairing,axiom,
    ! [X161,X56,X100] : X100 = hAPP(hAPP(c_Product__Type_OPair(X56,X161),hAPP(c_Product__Type_Ofst(X56,X161),X100)),hAPP(c_Product__Type_Osnd(X56,X161),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjective__pairing) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),c_List_Olist_ONil(X5)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_distinct__insert,axiom,
    ! [X55,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),c_List_Oinsert(X56,X55,X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).

fof(fact_distinct__takeWhile,axiom,
    ! [X30,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OtakeWhile(X5,X30,X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_distinct__remove1,axiom,
    ! [X55,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),c_List_Oremove1(X56,X55,X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1) ).

fof(fact_distinct__sublistI,axiom,
    ! [X111,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Osublist(X5,X224,X111))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sublistI) ).

fof(fact__01,axiom,
    ! [X275,X276,X55,X56] : c_Lazy__Sequence_Oappend(X56,c_Lazy__Sequence_Olazy__sequence_OInsert(X56,X55,X276),X275) = c_Lazy__Sequence_Olazy__sequence_OInsert(X56,X55,c_Lazy__Sequence_Oappend(X56,X276,X275)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__01) ).

fof(fact_remove1__commute,axiom,
    ! [X237,X57,X55,X56] : c_List_Oremove1(X56,X55,c_List_Oremove1(X56,X57,X237)) = c_List_Oremove1(X56,X57,c_List_Oremove1(X56,X55,X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__commute) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [X26,X24,X20,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => hAPP(hAPP(X2,X20),hAPP(hAPP(X2,X24),X26)) = hAPP(hAPP(X2,X24),hAPP(hAPP(X2,X20),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [X6,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_wfP__empty,axiom,
    ! [X5] : c_Wellfounded_OwfP(X5,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__empty) ).

fof(fact_of__nat__induct,axiom,
    ! [X20,X30] :
      ( ! [X38] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
         => hBOOL(hAPP(X30,hAPP(c_Code__Numeral_Oof__nat,X38))) )
     => hBOOL(hAPP(X30,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__induct) ).

fof(fact_dvd__triv__left,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

fof(fact_dvd__triv__right,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

fof(fact_sup__ge1,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge2,axiom,
    ! [X55,X57,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge2) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [X55,X57,X56] :
      ( class_Lattices_Olattice(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_le__maxI1,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI2) ).

fof(fact_mem__Collect__eq,axiom,
    ! [X30,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X30)))
    <=> hBOOL(hAPP(X30,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_CollectD,axiom,
    ! [X30,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X30)))
     => hBOOL(hAPP(X30,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectD) ).

fof(fact_CollectE,axiom,
    ! [X30,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X30)))
     => hBOOL(hAPP(X30,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X58)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [X222,X56,X57,X55] :
      ( ( X55 = X57
       => c_List_Oremove1(X56,X55,hAPP(hAPP(c_List_Olist_OCons(X56),X57),X222)) = X222 )
      & ( X55 != X57
       => c_List_Oremove1(X56,X55,hAPP(hAPP(c_List_Olist_OCons(X56),X57),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X57),c_List_Oremove1(X56,X55,X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_dvd__div__eq__mult,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Divides_Osemiring__div(X5)
     => ( X6 != c_Groups_Ozero__class_Ozero(X5)
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21))
         => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X21),X6) = X23
          <=> X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).

fof(fact_less__Suc__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
        | X51 = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Image__Id__on,axiom,
    ! [X22,X19,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId__on(X5,X19)),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id__on) ).

fof(fact_inf__left__commute,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X61),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X59)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_sup__left__commute,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__commute) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X61),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X59)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X61),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X59)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X58)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X61),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X59)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X61),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [X58,X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X58)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X80,X81,X83,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),X80)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X81),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X83),X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X73,X59,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X73)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_add__minus__cancel,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61)) = X61 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)
      <=> X51 = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,X89)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [X166] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_split__nat,axiom,
    ! [X96,X30] :
      ( hBOOL(hAPP(X30,hAPP(c_Int_Onat,X96)))
    <=> ( ! [X130] :
            ( X96 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X130)
           => hBOOL(hAPP(X30,X130)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).

fof(fact_distinct__drop,axiom,
    ! [X98,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),hAPP(hAPP(c_List_Odrop(X56),X98),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__drop) ).

fof(fact_distinct__take,axiom,
    ! [X98,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),hAPP(hAPP(c_List_Otake(X56),X98),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__take) ).

fof(fact_finite_OinsertI,axiom,
    ! [X6,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [X95,X96] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X96,X95)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X96),hAPP(c_Nat_OSuc,X95)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_INT__empty,axiom,
    ! [X22,X5,X17] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))),X22) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__empty) ).

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [X126,X122] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_map__butlast,axiom,
    ! [X224,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Obutlast(X17,X224)) = c_List_Obutlast(X5,hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__butlast) ).

fof(fact_Min__in,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X19)),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__in) ).

fof(fact_Max__in,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X19)),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__in) ).

fof(fact_nat__of__cases,axiom,
    ! [X24] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ~ ! [X3] : X24 != hAPP(c_Code__Numeral_Onat__of,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__cases) ).

fof(fact_all__nat,axiom,
    ! [X30] :
      ( ! [X77] : hBOOL(hAPP(X30,X77))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X30,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).

fof(fact_insertI1,axiom,
    ! [X22,X6,X5] : hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_mod__Suc,axiom,
    ! [X92,X86] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)) = X92
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)) != X92
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X86),X92) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).

fof(fact_inv__id,axiom,
    ! [X5] : c_Hilbert__Choice_Oinv__into(X5,X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Fun_Oid(X5)) = c_Fun_Oid(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__id) ).

fof(fact_insert__commute,axiom,
    ! [X19,X24,X20,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Set_Oinsert(X5),X24),X19)) = hAPP(hAPP(c_Set_Oinsert(X5),X24),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [X20,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_fold__empty,axiom,
    ! [X26,X2,X5,X17] : hAPP(hAPP(c_Finite__Set_Ofold(X17,X5,X2),X26),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__empty) ).

fof(fact_length__drop,axiom,
    ! [X222,X92,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__drop) ).

fof(fact_length__take,axiom,
    ! [X222,X92,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(hAPP(c_List_Otake(X56),X92),X222)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__take) ).

fof(fact_inj__of__nat,axiom,
    ! [X5] :
      ( class_Nat_Osemiring__char__0(X5)
     => c_Fun_Oinj__on(tc_Nat_Onat,X5,c_Nat_Osemiring__1__class_Oof__nat(X5),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__of__nat) ).

fof(fact_take__tl,axiom,
    ! [X222,X92,X56] : hAPP(hAPP(c_List_Otake(X56),X92),hAPP(c_List_Otl(X56),X222)) = hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Otake(X56),hAPP(c_Nat_OSuc,X92)),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__tl) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
    <=> ? [X97] : X89 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_drop__replicate,axiom,
    ! [X55,X93,X98,X56] : hAPP(hAPP(c_List_Odrop(X56),X98),c_List_Oreplicate(X56,X93,X55)) = c_List_Oreplicate(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X98),X55),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__replicate) ).

fof(fact_take__replicate,axiom,
    ! [X55,X93,X98,X56] : hAPP(hAPP(c_List_Otake(X56),X98),c_List_Oreplicate(X56,X93,X55)) = c_List_Oreplicate(X56,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),X93),X55),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__replicate) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X89] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [X224,X20,X30,X5] :
      ( c_List_Olist__all(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))
    <=> ( hBOOL(hAPP(X30,X20))
        & c_List_Olist__all(X5,X30,X224) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [X60,X61,X56] :
      ( class_Fields_Olinordered__field(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_card_Oneutral,axiom,
    ! [X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oneutral) ).

fof(fact_Compl__disjoint,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_Compl__partition,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__partition) ).

fof(fact_inj__on__empty,axiom,
    ! [X2,X17,X5] : c_Fun_Oinj__on(X5,X17,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).

fof(fact_zle__antisym,axiom,
    ! [X126,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),X126))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X126),X58))
       => X58 = X126 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__antisym,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
       => X86 = X92 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_zmod__minus1,axiom,
    ! [X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X61) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1) ).

fof(fact_babs__reg__eqv,axiom,
    ! [X30,X17,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => c_Quotient_OBabs(X5,X17,c_Quotient_ORespects(X5,X37),X30) = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_babs__reg__eqv) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Min__insert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__insert) ).

fof(fact_Max__insert,axiom,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__insert) ).

fof(fact_Un__empty,axiom,
    ! [X22,X19,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X22 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty) ).

fof(fact_listsum__append,axiom,
    ! [X221,X222,X56] :
      ( class_Groups_Omonoid__add(X56)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_List_Omonoid__add__class_Olistsum(X56),X222)),hAPP(c_List_Omonoid__add__class_Olistsum(X56),X221)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__append) ).

fof(fact_abs__divide,axiom,
    ! [X61,X60,X56] :
      ( class_Fields_Olinordered__field__inverse__zero(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

fof(fact_abs__mult,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

fof(fact_compl__inf,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf) ).

fof(fact_compl__sup,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup) ).

fof(fact_minus__max__eq__min,axiom,
    ! [X57,X55,X56] :
      ( class_Groups_Olinordered__ab__group__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [X57,X55,X56] :
      ( class_Groups_Olinordered__ab__group__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_minus__add__distrib,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oab__group__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_Cantors__paradox,axiom,
    ! [X19,X5] :
      ~ ? [X68] : hAPP(c_Set_Oimage(X5,tc_fun(X5,tc_HOL_Obool),X68),X19) = hAPP(c_Set_OPow(X5),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_equalityD1,axiom,
    ! [X5,X22,X19] :
      ( X19 = X22
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X5,X22,X19] :
      ( X19 = X22
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_last__in__set,axiom,
    ! [X5,X252] :
      ( X252 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_List_Olast(X5,X252)),hAPP(c_List_Oset(X5),X252))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__in__set) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X89)
    <=> X51 = X89 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_Pair__eq,axiom,
    ! [X181,X182,X21,X6,X17,X5] :
      ( hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21) = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X182),X181)
    <=> ( X6 = X182
        & X21 = X181 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).

fof(fact_Pair__inject,axiom,
    ! [X137,X140,X61,X60,X161,X56] :
      ( hAPP(hAPP(c_Product__Type_OPair(X56,X161),X60),X61) = hAPP(hAPP(c_Product__Type_OPair(X56,X161),X140),X137)
     => ~ ( X60 = X140
         => X61 != X137 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [X61,X60] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),X61) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X61),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_subset__refl,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X95,X96] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X96),X95)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X96)),hAPP(c_Nat_OSuc,X95)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_rev__append,axiom,
    ! [X221,X222,X56] : hAPP(c_List_Orev(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(c_List_Orev(X56),X221)),hAPP(c_List_Orev(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__append) ).

fof(fact_rotate__simps,axiom,
    ! [X222,X55,X161,X56] :
      ( hAPP(c_List_Orotate1(X56),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56)
      & hAPP(c_List_Orotate1(X161),hAPP(hAPP(c_List_Olist_OCons(X161),X55),X222)) = hAPP(hAPP(c_List_Oappend(X161),X222),hAPP(hAPP(c_List_Olist_OCons(X161),X55),c_List_Olist_ONil(X161))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).

fof(fact_less__SucI,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_le__SucI,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [X95,X96] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X96,X95) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),X95)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [X6,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
        <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_div__eq__minus1,axiom,
    ! [X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X61) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq__minus1) ).

fof(fact_Int__commute,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).

fof(fact_Un__commute,axiom,
    ! [X22,X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X22),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__commute) ).

fof(fact_triple_Osize_I1_J,axiom,
    ! [X10,X11,X12,X123,X5] : c_Hoare__Mirabelle_Otriple_Otriple__size(X5,X123,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Osize_I1_J) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
     => ? [X130] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X130))
          & X93 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X130) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_frac__eq__eq,axiom,
    ! [X84,X20,X26,X24,X5] :
      ( class_Fields_Ofield(X5)
     => ( X24 != c_Groups_Ozero__class_Ozero(X5)
       => ( X26 != c_Groups_Ozero__class_Ozero(X5)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X20),X24) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X84),X26)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X84),X24) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_zmult__div__cancel,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_mult__div__cancel,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_div__code__numeral__def,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X92),X86) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X92)),hAPP(c_Code__Numeral_Onat__of,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_times__code__numeral__def,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X92),X86) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X92)),hAPP(c_Code__Numeral_Onat__of,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X92),X86) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X92)),hAPP(c_Code__Numeral_Onat__of,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X92),X86) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X92)),hAPP(c_Code__Numeral_Onat__of,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_diff__diff__cancel,axiom,
    ! [X92,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X92))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X98)) = X98 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_nat__case__Suc,axiom,
    ! [X114,X149,X28,X5] : c_Nat_Onat_Onat__case(X5,X28,X149,hAPP(c_Nat_OSuc,X114)) = hAPP(X149,X114),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [X231] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_List_Oset(tc_Nat_Onat),X231)))
         => X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).

fof(fact_order__less__le,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & X20 != X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_order__le__less,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
          | X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Oorder(X56)
     => ( X60 != X61
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
          | X55 = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X61))
       => ( X60 != X61
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_xt1_I11_J,axiom,
    ! [X60,X61,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
       => ( X60 != X61
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_xt1_I12_J,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Oorder(X56)
     => ( X60 != X61
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X60))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_add__number__of__eq,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_number__of__mult,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_number__of__add,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_number__of__diff,axiom,
    ! [X126,X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X122),X126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X122)),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).

fof(fact_of__int__mult,axiom,
    ! [X58,X126,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X58)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Oring__1__class_Oof__int(X56),X126)),hAPP(c_Int_Oring__1__class_Oof__int(X56),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__mult) ).

fof(fact_of__int__add,axiom,
    ! [X58,X126,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Oring__1__class_Oof__int(X56),X126)),hAPP(c_Int_Oring__1__class_Oof__int(X56),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__add) ).

fof(fact_of__int__diff,axiom,
    ! [X58,X126,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X126),X58)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(c_Int_Oring__1__class_Oof__int(X56),X126)),hAPP(c_Int_Oring__1__class_Oof__int(X56),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__diff) ).

fof(fact_of__nat__mult,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).

fof(fact_of__nat__add,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [X258,X161,X56] : c_Enum_Oproduct(X56,X161,c_List_Olist_ONil(X56),X258) = c_List_Olist_ONil(tc_prod(X56,X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_minus1__divide,axiom,
    ! [X55,X56] :
      ( ( class_Fields_Ofield__inverse__zero(X56)
        & class_Int_Onumber__ring(X56) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)),X55) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),c_Groups_Oone__class_Oone(X56)),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus1__divide) ).

fof(fact_setprod__1,axiom,
    ! [X19,X17,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),hAPP(c_COMBK(X5,X17),c_Groups_Oone__class_Oone(X5))),X19) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__1) ).

fof(fact_setsum__0,axiom,
    ! [X19,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),hAPP(c_COMBK(X5,X17),c_Groups_Ozero__class_Ozero(X5))),X19) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__0) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [X102,X106] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),c_Groups_Oone__class_Oone(tc_Int_Oint))),X102) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_order__less__imp__le,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_tl__replicate,axiom,
    ! [X55,X56,X92] :
      ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(X56),c_List_Oreplicate(X56,X92,X55)) = c_List_Oreplicate(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__replicate) ).

fof(fact_negateSnd__eq,axiom,
    ! [X119,X107] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X119)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_abs__power__minus__one,axiom,
    ! [X92,X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Rings_Olinordered__idom(X56) )
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)),X92)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
    ! [X22,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( c_Nat__Transfer_Onat__set(X22)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X19),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_zle__iff__zadd,axiom,
    ! [X26,X84] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X26))
    <=> ? [X130] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X130)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_map__replicate,axiom,
    ! [X20,X89,X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Oreplicate(X17,X89,X20)) = c_List_Oreplicate(X5,X89,hAPP(X2,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate) ).

fof(fact_filter__remove1,axiom,
    ! [X224,X20,X29,X5] : hAPP(c_List_Ofilter(X5,X29),c_List_Oremove1(X5,X20,X224)) = c_List_Oremove1(X5,X20,hAPP(c_List_Ofilter(X5,X29),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__remove1) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [X223,X20,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5))) = X223
    <=> ( X223 != c_List_Olist_ONil(X5)
        & c_List_Obutlast(X5,X223) = X224
        & c_List_Olast(X5,X223) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_negD,axiom,
    ! [X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X55),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [X130] : X55 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X130))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).

fof(fact_Ints__number__of,axiom,
    ! [X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__number__of) ).

fof(fact_Ints__of__int,axiom,
    ! [X26,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__int) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [X89,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Ints__of__nat,axiom,
    ! [X89,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_Suc__diff__1,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X92 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_Suc__pred_H,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => X92 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_nat__of,axiom,
    ! [X20] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X20)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of) ).

fof(fact_mod__div__trivial,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),c_Divides_Odiv__class_Omod(X56,X60,X61)),X61) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [X61] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_set__replicate__Suc,axiom,
    ! [X20,X89,X5] : hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,hAPP(c_Nat_OSuc,X89),X20)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate__Suc) ).

fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [X24,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X20,X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_Int__empty__left,axiom,
    ! [X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X22) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).

fof(fact_Un__UNIV__left,axiom,
    ! [X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X22) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_empty__Diff,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).

fof(fact_Sigma__empty1,axiom,
    ! [X22,X17,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X22) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_le__square,axiom,
    ! [X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(fact_le__add1,axiom,
    ! [X86,X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X86,X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [X6,X84,X21,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)) = X6
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) != c_Groups_Ozero__class_Ozero(X5)
           => X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [X84,X21,X6,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)) = X21 )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X84) = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_nat__less__cases,axiom,
    ! [X30,X89,X51] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
       => hBOOL(hAPP(hAPP(X30,X89),X51)) )
     => ( ( X51 = X89
         => hBOOL(hAPP(hAPP(X30,X89),X51)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
           => hBOOL(hAPP(hAPP(X30,X89),X51)) )
         => hBOOL(hAPP(hAPP(X30,X89),X51)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X19] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X19) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_append__eq__appendI,axiom,
    ! [X241,X221,X237,X240,X222,X56] :
      ( hAPP(hAPP(c_List_Oappend(X56),X222),X240) = X237
     => ( X221 = hAPP(hAPP(c_List_Oappend(X56),X240),X241)
       => hAPP(hAPP(c_List_Oappend(X56),X222),X221) = hAPP(hAPP(c_List_Oappend(X56),X237),X241) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [X237,X222,X221,X240,X55,X56] :
      ( hAPP(hAPP(c_List_Olist_OCons(X56),X55),X240) = X221
     => ( X222 = hAPP(hAPP(c_List_Oappend(X56),X240),X237)
       => hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222) = hAPP(hAPP(c_List_Oappend(X56),X221),X237) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_zadd__left__commute,axiom,
    ! [X58,X57,X55] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X57),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X58,X57,X55] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [X95,X96] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X96),X95) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X96,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X95),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__upto) ).

fof(fact_nat__minus__add__max,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X86)),X86) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X92),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).

fof(fact_dual__max,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Orderings_Oord_Omax(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5))) = c_Orderings_Oord__class_Omin(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__max) ).

fof(fact_dual__min,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Orderings_Oord_Omin(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5))) = c_Orderings_Oord__class_Omax(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__min) ).

fof(fact_listsum__foldl,axiom,
    ! [X5] :
      ( class_Groups_Omonoid__add(X5)
     => c_List_Omonoid__add__class_Olistsum(X5) = c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__foldl) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60)),X61) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)),X61) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [X90,X95,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X95))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X96) = X90
      <=> X95 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_zmod__zminus2,axiom,
    ! [X61,X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_remove1__remdups,axiom,
    ! [X55,X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => c_List_Oremove1(X56,X55,c_List_Oremdups(X56,X222)) = c_List_Oremdups(X56,c_List_Oremove1(X56,X55,X222)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__remdups) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [X78,X5] :
      ( c_Nitpick_Owf_H(X5,X78)
    <=> ( c_Wellfounded_Oacyclic(X5,X78)
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78))
          | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Owf_H__def) ).

fof(fact_wf__iff__acyclic__if__finite,axiom,
    ! [X78,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78))
     => ( c_Wellfounded_Owf(X5,X78)
      <=> c_Wellfounded_Oacyclic(X5,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [X78,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X78))
     => ( c_Wellfounded_Oacyclic(X5,X78)
       => c_Wellfounded_Owf(X5,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_inj__on__rev,axiom,
    ! [X19,X5] : c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orev(X5),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__rev) ).

fof(fact_distinct__filter,axiom,
    ! [X30,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Ofilter(X5,X30),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__filter) ).

fof(fact_triple_Osize_I2_J,axiom,
    ! [X10,X11,X12,X5] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Osize_I2_J) ).

fof(fact_equivp__def,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
    <=> ! [X3,X38] :
          ( hBOOL(hAPP(hAPP(X37,X3),X38))
        <=> hAPP(X37,X3) = hAPP(X37,X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).

fof(fact_diff__add__cancel,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)),X61) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_add__diff__cancel,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)),X61) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => c_List_Olinorder__class_Osort__key(X5,X17,X2,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I1_J) ).

fof(fact_fst__eq__Domain,axiom,
    ! [X37,X17,X5] : hAPP(c_Set_Oimage(tc_prod(X5,X17),X5,c_Product__Type_Ofst(X5,X17)),X37) = hAPP(c_Relation_ODomain(X5,X17),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_snd__eq__Range,axiom,
    ! [X37,X5,X17] : hAPP(c_Set_Oimage(tc_prod(X17,X5),X5,c_Product__Type_Osnd(X17,X5)),X37) = hAPP(c_Relation_ORange(X17,X5),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_total__on__converse,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Ototal__on(X5,X19,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Relation_Ototal__on(X5,X19,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).

fof(fact_refl__on__converse,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Relation_Orefl__on(X5,X19,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).

fof(fact_com_Osize_I11_J,axiom,
    ! [X11,X52,X159] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X159,X52,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I11_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X19) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
    ! [X20,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X20),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_nat__set__def,axiom,
    ! [X36] :
      ( c_Nat__Transfer_Onat__set(X36)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__set__def) ).

fof(fact_refl__on__empty,axiom,
    ! [X5] : c_Relation_Orefl__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).

fof(fact_card__eq__setsum,axiom,
    ! [X19,X5] : hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [X186,X185,X92,X86] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),X185))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X86,X92),X186))
       => X185 = X186 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_inj__uminus,axiom,
    ! [X19,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => c_Fun_Oinj__on(X5,X5,c_Groups_Ouminus__class_Ouminus(X5),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__uminus) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [X86,X92] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X92,X86) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X92),hAPP(c_Code__Numeral_Onat__of,X86))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_nth__Cons__0,axiom,
    ! [X222,X55,X56] : hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_part__equivp__refl__symp__transp,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X37,X3),X3))
        & c_Predicate_Osymp(X5,X37)
        & c_Predicate_Otransp(X5,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).

fof(fact_image__is__empty,axiom,
    ! [X19,X2,X5,X17] :
      ( hAPP(c_Set_Oimage(X17,X5,X2),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).

fof(fact_empty__is__image,axiom,
    ! [X19,X2,X17,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X17,X5,X2),X19)
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).

fof(fact_listrelp_ONil,axiom,
    ! [X78,X5] : c_List_Olistrelp(X5,X78,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [X78,X5] : c_List_Olistrelp(X5,X78,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_hd__map,axiom,
    ! [X2,X17,X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => hAPP(c_List_Ohd(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) = hAPP(X2,hAPP(c_List_Ohd(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__map) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [X96,X134,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X134,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X96) = X96 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21) = hAPP(hAPP(c_Set_Oinsert(X5),X23),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
      <=> ( X6 = X21
          & X21 = X23 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_pos__single__def,axiom,
    ! [X264,X265,X266,X20,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X5),X20),X266),X265),X264) = c_New__DSequence_Opos__single(X5,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).

fof(fact_neg__single__def,axiom,
    ! [X264,X265,X266,X20,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X5),X20),X266),X265),X264) = c_New__DSequence_Oneg__single(X5,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).

fof(fact_power__abs,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

fof(fact_minus__divide__left,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__mult__left,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oring(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [X6,X115,X116,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X116,X115),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X116,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact__07,axiom,
    ! [X2,X5,X17] : c_Lazy__Sequence_Omap(X17,X5,X2,c_Lazy__Sequence_Olazy__sequence_OEmpty(X17)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__07) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [X2,X5,X17] : c_List_Omaps(X17,X5,X2,c_List_Olist_ONil(X17)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6))
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).

fof(fact_greaterThanAtMost__empty,axiom,
    ! [X90,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X90))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanLessThan__empty,axiom,
    ! [X90,X106,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X106),X90))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [X51] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X51 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).

fof(fact_tl__append2,axiom,
    ! [X221,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),hAPP(c_List_Otl(X56),X222)),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append2) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).

fof(fact_prod__eqI,axiom,
    ! [X107,X108,X161,X56] :
      ( hAPP(c_Product__Type_Ofst(X56,X161),X108) = hAPP(c_Product__Type_Ofst(X56,X161),X107)
     => ( hAPP(c_Product__Type_Osnd(X56,X161),X108) = hAPP(c_Product__Type_Osnd(X56,X161),X107)
       => X108 = X107 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__eqI) ).

fof(fact_Pair__fst__snd__eq,axiom,
    ! [X17,X5,X15,X146] :
      ( X146 = X15
    <=> ( hAPP(c_Product__Type_Ofst(X5,X17),X146) = hAPP(c_Product__Type_Ofst(X5,X17),X15)
        & hAPP(c_Product__Type_Osnd(X5,X17),X146) = hAPP(c_Product__Type_Osnd(X5,X17),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_inj__on__id,axiom,
    ! [X19,X5] : c_Fun_Oinj__on(X5,X5,c_Fun_Oid(X5),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id) ).

fof(fact_inj__on__id2,axiom,
    ! [X19,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_sgn__times,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => c_Groups_Osgn__class_Osgn(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Osgn__class_Osgn(X56,X60)),c_Groups_Osgn__class_Osgn(X56,X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [X223,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X224)
       => ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
         => ( c_List_Olinorder__class_Osorted(X5,X223)
           => ( hBOOL(hAPP(c_List_Odistinct(X5),X223))
             => ( hAPP(c_List_Oset(X5),X224) = hAPP(c_List_Oset(X5),X223)
               => X224 = X223 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [X222,X55,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_OSuc,X92)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Odrop(X56),X92),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Suc__Cons) ).

fof(fact_less__than__def,axiom,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__def) ).

fof(fact_abs__minus__commute,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)) = hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X61),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [X149,X28,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X28,X149,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [X149,X28,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X28,X149,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_nat__case__0,axiom,
    ! [X149,X28,X5] : c_Nat_Onat_Onat__case(X5,X28,X149,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X57,X55] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [X126,X122] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X57,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmult__int,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X126,X122] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X57,X55] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zadd__int,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).

fof(fact_zdiv__int,axiom,
    ! [X61,X60] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X60),X61)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X60)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__int) ).

fof(fact_int__mult,axiom,
    ! [X92,X86] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X126,X58] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_Int__UNIV__left,axiom,
    ! [X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X22) = X22,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__empty__left,axiom,
    ! [X22,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X22) = X22,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X89) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X51 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X89 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(fact_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Pls) ).

fof(fact_fold1__singleton,axiom,
    ! [X6,X2,X5] : hAPP(c_Finite__Set_Ofold1(X5,X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton) ).

fof(fact_length__map,axiom,
    ! [X224,X2,X17,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17)),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__map) ).

fof(fact_length__list__update,axiom,
    ! [X55,X98,X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(hAPP(c_List_Olist__update(X56,X222),X98),X55)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__list__update) ).

fof(fact_of__int__power,axiom,
    ! [X92,X58,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X58),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Int_Oring__1__class_Oof__int(X56),X58)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__power) ).

fof(fact_of__nat__power,axiom,
    ! [X92,X86,X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).

fof(fact_zless__le,axiom,
    ! [X84,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X84))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),X84))
        & X26 != X84 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => ( X86 != X92
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
        | X51 = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_nat__less__le,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
        & X51 != X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_fold1__singleton__def,axiom,
    ! [X6,X2,X5,X1] :
      ( X1 = c_Finite__Set_Ofold1(X5,X2)
     => hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_length__tl,axiom,
    ! [X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(c_List_Otl(X56),X222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__tl) ).

fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [X26,X20,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X17,X2)
     => hAPP(hAPP(X2,X20),hAPP(hAPP(X2,X20),X26)) = hAPP(hAPP(X2,X20),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
    ! [X62] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X62)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X106,X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_less__Suc0,axiom,
    ! [X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X41] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X55),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
        | X86 = X92 )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_eq__mem,axiom,
    ! [X24,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_fequal,X24)))
    <=> X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_last__map,axiom,
    ! [X2,X17,X5,X224] :
      ( X224 != c_List_Olist_ONil(X5)
     => c_List_Olast(X17,hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) = hAPP(X2,c_List_Olast(X5,X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__map) ).

fof(fact_minus__add__cancel,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61)) = X61 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_ex__in__conv,axiom,
    ! [X19,X5] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
    <=> X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).

fof(fact_of__nat__nat,axiom,
    ! [X58,X56] :
      ( class_Rings_Oring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,X58)) = hAPP(c_Int_Oring__1__class_Oof__int(X56),X58) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X57,X55] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X55,X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [X61,X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_zmod__int,axiom,
    ! [X61,X60] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X60,X61)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X60),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__int) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [X224,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X224) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X5),c_COMBI(X5)),hAPP(c_List_Oset(X5),X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [X107,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X107)) = hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Nat_OSuc,X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_power__Suc,axiom,
    ! [X92,X60,X56] :
      ( class_Power_Opower(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [X107,X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Nat_OSuc,X107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_image__uminus__atMost,axiom,
    ! [X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X20)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X20)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X20)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [X20,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X20)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_replicate__Suc,axiom,
    ! [X55,X92,X56] : c_List_Oreplicate(X56,hAPP(c_Nat_OSuc,X92),X55) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Oreplicate(X56,X92,X55)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__Suc) ).

fof(fact_set__replicate__conv__if,axiom,
    ! [X20,X5,X89] :
      ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X20)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
      & ( X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X20)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate__conv__if) ).

fof(fact_set__replicate,axiom,
    ! [X20,X5,X89] :
      ( X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X89,X20)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate) ).

fof(fact_abs__of__pos,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__of__neg,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_sgn__1__neg,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_sgn__neg,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
       => c_Groups_Osgn__class_Osgn(X56,X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_part__equivp__symp,axiom,
    ! [X24,X20,X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
     => ( hBOOL(hAPP(hAPP(X37,X20),X24))
       => hBOOL(hAPP(hAPP(X37,X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__symp) ).

fof(fact_sympE,axiom,
    ! [X24,X20,X78,X5] :
      ( c_Predicate_Osymp(X5,X78)
     => ( hBOOL(hAPP(hAPP(X78,X20),X24))
       => hBOOL(hAPP(hAPP(X78,X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sympE) ).

fof(fact_equivp__symp,axiom,
    ! [X24,X20,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ( hBOOL(hAPP(hAPP(X37,X20),X24))
       => hBOOL(hAPP(hAPP(X37,X24),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).

fof(fact_dvd__eq__mod__eq__0,axiom,
    ! [X21,X6,X5] :
      ( class_Divides_Osemiring__div(X5)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X21))
      <=> c_Divides_Odiv__class_Omod(X5,X21,X6) = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).

fof(fact_dvd__imp__mod__0,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X61))
       => c_Divides_Odiv__class_Omod(X56,X61,X60) = c_Groups_Ozero__class_Ozero(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).

fof(fact_length__butlast,axiom,
    ! [X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),c_List_Obutlast(X56,X222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__butlast) ).

fof(fact_lists_ONil,axiom,
    ! [X19,X5] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olists(X5,X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_ONil) ).

fof(fact_sgn__1__pos,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Oone__class_Oone(X5)
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_sgn__pos,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => c_Groups_Osgn__class_Osgn(X56,X60) = c_Groups_Oone__class_Oone(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X60,X61,X56] :
      ( class_Rings_Odivision__ring(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [X5] : c_List_Olistset(X5,c_List_Olist_ONil(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_lists__empty,axiom,
    ! [X5] : c_List_Olists(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__empty) ).

fof(fact_CollectI,axiom,
    ! [X5,X6,X30] :
      ( hBOOL(hAPP(X30,X6))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).

fof(fact_distinct__rev,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orev(X5),X224)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rev) ).

fof(fact_distinct1__rotate,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate1(X5),X224)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_quotient__empty,axiom,
    ! [X78,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X78) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__empty) ).

fof(fact_split__Pair,axiom,
    ! [X17,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X17,tc_prod(X5,X17)),c_Product__Type_OPair(X5,X17)) = c_Fun_Oid(tc_prod(X5,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__Pair) ).

fof(fact_inf__absorb1,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) = X55 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).

fof(fact_le__iff__inf,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),X24) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).

fof(fact_inf__absorb2,axiom,
    ! [X55,X57,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) = X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).

fof(fact_sup__absorb2,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) = X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb2) ).

fof(fact_le__iff__sup,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),X24) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__sup) ).

fof(fact_sup__absorb1,axiom,
    ! [X55,X57,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) = X55 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb1) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),X24) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57) = X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57) = X55 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),X24) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57) = X55 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57) = X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_Sup__singleton,axiom,
    ! [X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Inf__singleton,axiom,
    ! [X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Min_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Max_Osingleton,axiom,
    ! [X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_mult__Suc,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).

fof(fact_cut,axiom,
    ! [X4,X13,X14,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X14,X13)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X14)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut) ).

fof(fact_diff__add__inverse,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)),X92) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__add__inverse2,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),X92) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_New__DSequence_Opos__union__def,axiom,
    ! [X96,X272,X254,X5] : hAPP(c_New__DSequence_Opos__union(X5,X254,X272),X96) = c_Lazy__Sequence_Oappend(X5,hAPP(X254,X96),hAPP(X272,X96)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).

fof(fact_Union__quotient,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__quotient) ).

fof(fact_minus__divide__divide,axiom,
    ! [X61,X60,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_abs__mult__self,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

fof(fact_minus__mult__minus,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__mult__commute,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_wfP__accp__iff,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_OwfP(X5,X78)
    <=> ! [X77] : hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X77)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X60,X61,X56] :
      ( class_Rings_Odivision__ring(X56)
     => ( X61 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_quotient__is__empty2,axiom,
    ! [X78,X19,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [X78,X19,X5] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty) ).

fof(fact_card__greaterThanAtMost__int,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X106,X102)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),X106)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X20 != X24
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
        | X55 = X57
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_mod__mod__trivial,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,c_Divides_Odiv__class_Omod(X56,X60,X61),X61) = c_Divides_Odiv__class_Omod(X56,X60,X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_Int__empty__right,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__right) ).

fof(fact_Un__UNIV__right,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).

fof(fact_Diff__UNIV,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_Domain__empty,axiom,
    ! [X17,X5] : hAPP(c_Relation_ODomain(X5,X17),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty) ).

fof(fact_Range__empty,axiom,
    ! [X5,X17] : hAPP(c_Relation_ORange(X17,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17,X5),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty) ).

fof(fact_fst__conv,axiom,
    ! [X61,X60,X161,X56] : hAPP(c_Product__Type_Ofst(X56,X161),hAPP(hAPP(c_Product__Type_OPair(X56,X161),X60),X61)) = X60,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__conv) ).

fof(fact_snd__conv,axiom,
    ! [X61,X60,X56,X161] : hAPP(c_Product__Type_Osnd(X161,X56),hAPP(hAPP(c_Product__Type_OPair(X161,X56),X60),X61)) = X61,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__conv) ).

fof(fact_minus__Min,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min) ).

fof(fact_le__iff__add,axiom,
    ! [X89,X51] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
    <=> ? [X97] : X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_insert__absorb,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(hAPP(c_Set_Oinsert(X5),X6),X19) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).

fof(fact_the__elem__eq,axiom,
    ! [X20,X5] : c_Set_Othe__elem(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__linear,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [X222,X55,X56] :
      ( class_Groups_Omonoid__add(X56)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(c_List_Omonoid__add__class_Olistsum(X56),X222)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_minus__divide__right,axiom,
    ! [X61,X60,X56] :
      ( class_Fields_Ofield__inverse__zero(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X61)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__mult__right,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Oring(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [X30,X5] : c_List_Opartition(X5,X30,c_List_Olist_ONil(X5)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_take__1__Cons,axiom,
    ! [X222,X55,X56] : hAPP(hAPP(c_List_Otake(X56),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__1__Cons) ).

fof(fact_sym__inv__image,axiom,
    ! [X2,X17,X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => c_Relation_Osym(X17,hAPP(hAPP(c_Relation_Oinv__image(X5,X17),X78),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__inv__image) ).

fof(fact_trans__inv__image,axiom,
    ! [X2,X17,X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => c_Relation_Otrans(X17,hAPP(hAPP(c_Relation_Oinv__image(X5,X17),X78),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__inv__image) ).

fof(fact_wf__inv__image,axiom,
    ! [X2,X17,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(X17,hAPP(hAPP(c_Relation_Oinv__image(X5,X17),X78),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [X2,X17,X30,X5] :
      ( c_FunDef_Oreduction__pair(X5,X30)
     => c_FunDef_Oreduction__pair(X17,hAPP(hAPP(c_FunDef_Orp__inv__image(X5,X17),X30),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_dvd__0__left,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),c_Groups_Ozero__class_Ozero(X56)),X60))
       => X60 = c_Groups_Ozero__class_Ozero(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

fof(fact_mod__add__self1,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X60),X61) = c_Divides_Odiv__class_Omod(X56,X60,X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__self2,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61),X61) = c_Divides_Odiv__class_Omod(X56,X60,X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).

fof(fact_nth__via__drop,axiom,
    ! [X221,X57,X222,X92,X56] :
      ( hAPP(hAPP(c_List_Odrop(X56),X92),X222) = hAPP(hAPP(c_List_Olist_OCons(X56),X57),X221)
     => hAPP(hAPP(c_List_Onth(X56),X222),X92) = X57 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__via__drop) ).

fof(fact_max__Suc__Suc,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Nat_OSuc,X92)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_min__Suc__Suc,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Nat_OSuc,X92)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_times__code__numeral__code,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X92)),hAPP(c_Code__Numeral_Oof__nat,X86)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X92)),hAPP(c_Code__Numeral_Oof__nat,X86)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [X92,X55] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55)),X92) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X55),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_zpower__int,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),X92) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).

fof(fact_zmult__zminus,axiom,
    ! [X126,X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)),X126) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(fact_int__power,axiom,
    ! [X92,X86] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X92)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).

fof(fact_List_Oset__insert,axiom,
    ! [X224,X20,X5] : hAPP(c_List_Oset(X5),c_List_Oinsert(X5,X20,X224)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [X268,X122,X56] : c_List_Osplice(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X122),X268),c_List_Olist_ONil(X56)) = hAPP(hAPP(c_List_Olist_OCons(X56),X122),X268),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).

fof(fact_abs__ge__zero,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Groups_Oabs__class_Oabs(X56),X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [X92,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_inf__left__idem,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [X61,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_sup__left__idem,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__idem) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [X61,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_mult__left__idem,axiom,
    ! [X61,X60,X56] :
      ( class_Lattices_Oab__semigroup__idem__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).

fof(fact__03,axiom,
    ! [X299,X276,X56] : c_Lazy__Sequence_Oflat(X56,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X56),X276,X299)) = c_Lazy__Sequence_Oappend(X56,X276,c_Lazy__Sequence_Oflat(X56,X299)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__03) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ? [X3] :
            ( hAPP(c_List_Oset(X5),X3) = X19
            & c_List_Olinorder__class_Osorted(X5,X3)
            & hBOOL(hAPP(c_List_Odistinct(X5),X3))
            & ! [X38] :
                ( ( hAPP(c_List_Oset(X5),X38) = X19
                  & c_List_Olinorder__class_Osorted(X5,X38)
                  & hBOOL(hAPP(c_List_Odistinct(X5),X38)) )
               => X38 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_drop__tl,axiom,
    ! [X222,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(c_List_Otl(X56),X222)) = hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [X222,X92,X56] : hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(c_List_Otl(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__drop) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [X224,X20,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(c_List_Oset(X5),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X106,X102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X102)),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).

fof(fact_surj__id,axiom,
    ! [X5] : hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__id) ).

fof(fact_Respects__def,axiom,
    ! [X20,X37,X5] :
      ( hBOOL(hAPP(c_Quotient_ORespects(X5,X37),X20))
    <=> hBOOL(hAPP(hAPP(X37,X20),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Respects__def) ).

fof(fact_some__eq__ex,axiom,
    ! [X5,X30] :
      ( hBOOL(hAPP(X30,c_Hilbert__Choice_OEps(X5,X30)))
    <=> ? [X77] : hBOOL(hAPP(X30,X77)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).

fof(fact_partition__filter1,axiom,
    ! [X224,X30,X5] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X30,X224)) = hAPP(c_List_Ofilter(X5,X30),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter1) ).

fof(fact_dvd__1__left,axiom,
    ! [X93] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X93)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_UNIV__I,axiom,
    ! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(fact_Compl__eq__Compl__iff,axiom,
    ! [X22,X19,X5] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)
    <=> X19 = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_fun__Compl__def,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,X5)),X19),X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X19,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_uminus__apply,axiom,
    ! [X20,X19,X17,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,X5)),X19),X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X19,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_nat__0__le,axiom,
    ! [X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = X58 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__le) ).

fof(fact_tsub__eq,axiom,
    ! [X55,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),X55))
     => c_Nat__Transfer_Otsub(X55,X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X92)),hAPP(c_Code__Numeral_Oof__nat,X86)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_int__eq__iff,axiom,
    ! [X26,X51] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) = X26
    <=> ( X51 = hAPP(c_Int_Onat,X26)
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [X19,X18,X2,X5] :
      ( c_Big__Operators_Osemilattice__big(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(X18,X19) = hAPP(c_Finite__Set_Ofold1(X5,X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(X18,X19) = hAPP(c_Finite__Set_Ofold1(X5,X2),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).

fof(fact_Union__UNIV,axiom,
    ! [X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Union__empty,axiom,
    ! [X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__empty) ).

fof(fact_Inter__UNIV,axiom,
    ! [X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_Inter__empty,axiom,
    ! [X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__empty) ).

fof(fact_insert__absorb2,axiom,
    ! [X19,X20,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).

fof(fact_Bit1__Min,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).

fof(fact_INF__const,axiom,
    ! [X76,X5,X19,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X17),X19),hAPP(c_COMBK(X17,X5),X76)) = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__const) ).

fof(fact_SUP__const,axiom,
    ! [X76,X5,X19,X17] :
      ( class_Complete__Lattice_Ocomplete__lattice(X17)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X17),X19),hAPP(c_COMBK(X17,X5),X76)) = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__const) ).

fof(fact_compl__unique,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) = c_Orderings_Obot__class_Obot(X56)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) = c_Orderings_Otop__class_Otop(X56)
         => hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55) = X57 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__unique) ).

fof(fact_mult__Suc__right,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [X102] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [X260,X56] : c_List_Otranspose(X56,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X56)),c_List_Olist_ONil(X56)),X260)) = c_List_Otranspose(X56,X260),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).

fof(fact_Field__empty,axiom,
    ! [X5] : hAPP(c_Relation_OField(X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__empty) ).

fof(fact_mod__less,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [X102,X106] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),c_Groups_Oone__class_Oone(tc_Int_Oint)),X102) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_Sup__insert,axiom,
    ! [X19,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Complete__Lattice_OSup__class_OSup(X5,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__insert) ).

fof(fact_Inf__insert,axiom,
    ! [X19,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Complete__Lattice_OInf__class_OInf(X5,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__insert) ).

fof(fact_infinite__UNIV__int,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).

fof(fact_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).

fof(fact_insert__remdups,axiom,
    ! [X222,X55,X56] : c_List_Oinsert(X56,X55,c_List_Oremdups(X56,X222)) = c_List_Oremdups(X56,c_List_Oinsert(X56,X55,X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__remdups) ).

fof(fact_list__all__rev,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__all(X5,X30,hAPP(c_List_Orev(X5),X224))
    <=> c_List_Olist__all(X5,X30,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__rev) ).

fof(fact_list__ex__rev,axiom,
    ! [X224,X30,X5] :
      ( c_List_Olist__ex(X5,X30,hAPP(c_List_Orev(X5),X224))
    <=> c_List_Olist__ex(X5,X30,X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__rev) ).

fof(fact_butlast__append,axiom,
    ! [X222,X56,X221] :
      ( ( X221 = c_List_Olist_ONil(X56)
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = c_List_Obutlast(X56,X222) )
      & ( X221 != c_List_Olist_ONil(X56)
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(hAPP(c_List_Oappend(X56),X222),c_List_Obutlast(X56,X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [X55,X56,X222] :
      ( ( X222 = c_List_Olist_ONil(X56)
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = c_List_Olist_ONil(X56) )
      & ( X222 != c_List_Olist_ONil(X56)
       => c_List_Obutlast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Obutlast(X56,X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_Image__empty,axiom,
    ! [X37,X5,X17] : hAPP(c_Relation_OImage(X17,X5,X37),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).

fof(fact_vimage__UNIV,axiom,
    ! [X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_vimage__empty,axiom,
    ! [X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__empty) ).

fof(fact_image__empty,axiom,
    ! [X2,X5,X17] : hAPP(c_Set_Oimage(X17,X5,X2),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__empty) ).

fof(fact_listrel__refl__on,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => c_Relation_Orefl__on(tc_List_Olist(X5),c_List_Olists(X5,X19),c_List_Olistrel(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_equiv__listrel,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(X5),c_List_Olists(X5,X19),c_List_Olistrel(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__listrel) ).

fof(fact_mem__def,axiom,
    ! [X19,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
    <=> hBOOL(hAPP(X19,X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_com_Osize_I3_J,axiom,
    ! [X11,X52,X159] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X159,X52,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I3_J) ).

fof(fact_dvdI,axiom,
    ! [X93,X61,X60,X56] :
      ( class_Rings_Odvd(X56)
     => ( X60 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X93)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X61),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).

fof(fact_div__less,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

fof(fact_diff__is__0__eq,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X89) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_Int__UNIV__right,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Un__empty__right,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).

fof(fact_Diff__empty,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).

fof(fact_double__complement,axiom,
    ! [X19,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).

fof(fact_rel__pow__1,axiom,
    ! [X37,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X37) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__1) ).

fof(fact_list__update__id,axiom,
    ! [X98,X222,X56] : hAPP(hAPP(c_List_Olist__update(X56,X222),X98),hAPP(hAPP(c_List_Onth(X56),X222),X98)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__id) ).

fof(fact_square__eq__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Oidom(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X21)
      <=> ( X6 = X21
          | X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact_add__Suc,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_drop__butlast,axiom,
    ! [X222,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),c_List_Obutlast(X56,X222)) = c_List_Obutlast(X56,hAPP(hAPP(c_List_Odrop(X56),X92),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__butlast) ).

fof(fact_butlast__drop,axiom,
    ! [X222,X92,X56] : c_List_Obutlast(X56,hAPP(hAPP(c_List_Odrop(X56),X92),X222)) = hAPP(hAPP(c_List_Odrop(X56),X92),c_List_Obutlast(X56,X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__drop) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [X96] :
      ( X96 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X96)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_Domain__empty__iff,axiom,
    ! [X78,X17,X5] :
      ( hAPP(c_Relation_ODomain(X5,X17),X78) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X78 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X17),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Range__empty__iff,axiom,
    ! [X78,X5,X17] :
      ( hAPP(c_Relation_ORange(X17,X5),X78) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X78 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17,X5),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [X92,X86] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X92)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X86) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_zless__linear,axiom,
    ! [X57,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X55),X57))
      | X55 = X57
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X57),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(fact_nat__neq__iff,axiom,
    ! [X89,X51] :
      ( X51 != X89
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X106),X102)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),X106)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_abs__ge__self,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),hAPP(c_Groups_Oabs__class_Oabs(X56),X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X106,X102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X106)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_part__equivpI,axiom,
    ! [X5,X37] :
      ( ? [X3] : hBOOL(hAPP(hAPP(X37,X3),X3))
     => ( c_Predicate_Osymp(X5,X37)
       => ( c_Predicate_Otransp(X5,X37)
         => c_Equiv__Relations_Opart__equivp(X5,X37) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpI) ).

fof(fact_zle__linear,axiom,
    ! [X126,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),X126))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X126),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_nat__le__linear,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_zdiv__zminus2,axiom,
    ! [X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60)),X61),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_drop__Suc,axiom,
    ! [X222,X92,X56] : hAPP(hAPP(c_List_Odrop(X56),hAPP(c_Nat_OSuc,X92)),X222) = hAPP(hAPP(c_List_Odrop(X56),X92),hAPP(c_List_Otl(X56),X222)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Suc) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
    <=> ? [X99] : X89 = hAPP(c_Nat_OSuc,X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm(X5,tc_List_Olist(X5),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_equivI,axiom,
    ! [X78,X19,X5] :
      ( c_Relation_Orefl__on(X5,X19,X78)
     => ( c_Relation_Osym(X5,X78)
       => ( c_Relation_Otrans(X5,X78)
         => c_Equiv__Relations_Oequiv(X5,X19,X78) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivI) ).

fof(fact_equiv__def,axiom,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
    <=> ( c_Relation_Orefl__on(X5,X19,X78)
        & c_Relation_Osym(X5,X78)
        & c_Relation_Otrans(X5,X78) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__def) ).

fof(fact_distinct__tl,axiom,
    ! [X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => hBOOL(hAPP(c_List_Odistinct(X56),hAPP(c_List_Otl(X56),X222))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__tl) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [X102,X106] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_neg__def,axiom,
    ! [X158] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X158))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__def) ).

fof(fact_card__distinct,axiom,
    ! [X224,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)
     => hBOOL(hAPP(c_List_Odistinct(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__distinct) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X57,X55] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X55),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X55),X57)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_singleton__rev__conv,axiom,
    ! [X224,X20,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) = hAPP(c_List_Orev(X5),X224)
    <=> X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [X20,X224,X5] :
      ( hAPP(c_List_Orev(X5),X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5))
    <=> X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_com_Osize_I14_J,axiom,
    ! [X11,X52] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X52,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I14_J) ).

fof(fact_listrel1__converse,axiom,
    ! [X78,X5] : c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__converse) ).

fof(fact_minus__diff__eq,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oab__group__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_rev__replicate,axiom,
    ! [X55,X92,X56] : hAPP(c_List_Orev(X56),c_List_Oreplicate(X56,X92,X55)) = c_List_Oreplicate(X56,X92,X55),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__replicate) ).

fof(fact_acc__wfD,axiom,
    ! [X20,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X78))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [X55,X56] :
      ( class_Rings_Ocomm__ring__1(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56))),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X106),X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [X102,X106] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X106),X102))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_list__all__iff__all__interval__int,axiom,
    ! [X95,X96,X30] :
      ( c_List_Olist__all(tc_Int_Oint,X30,c_List_Oupto(X96,X95))
    <=> c_List_Oall__interval__int(X30,X96,X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).

fof(fact_enum__all,axiom,
    ! [X30,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X30))
      <=> ! [X77] : hBOOL(hAPP(X30,X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).

fof(fact_all__code,axiom,
    ! [X30,X5] :
      ( class_Enum_Oenum(X5)
     => ( ! [X77] : hBOOL(hAPP(X30,X77))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [X190] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X190)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_less__imp__neq,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => X55 != X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => X55 != X57 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => X57 != X55 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [X24,X89,X20,X51,X5] :
      ( c_List_Oreplicate(X5,X51,X20) = c_List_Oreplicate(X5,X89,X24)
    <=> ( X51 = X89
        & ( X51 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X20 = X24 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [X27,X23,X21,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X27)
       => ( X6 = X21
        <=> X23 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_rev__filter,axiom,
    ! [X224,X30,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),hAPP(c_List_Orev(X5),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__filter) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [X91,X93] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93),X91) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(fact_zmod__zminus2__not__zero,axiom,
    ! [X91,X93] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).

fof(fact_neq0__conv,axiom,
    ! [X89] :
      ( X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_n__lists__Nil,axiom,
    ! [X56,X92] :
      ( ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X56,X92,c_List_Olist_ONil(X56)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X56)),c_List_Olist_ONil(X56)),c_List_Olist_ONil(tc_List_Olist(X56))) )
      & ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X56,X92,c_List_Olist_ONil(X56)) = c_List_Olist_ONil(tc_List_Olist(X56)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists__Nil) ).

fof(fact_add__right__cancel,axiom,
    ! [X23,X6,X21,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)
      <=> X21 = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X59,X60,X61,X56] :
      ( class_Groups_Ocancel__semigroup__add(X56)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X61),X60) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60)
       => X61 = X59 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Ocancel__ab__semigroup__add(X56)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)
       => X61 = X59 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)
      <=> X21 = X23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X59,X61,X60,X56] :
      ( class_Groups_Ocancel__semigroup__add(X56)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59)
       => X61 = X59 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [X277,X182,X278,X6,X5] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X278) = c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X182,X277)
    <=> ( X6 = X182
        & X278 = X277 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact_com_Osimps_I2_J,axiom,
    ! [X8,X46,X160,X11,X52,X159] :
      ( c_Com_Ocom_OLocal(X159,X52,X11) = c_Com_Ocom_OLocal(X160,X46,X8)
    <=> ( X159 = X160
        & X52 = X46
        & X11 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).

fof(fact_com_Osimps_I4_J,axiom,
    ! [X53,X54,X46,X47,X48,X52] :
      ( c_Com_Ocom_OCond(X52,X48,X47) = c_Com_Ocom_OCond(X46,X54,X53)
    <=> ( X52 = X46
        & X48 = X54
        & X47 = X53 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).

fof(fact_nat__le__0,axiom,
    ! [X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,X58) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__0) ).

fof(fact_nat__0__iff,axiom,
    ! [X96] :
      ( hAPP(c_Int_Onat,X96) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__iff) ).

fof(fact_is__nat__def,axiom,
    ! [X20] :
      ( c_Nat__Transfer_Ois__nat(X20)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__nat__def) ).

fof(fact_add__Suc__right,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_com_Osimps_I36_J,axiom,
    ! [X53,X54,X46,X11,X52,X159] : c_Com_Ocom_OLocal(X159,X52,X11) != c_Com_Ocom_OCond(X46,X54,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).

fof(fact_com_Osimps_I37_J,axiom,
    ! [X11,X52,X159,X53,X54,X46] : c_Com_Ocom_OCond(X46,X54,X53) != c_Com_Ocom_OLocal(X159,X52,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [X78,X5] : hAPP(c_List_Olexn(X5,X78),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_zero__zle__int,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [X58] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X58))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_Diff__cancel,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).

fof(fact_antisym__empty,axiom,
    ! [X5] : c_Relation_Oantisym(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__empty) ).

fof(fact_wf__empty,axiom,
    ! [X5] : c_Wellfounded_Owf(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__empty) ).

fof(fact_atLeastAtMost__singleton_H,axiom,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X6 = X21
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_sorted__list__of__set,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X19)) = X19
          & c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osorted__list__of__set(X5,X19))
          & hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X19))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [X60,X61,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60),X61) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [X61,X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61),X61) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_distinct__butlast,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
       => hBOOL(hAPP(c_List_Odistinct(X56),c_List_Obutlast(X56,X222))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X106,X102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_list_Oinject,axiom,
    ! [X225,X182,X226,X6,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X6),X226) = hAPP(hAPP(c_List_Olist_OCons(X5),X182),X225)
    <=> ( X6 = X182
        & X226 = X225 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).

fof(fact_append__same__eq,axiom,
    ! [X228,X224,X223,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X223),X224) = hAPP(hAPP(c_List_Oappend(X5),X228),X224)
    <=> X223 = X228 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).

fof(fact_same__append__eq,axiom,
    ! [X228,X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = hAPP(hAPP(c_List_Oappend(X5),X224),X228)
    <=> X223 = X228 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [X6,X5] :
      ( class_Orderings_Oorder(X5)
     => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X6) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_upto__empty,axiom,
    ! [X98,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X98))
     => c_List_Oupto(X98,X94) = c_List_Olist_ONil(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto__empty) ).

fof(fact_n__lists_Osimps_I1_J,axiom,
    ! [X222,X56] : c_Enum_On__lists(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X222) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X56)),c_List_Olist_ONil(X56)),c_List_Olist_ONil(tc_List_Olist(X56))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).

fof(fact_atMost__Suc,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X90)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Suc) ).

fof(fact_eq__number__of__0,axiom,
    ! [X75] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [X122] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [X75] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_inf__sup__absorb,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_sup__inf__absorb,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_conversep__conversep,axiom,
    ! [X78,X5,X17] : c_Predicate_Oconversep(X17,X5,c_Predicate_Oconversep(X5,X17,X78)) = X78,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).

fof(fact_le__0__eq,axiom,
    ! [X89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X89),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_drop__1__Cons,axiom,
    ! [X222,X55,X56] : hAPP(hAPP(c_List_Odrop(X56),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),hAPP(c_Nat_OSuc,X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X86)),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_fold1__def,axiom,
    ! [X19,X2,X5] : hAPP(c_Finite__Set_Ofold1(X5,X2),X19) = c_HOL_OThe(X5,c_Finite__Set_Ofold1Set(X5,X2,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__def) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [X27,X51] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X51,X27) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X144] : X51 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X144) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [X27,X51] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X51,X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X144] : X51 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X144) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
    ! [X20,X19] :
      ( c_Nat__Transfer_Onat__set(X19)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X20),X19))
       => c_Nat__Transfer_Ois__nat(X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_sym__converse,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Relation_Osym(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__converse) ).

fof(fact_antisym__converse,axiom,
    ! [X78,X5] :
      ( c_Relation_Oantisym(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Relation_Oantisym(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__converse) ).

fof(fact_trans__converse,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Relation_Otrans(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__converse) ).

fof(fact_acyclic__converse,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(c_Relation_Oconverse(X5,X5),X78))
    <=> c_Wellfounded_Oacyclic(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).

fof(fact_distinct__card,axiom,
    ! [X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__card) ).

fof(fact_length__remdups__eq,axiom,
    ! [X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)
    <=> c_List_Oremdups(X5,X224) = X224 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_Domain__converse,axiom,
    ! [X78,X17,X5] : hAPP(c_Relation_ODomain(X5,X17),hAPP(c_Relation_Oconverse(X17,X5),X78)) = hAPP(c_Relation_ORange(X17,X5),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [X78,X5,X17] : hAPP(c_Relation_ORange(X17,X5),hAPP(c_Relation_Oconverse(X5,X17),X78)) = hAPP(c_Relation_ODomain(X5,X17),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).

fof(fact_remdups__filter,axiom,
    ! [X224,X30,X5] : c_List_Oremdups(X5,hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),c_List_Oremdups(X5,X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__filter) ).

fof(fact_rtrancl__converse,axiom,
    ! [X78,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X78)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Ortrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_Range__def,axiom,
    ! [X78,X5,X17] : hAPP(c_Relation_ORange(X17,X5),X78) = hAPP(c_Relation_ODomain(X5,X17),hAPP(c_Relation_Oconverse(X17,X5),X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).

fof(fact_exists__code,axiom,
    ! [X30,X5] :
      ( class_Enum_Oenum(X5)
     => ( ? [X77] : hBOOL(hAPP(X30,X77))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).

fof(fact_enum__ex,axiom,
    ! [X30,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X30))
      <=> ? [X77] : hBOOL(hAPP(X30,X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).

fof(fact_list__update__nonempty,axiom,
    ! [X20,X90,X224,X5] :
      ( hAPP(hAPP(c_List_Olist__update(X5,X224),X90),X20) = c_List_Olist_ONil(X5)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [X224,X2,X5,X17] :
      ( hAPP(hAPP(c_List_Omap(X17,X5),X2),X224) = c_List_Olist_ONil(X5)
    <=> X224 = c_List_Olist_ONil(X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [X224,X2,X17,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Omap(X17,X5),X2),X224)
    <=> X224 = c_List_Olist_ONil(X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [X92,X86] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X86) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X86 = X92 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_setprod__empty,axiom,
    ! [X2,X17,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oempty,axiom,
    ! [X1,X17,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_setsum_Oempty,axiom,
    ! [X1,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum__empty,axiom,
    ! [X2,X17,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__empty) ).

fof(fact_gr__implies__not0,axiom,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_finite__UNIV,axiom,
    ! [X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(fact_divide__eq__eq,axiom,
    ! [X6,X23,X21,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23) = X6
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [X23,X21,X6,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) = X21 )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_of__nat__Suc,axiom,
    ! [X86,X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Nat_OSuc,X86)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Oone__class_Oone(X56)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_zero__less__Suc,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl3,axiom,
    ! [X100,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X100))
     => X101 != X100 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X86))
     => X86 != X92 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [X51] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X51)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X51),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).

fof(fact_sorted__takeWhile,axiom,
    ! [X30,X224,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X224)
       => c_List_Olinorder__class_Osorted(X5,c_List_OtakeWhile(X5,X30,X224)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_sorted__remove1,axiom,
    ! [X60,X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X222)
       => c_List_Olinorder__class_Osorted(X56,c_List_Oremove1(X56,X60,X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remove1) ).

fof(fact_mult__cancel2,axiom,
    ! [X89,X90,X51] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X89),X90)
    <=> ( X51 = X89
        | X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(fact_mult__cancel1,axiom,
    ! [X89,X51,X90] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)
    <=> ( X51 = X89
        | X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [X89,X51,X90] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X89)
    <=> ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X51 = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_hd__append,axiom,
    ! [X221,X56,X222] :
      ( ( X222 = c_List_Olist_ONil(X56)
       => hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(c_List_Ohd(X56),X221) )
      & ( X222 != c_List_Olist_ONil(X56)
       => hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(c_List_Ohd(X56),X222) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append) ).

fof(fact_mult__sgn__abs,axiom,
    ! [X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Osgn__class_Osgn(X56,X55)),hAPP(c_Groups_Oabs__class_Oabs(X56),X55)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_zero__less__one,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),c_Groups_Oone__class_Oone(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_zero__le__one,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Ozero__class_Ozero(X56)),c_Groups_Oone__class_Oone(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_Nats__0,axiom,
    ! [X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__0) ).

fof(fact_Ints__0,axiom,
    ! [X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).

fof(fact_Nats__1,axiom,
    ! [X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__1) ).

fof(fact_Ints__1,axiom,
    ! [X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).

fof(fact_divide__eq__imp,axiom,
    ! [X60,X61,X59,X56] :
      ( class_Rings_Odivision__ring(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => ( X61 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59) = X60 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X6,X21,X23,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X23 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23) = X6
        <=> X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [X21,X6,X23,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X23 != c_Groups_Ozero__class_Ozero(X5)
       => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_eq__divide__imp,axiom,
    ! [X61,X60,X59,X56] :
      ( class_Rings_Odivision__ring(X56)
     => ( X59 != c_Groups_Ozero__class_Ozero(X56)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X59) = X61
         => X60 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X61),X59) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_diff__eq,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),X57) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [X57,X55,X56] :
      ( class_Rings_Ocomm__ring__1(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X55),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X55),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_diff__def,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

fof(fact_ab__diff__minus,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Oab__group__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_mult__minus1,axiom,
    ! [X58,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)),X58) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1) ).

fof(fact_bin__less__0__simps_I1_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_hd__append2,axiom,
    ! [X221,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = hAPP(c_List_Ohd(X56),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append2) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X89,X90,X51] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),X90)
    <=> X51 = X89 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X89,X51,X90] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X89)
    <=> X51 = X89 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_singleton__conv2,axiom,
    ! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).

fof(fact_sorted__drop,axiom,
    ! [X92,X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X222)
       => c_List_Olinorder__class_Osorted(X56,hAPP(hAPP(c_List_Odrop(X56),X92),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__drop) ).

fof(fact_sorted__take,axiom,
    ! [X92,X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X222)
       => c_List_Olinorder__class_Osorted(X56,hAPP(hAPP(c_List_Otake(X56),X92),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__take) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite_OemptyI,axiom,
    ! [X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_Pow__not__empty,axiom,
    ! [X19,X5] : hAPP(c_Set_OPow(X5),X19) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_Pow__UNIV,axiom,
    ! [X5] : hAPP(c_Set_OPow(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__UNIV) ).

fof(fact_Id__on__empty,axiom,
    ! [X5] : c_Relation_OId__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__empty) ).

fof(fact_Int__absorb,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X19) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).

fof(fact_Un__absorb,axiom,
    ! [X19,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X19) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).

fof(fact_wf__in__rel,axiom,
    ! [X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
     => c_Wellfounded_OwfP(X5,c_FunDef_Oin__rel(X5,X5,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wf__mlex,axiom,
    ! [X2,X37,X5] :
      ( c_Wellfounded_Owf(X5,X37)
     => c_Wellfounded_Owf(X5,c_Wellfounded_Omlex__prod(X5,X2,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Min_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olinorder__class_OMin(X5,X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Big__Operators_Olinorder__class_OMax(X5,X19) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_lessI,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_OSuc,X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(fact_length__replicate,axiom,
    ! [X55,X92,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),c_List_Oreplicate(X56,X92,X55)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__replicate) ).

fof(fact_compl__inf__bot,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),X55) = c_Orderings_Obot__class_Obot(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_compl__sup__top,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)),X55) = c_Orderings_Otop__class_Otop(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup__top) ).

fof(fact_left__minus,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_ab__left__minus,axiom,
    ! [X60,X56] :
      ( class_Groups_Oab__group__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_last__appendL,axiom,
    ! [X222,X56,X221] :
      ( X221 = c_List_Olist_ONil(X56)
     => c_List_Olast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = c_List_Olast(X56,X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).

fof(fact_last__append,axiom,
    ! [X222,X56,X221] :
      ( ( X221 = c_List_Olist_ONil(X56)
       => c_List_Olast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = c_List_Olast(X56,X222) )
      & ( X221 != c_List_Olist_ONil(X56)
       => c_List_Olast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = c_List_Olast(X56,X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).

fof(fact_diff__add__0,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).

fof(fact_sublist__upt__eq__take,axiom,
    ! [X89,X106,X5] : c_List_Osublist(X5,X106,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89)) = hAPP(hAPP(c_List_Otake(X5),X89),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_bot__least,axiom,
    ! [X55,X56] :
      ( class_Orderings_Obot(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Orderings_Obot__class_Obot(X56)),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).

fof(fact_divmod__int__correct,axiom,
    ! [X60,X61] :
      ( X61 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),c_Divides_Odivmod__int(X60,X61))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [X93,X91] :
      ( ( X91 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X93,X91) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93)) )
      & ( X91 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X93,X91) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_sorted__single,axiom,
    ! [X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => c_List_Olinorder__class_Osorted(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__single) ).

fof(fact_last__appendR,axiom,
    ! [X222,X56,X221] :
      ( X221 != c_List_Olist_ONil(X56)
     => c_List_Olast(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)) = c_List_Olast(X56,X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).

fof(fact_last__ConsR,axiom,
    ! [X55,X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => c_List_Olast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = c_List_Olast(X56,X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).

fof(fact_last_Osimps,axiom,
    ! [X55,X56,X222] :
      ( ( X222 = c_List_Olist_ONil(X56)
       => c_List_Olast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = X55 )
      & ( X222 != c_List_Olist_ONil(X56)
       => c_List_Olast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = c_List_Olast(X56,X222) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [X55,X57] :
      ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X55,X57) = X55 )
      & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X55,X57) = c_Nitpick_Onat__gcd(X57,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X55,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X102,X106] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X106)),X102) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [X102,X106] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X106),X102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X106),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_rel__simps_I7_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).

fof(fact_rel__simps_I3_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_rel__simps_I20_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).

fof(conj_2,hypothesis,
    ~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

fof(fact_not__neg__number__of__Pls,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).

fof(fact_zip__Nil,axiom,
    ! [X221,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),c_List_Olist_ONil(X56)),X221) = c_List_Olist_ONil(tc_prod(X56,X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Nil) ).

fof(fact_top1I,axiom,
    ! [X20,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).

fof(fact_vimage__id,axiom,
    ! [X19,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X19) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).

fof(fact_vimage__ident,axiom,
    ! [X43,X5] : hAPP(c_Set_Ovimage(X5,X5,c_COMBI(X5)),X43) = X43,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).

fof(fact_image__id,axiom,
    ! [X43,X5] : hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),X43) = X43,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__id) ).

fof(fact_image__ident,axiom,
    ! [X43,X5] : hAPP(c_Set_Oimage(X5,X5,c_COMBI(X5)),X43) = X43,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_refl__rtrancl,axiom,
    ! [X78,X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_hd__replicate,axiom,
    ! [X55,X56,X92] :
      ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(X56),c_List_Oreplicate(X56,X92,X55)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__replicate) ).

fof(fact_Compl__atMost,axiom,
    ! [X90,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X90)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X90) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atMost) ).

fof(fact_Compl__atLeast,axiom,
    ! [X90,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X90)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X90) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Compl__greaterThan,axiom,
    ! [X90,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X90)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X90) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__lessThan,axiom,
    ! [X90,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X90)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X90) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_hoare__derivs_Oequations_I1_J,axiom,
    ! [X6,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

fof(fact_empty,axiom,
    ! [X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,X19) = c_Complete__Lattice_OSup__class_OSup(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [X19,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,X19) = c_Complete__Lattice_OInf__class_OInf(X5,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_add__numeral__0,axiom,
    ! [X60,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__is__1,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X51 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X89 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(fact_one__is__add,axiom,
    ! [X89,X51] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89)
    <=> ( ( X51 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X89 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(fact_someI__ex,axiom,
    ! [X5,X30] :
      ( ? [X77] : hBOOL(hAPP(X30,X77))
     => hBOOL(hAPP(X30,c_Hilbert__Choice_OEps(X5,X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).

fof(fact_someI,axiom,
    ! [X5,X20,X30] :
      ( hBOOL(hAPP(X30,X20))
     => hBOOL(hAPP(X30,c_Hilbert__Choice_OEps(X5,X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).

fof(fact_tfl__some,axiom,
    ! [X5,X210] :
      ( ? [X3] : hBOOL(hAPP(X210,X3))
     => hBOOL(hAPP(X210,c_Hilbert__Choice_OEps(X5,X210))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X102,X106] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X106),X102) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_square__eq__1__iff,axiom,
    ! [X20,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X20) = c_Groups_Oone__class_Oone(X5)
      <=> ( X20 = c_Groups_Oone__class_Oone(X5)
          | X20 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

fof(fact_ext,axiom,
    ! [X1,X2] :
      ( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
     => X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

fof(fact_zip_Osimps_I1_J,axiom,
    ! [X222,X161,X56] : hAPP(hAPP(c_List_Ozip(X56,X161),X222),c_List_Olist_ONil(X161)) = c_List_Olist_ONil(tc_prod(X56,X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [X20,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X18)
     => hAPP(hAPP(X2,X20),X20) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [X56] : c_Enum_Osublists(X56,c_List_Olist_ONil(X56)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X56)),c_List_Olist_ONil(X56)),c_List_Olist_ONil(tc_List_Olist(X56))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).

fof(fact_dvd__0__right,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),c_Groups_Ozero__class_Ozero(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

fof(fact_top__greatest,axiom,
    ! [X55,X56] :
      ( class_Orderings_Otop(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),c_Orderings_Otop__class_Otop(X56))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_last__ConsL,axiom,
    ! [X55,X56,X222] :
      ( X222 = c_List_Olist_ONil(X56)
     => c_List_Olast(X56,hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__replicate,axiom,
    ! [X55,X56,X92] :
      ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(X56,c_List_Oreplicate(X56,X92,X55)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__replicate) ).

fof(fact_nat__rec__0,axiom,
    ! [X149,X28,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X28,X149),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__0) ).

fof(fact_insert__not__empty,axiom,
    ! [X19,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X19) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).

fof(fact_empty__not__insert,axiom,
    ! [X19,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X5),X6),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).

fof(fact_int__Suc,axiom,
    ! [X86] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X86)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [X126,X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X58),X126),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [X126,X58] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X58),X126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [X222,X55,X56] : hAPP(c_List_Otl(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_hd_Osimps,axiom,
    ! [X222,X55,X56] : hAPP(c_List_Ohd(X56),hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222)) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd_Osimps) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X89,X6,X5] :
      ( ( class_Power_Opower(X5)
        & class_Rings_Omult__zero(X5)
        & class_Rings_Ono__zero__divisors(X5)
        & class_Rings_Ozero__neq__one(X5) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X89) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          & X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X57,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => ( c_Nat__Transfer_Ois__nat(X57)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_divide__minus1,axiom,
    ! [X55,X56] :
      ( ( class_Fields_Ofield__inverse__zero(X56)
        & class_Int_Onumber__ring(X56) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__minus1) ).

fof(fact_wf__lexn,axiom,
    ! [X89,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(tc_List_Olist(X5),hAPP(c_List_Olexn(X5,X78),X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lexn) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [X122,X98,X56] : hAPP(hAPP(c_List_Olist__update(X56,c_List_Olist_ONil(X56)),X98),X122) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [X57,X98,X56] : hAPP(hAPP(c_List_Olist__update(X56,c_List_Olist_ONil(X56)),X98),X57) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_power__Suc__0,axiom,
    ! [X92] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X92) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(fact_insert__Nil,axiom,
    ! [X55,X56] : c_List_Oinsert(X56,X55,c_List_Olist_ONil(X56)) = hAPP(hAPP(c_List_Olist_OCons(X56),X55),c_List_Olist_ONil(X56)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).

fof(fact_finite__set,axiom,
    ! [X224,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X224))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__set) ).

fof(fact_converse__converse,axiom,
    ! [X78,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(c_Relation_Oconverse(X5,X17),X78)) = X78,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).

fof(fact_lessThan__Suc,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X90),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X90)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_Field__converse,axiom,
    ! [X78,X5] : hAPP(c_Relation_OField(X5),hAPP(c_Relation_Oconverse(X5,X5),X78)) = hAPP(c_Relation_OField(X5),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).

fof(fact_number__of__minus,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_of__int__minus,axiom,
    ! [X58,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Oring__1__class_Oof__int(X56),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X126,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [X51,X20] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20),X51) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_order__eq__refl,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( X55 = X57
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_com_Osize_I6_J,axiom,
    ! [X11,X52] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X52,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I6_J) ).

fof(fact_minus__unique,axiom,
    ! [X61,X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X61) = c_Groups_Ozero__class_Ozero(X56)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) = X61 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21) = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [X224,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X224)) = hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X224)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_UNIV__def,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).

fof(fact_empty__def,axiom,
    ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [X24,X20] :
      ( c_Nat__Transfer_Ois__nat(X20)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X20,X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_mult__minus1__right,axiom,
    ! [X58,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X58),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X51 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X89 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

fof(fact_nat_Osize_I2_J,axiom,
    ! [X190] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X190)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_dvd__refl,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X56),X60),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

fof(fact_order__refl,axiom,
    ! [X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [X102] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102)) = hAPP(c_Int_Onat,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)),X58) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X102,X106] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X106),hAPP(c_Nat_OSuc,X102)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X106,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_mod__int__def,axiom,
    ! [X61,X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X61) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__int__def) ).

fof(fact_inf__commute,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).

fof(fact_inf_Ocommute,axiom,
    ! [X61,X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X57) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_sup__commute,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__commute) ).

fof(fact_sup_Ocommute,axiom,
    ! [X61,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [X57,X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X57) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X57) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X57) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X57),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X61),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X59,X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X59),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_nat__zminus__int,axiom,
    ! [X92] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_gr0I,axiom,
    ! [X92] :
      ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X57,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => ( c_Nat__Transfer_Ois__nat(X57)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X57,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => ( c_Nat__Transfer_Ois__nat(X57)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X57,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => ( c_Nat__Transfer_Ois__nat(X57)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_negative__eq__positive,axiom,
    ! [X51,X89] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51)
    <=> ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__eq__positive) ).

fof(fact_com_Osimps_I38_J,axiom,
    ! [X8,X46,X11,X52,X159] : c_Com_Ocom_OLocal(X159,X52,X11) != c_Com_Ocom_OWhile(X46,X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).

fof(fact_com_Osimps_I34_J,axiom,
    ! [X53,X54,X11,X52,X159] : c_Com_Ocom_OLocal(X159,X52,X11) != c_Com_Ocom_OSemi(X54,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).

fof(fact_com_Osimps_I52_J,axiom,
    ! [X8,X46,X47,X48,X52] : c_Com_Ocom_OCond(X52,X48,X47) != c_Com_Ocom_OWhile(X46,X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).

fof(fact_com_Osimps_I45_J,axiom,
    ! [X47,X48,X53,X54,X46] : c_Com_Ocom_OCond(X46,X54,X53) != c_Com_Ocom_OSemi(X48,X47),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).

fof(fact_com_Osimps_I39_J,axiom,
    ! [X11,X52,X159,X8,X46] : c_Com_Ocom_OWhile(X46,X8) != c_Com_Ocom_OLocal(X159,X52,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).

fof(fact_com_Osimps_I53_J,axiom,
    ! [X47,X48,X52,X8,X46] : c_Com_Ocom_OWhile(X46,X8) != c_Com_Ocom_OCond(X52,X48,X47),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).

fof(fact_com_Osimps_I35_J,axiom,
    ! [X11,X52,X159,X53,X54] : c_Com_Ocom_OSemi(X54,X53) != c_Com_Ocom_OLocal(X159,X52,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).

fof(fact_com_Osimps_I44_J,axiom,
    ! [X53,X54,X46,X47,X48] : c_Com_Ocom_OSemi(X48,X47) != c_Com_Ocom_OCond(X46,X54,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_total__on__empty,axiom,
    ! [X78,X5] : c_Relation_Ototal__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Rings_Oring__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          | X21 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_divisors__zero,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Ono__zero__divisors(X56)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61) = c_Groups_Ozero__class_Ozero(X56)
       => ( X60 = c_Groups_Ozero__class_Ozero(X56)
          | X61 = c_Groups_Ozero__class_Ozero(X56) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [X61,X60,X56] :
      ( class_Rings_Ono__zero__divisors(X56)
     => ( X60 != c_Groups_Ozero__class_Ozero(X56)
       => ( X61 != c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X61) != c_Groups_Ozero__class_Ozero(X56) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_posDivAlg__0,axiom,
    ! [X61] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__0) ).

fof(fact_div__int__def,axiom,
    ! [X61,X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X61) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__int__def) ).

fof(fact_power__0__Suc,axiom,
    ! [X92,X56] :
      ( ( class_Power_Opower(X56)
        & class_Rings_Osemiring__0(X56) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Ozero__class_Ozero(X56)),hAPP(c_Nat_OSuc,X92)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(fact_divide__Numeral0,axiom,
    ! [X55,X56] :
      ( ( class_Fields_Ofield__inverse__zero(X56)
        & class_Int_Onumber__ring(X56) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_abs__sgn,axiom,
    ! [X93,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X93),c_Groups_Osgn__class_Osgn(X56,X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).

fof(fact_lists__UNIV,axiom,
    ! [X5] : c_List_Olists(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__UNIV) ).

fof(fact_map__ident,axiom,
    ! [X224,X5] : hAPP(hAPP(c_List_Omap(X5,X5),c_COMBI(X5)),X224) = X224,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__ident) ).

fof(fact_accp__wfPD,axiom,
    ! [X20,X78,X5] :
      ( c_Wellfounded_OwfP(X5,X78)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X78),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).

fof(fact_reflpE,axiom,
    ! [X20,X78,X5] :
      ( c_Predicate_Oreflp(X5,X78)
     => hBOOL(hAPP(hAPP(X78,X20),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).

fof(fact_equivp__reflp,axiom,
    ! [X20,X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => hBOOL(hAPP(hAPP(X37,X20),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).

fof(fact_sublist__empty,axiom,
    ! [X224,X5] : c_List_Osublist(X5,X224,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__empty) ).

fof(fact_right__inverse__eq,axiom,
    ! [X6,X21,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X21 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X21) = c_Groups_Oone__class_Oone(X5)
        <=> X6 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_length__rev,axiom,
    ! [X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(c_List_Orev(X56),X222)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rev) ).

fof(fact_length__rotate1,axiom,
    ! [X222,X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),hAPP(c_List_Orotate1(X56),X222)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).

fof(fact_exE__some,axiom,
    ! [X5,X23,X30] :
      ( ? [X77] : hBOOL(hAPP(X30,X77))
     => ( X23 = c_Hilbert__Choice_OEps(X5,X30)
       => hBOOL(hAPP(X30,X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [X2,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [X2,X5,X17] : hAPP(hAPP(c_List_Omap(X17,X5),X2),c_List_Olist_ONil(X17)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_inf__compl__bot,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)) = c_Orderings_Obot__class_Obot(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_sup__compl__top,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)) = c_Orderings_Otop__class_Otop(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__compl__top) ).

fof(fact_right__minus,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [X92,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X55),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X89) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X51 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X89 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X51 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & X89 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).

fof(fact_inf__eq__top__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Obounded__lattice__top(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),X24) = c_Orderings_Otop__class_Otop(X5)
      <=> ( X20 = c_Orderings_Otop__class_Otop(X5)
          & X24 = c_Orderings_Otop__class_Otop(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Obounded__lattice__bot(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),X24) = c_Orderings_Obot__class_Obot(X5)
      <=> ( X20 = c_Orderings_Obot__class_Obot(X5)
          & X24 = c_Orderings_Obot__class_Obot(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).

fof(fact_field__power__not__zero,axiom,
    ! [X92,X60,X56] :
      ( class_Rings_Oring__1__no__zero__divisors(X56)
     => ( X60 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),X92) != c_Groups_Ozero__class_Ozero(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_finite__atMost,axiom,
    ! [X90] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X90))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).

fof(fact_finite__lessThan,axiom,
    ! [X90] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X90))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X126] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_right__minus__eq,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( X6 = X21
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X21) = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_eq__imp__le,axiom,
    ! [X92,X86] :
      ( X86 = X92
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_take__eq__Nil,axiom,
    ! [X224,X89,X5] :
      ( hAPP(hAPP(c_List_Otake(X5),X89),X224) = c_List_Olist_ONil(X5)
    <=> ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X224 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
    ! [X92,X86] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X92) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X86 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X86 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).

fof(fact_add__0__iff,axiom,
    ! [X6,X21,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_replicate__empty,axiom,
    ! [X20,X89,X5] :
      ( c_List_Oreplicate(X5,X89,X20) = c_List_Olist_ONil(X5)
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__empty) ).

fof(fact_empty__replicate,axiom,
    ! [X20,X89,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oreplicate(X5,X89,X20)
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__replicate) ).

fof(fact_diff__Suc__1,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X92)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_set__upto,axiom,
    ! [X95,X96] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X96,X95)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upto) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [X95,X96] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X96,X95)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X60,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [X55] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X55),X55)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_zle__refl,axiom,
    ! [X126] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X126),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_le__refl,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X92),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [X19,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X19),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_listsp_ONil,axiom,
    ! [X19,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X19),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).

fof(fact_distinct__remdups,axiom,
    ! [X222,X56] : hBOOL(hAPP(c_List_Odistinct(X56),c_List_Oremdups(X56,X222))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = c_List_Olist_ONil(X5)
    <=> ( X224 = c_List_Olist_ONil(X5)
        & X223 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [X223,X224,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Oappend(X5),X224),X223)
    <=> ( X224 = c_List_Olist_ONil(X5)
        & X223 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_Domain__rtrancl,axiom,
    ! [X37,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Ortrancl(X5,X37)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_Range__rtrancl,axiom,
    ! [X37,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Ortrancl(X5,X37)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__rtrancl) ).

fof(help_c__COMBK__1,axiom,
    ! [X303,X302,X161,X56] : hAPP(hAPP(c_COMBK(X56,X161),X302),X303) = X302,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_lazy__sequence_Osimps_I3_J,axiom,
    ! [X282,X140,X56] : c_Lazy__Sequence_Olazy__sequence_OInsert(X56,X140,X282) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).

fof(fact_lazy__sequence_Osimps_I2_J,axiom,
    ! [X282,X140,X56] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X56) != c_Lazy__Sequence_Olazy__sequence_OInsert(X56,X140,X282),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [X60] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_zmult__commute,axiom,
    ! [X126,X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),X126) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X58),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(fact_nat__mult__commute,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_zadd__commute,axiom,
    ! [X126,X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),X126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X58),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [X61,X60,X56] : hAPP(hAPP(c_Nitpick_Ofrac(X56),X60),X61) = c_Nitpick_OAbs__Frac(X56,c_Nitpick_Onorm__frac(X60,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_diff__0,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

fof(fact_append__self__conv2,axiom,
    ! [X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = X223
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [X223,X224,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X224),X223) = X224
    <=> X223 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).

fof(fact_self__append__conv,axiom,
    ! [X223,X5,X224] :
      ( X224 = hAPP(hAPP(c_List_Oappend(X5),X224),X223)
    <=> X223 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [X224,X5,X223] :
      ( X223 = hAPP(hAPP(c_List_Oappend(X5),X224),X223)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).

fof(fact_power__0__left,axiom,
    ! [X92,X56] :
      ( ( class_Power_Opower(X56)
        & class_Rings_Osemiring__0(X56) )
     => ( ( X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Ozero__class_Ozero(X56)),X92) = c_Groups_Oone__class_Oone(X56) )
        & ( X92 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Ozero__class_Ozero(X56)),X92) = c_Groups_Ozero__class_Ozero(X56) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [X236,X140,X56] : hAPP(hAPP(c_List_Olist_OCons(X56),X140),X236) != c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [X236,X140,X56] : c_List_Olist_ONil(X56) != hAPP(hAPP(c_List_Olist_OCons(X56),X140),X236),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_distinct__upto,axiom,
    ! [X94,X98] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X98,X94))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upto) ).

fof(fact_com_Osimps_I11_J,axiom,
    ! [X8,X46,X160] : c_Com_Ocom_OLocal(X160,X46,X8) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).

fof(fact_com_Osimps_I15_J,axiom,
    ! [X53,X54,X46] : c_Com_Ocom_OCond(X46,X54,X53) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).

fof(fact_com_Osimps_I10_J,axiom,
    ! [X8,X46,X160] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X160,X46,X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).

fof(fact_com_Osimps_I14_J,axiom,
    ! [X53,X54,X46] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X46,X54,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [X78,X5] : c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X78)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_max__ext__wf,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omax__ext(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__wf) ).

fof(fact_min__ext__wf,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omin__ext(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).

fof(fact_listsum__rev,axiom,
    ! [X222,X56] :
      ( class_Groups_Ocomm__monoid__add(X56)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X56),hAPP(c_List_Orev(X56),X222)) = hAPP(c_List_Omonoid__add__class_Olistsum(X56),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__rev) ).

fof(fact_abs__idempotent,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)) = hAPP(c_Groups_Oabs__class_Oabs(X56),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

fof(fact_abs__of__nat,axiom,
    ! [X92,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nat) ).

fof(fact_abs__minus__cancel,axiom,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)) = hAPP(c_Groups_Oabs__class_Oabs(X56),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_UNIV__not__empty,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_zmod__minus1__right,axiom,
    ! [X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).

fof(fact_mod__1,axiom,
    ! [X86] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).

fof(fact_mult__is__0,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

fof(fact_not__Cons__self2,axiom,
    ! [X222,X55,X56] : hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222) != X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_not__Cons__self,axiom,
    ! [X55,X56,X222] : X222 != hAPP(hAPP(c_List_Olist_OCons(X56),X55),X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).

fof(fact_fun__left__comm__idem__insert,axiom,
    ! [X5] : c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_top__apply,axiom,
    ! [X20,X17,X5] :
      ( class_Orderings_Otop(X5)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X17,X5)),X20) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_bot__apply,axiom,
    ! [X20,X17,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17,X5)),X20) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).

fof(fact_bot__fun__def,axiom,
    ! [X20,X17,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17,X5)),X20) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [X86,X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X92),X86) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X92),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_equivp__reflp__symp__transp,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
    <=> ( c_Predicate_Oreflp(X5,X37)
        & c_Predicate_Osymp(X5,X37)
        & c_Predicate_Otransp(X5,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp__symp__transp) ).

fof(fact_equivpI,axiom,
    ! [X37,X5] :
      ( c_Predicate_Oreflp(X5,X37)
     => ( c_Predicate_Osymp(X5,X37)
       => ( c_Predicate_Otransp(X5,X37)
         => c_Equiv__Relations_Oequivp(X5,X37) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpI) ).

fof(fact_sorted__tl,axiom,
    ! [X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X222)
       => c_List_Olinorder__class_Osorted(X56,hAPP(c_List_Otl(X56),X222)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__tl) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [X224,X5] :
      ( c_List_Oremdups(X5,X224) = X224
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X224)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_distinct__remdups__id,axiom,
    ! [X222,X56] :
      ( hBOOL(hAPP(c_List_Odistinct(X56),X222))
     => c_List_Oremdups(X56,X222) = X222 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).

fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [X92,X86] :
      ( X86 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X92)
     => ( X92 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X86 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_hd__conv__nth,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Ohd(X56),X222) = hAPP(hAPP(c_List_Onth(X56),X222),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__conv__nth) ).

fof(help_c__fimplies__1,axiom,
    ! [X29,X30] :
      ( hBOOL(X30)
      | hBOOL(hAPP(hAPP(c_fimplies,X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).

fof(fact_single__valued__Id__on,axiom,
    ! [X19,X5] : c_Relation_Osingle__valued(X5,X5,c_Relation_OId__on(X5,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_refl__on__Id__on,axiom,
    ! [X19,X5] : c_Relation_Orefl__on(X5,X19,c_Relation_OId__on(X5,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_add__is__0,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X89) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [X89,X51] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X51 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X89 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [X89,X51] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X89)
    <=> ( X51 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X89 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_eq__number__of,axiom,
    ! [X24,X20,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Int_Oring__char__0(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X20) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_converse__Id__on,axiom,
    ! [X19,X5] : hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId__on(X5,X19)) = c_Relation_OId__on(X5,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).

fof(help_c__fequal__2,axiom,
    ! [X24,X20] :
      ( X20 != X24
      | hBOOL(hAPP(hAPP(c_fequal,X20),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X122) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [X92,X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_set__empty2,axiom,
    ! [X224,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),X224)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [X224,X5] :
      ( hAPP(c_List_Oset(X5),X224) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty) ).

fof(fact_sym__conv__converse__eq,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
    <=> hAPP(c_Relation_Oconverse(X5,X5),X78) = X78 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).

fof(fact_set__rev,axiom,
    ! [X224,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orev(X5),X224)) = hAPP(c_List_Oset(X5),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev) ).

fof(fact_set__rotate1,axiom,
    ! [X224,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate1(X5),X224)) = hAPP(c_List_Oset(X5),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate1) ).

fof(fact_power__power__power,axiom,
    ! [X5] :
      ( class_Power_Opower(X5)
     => c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X92,X86] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92) = X86
     => X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_hd__rev,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => hAPP(c_List_Ohd(X56),hAPP(c_List_Orev(X56),X222)) = c_List_Olast(X56,X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rev) ).

fof(fact_last__rev,axiom,
    ! [X56,X222] :
      ( X222 != c_List_Olist_ONil(X56)
     => c_List_Olast(X56,hAPP(c_List_Orev(X56),X222)) = hAPP(c_List_Ohd(X56),X222) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__rev) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted__list__of__set(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_Sup__UNIV,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_Sup__empty,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__empty) ).

fof(fact_Inf__UNIV,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Inf__empty,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__empty) ).

fof(fact_div__1,axiom,
    ! [X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

fof(fact_Union__Pow__eq,axiom,
    ! [X19,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OPow(X5),X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_divide__zero__left,axiom,
    ! [X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_div__0,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

fof(fact_inf__bot__left,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__bot(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),c_Orderings_Obot__class_Obot(X56)),X55) = c_Orderings_Obot__class_Obot(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).

fof(fact_power__one,axiom,
    ! [X92,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),c_Groups_Oone__class_Oone(X56)),X92) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(fact_sup__top__left,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__top(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),c_Orderings_Otop__class_Otop(X56)),X55) = c_Orderings_Otop__class_Otop(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__left) ).

fof(fact_mult__zero__left,axiom,
    ! [X60,X56] :
      ( class_Rings_Omult__zero(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_sorted__butlast,axiom,
    ! [X222,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( X222 != c_List_Olist_ONil(X56)
       => ( c_List_Olinorder__class_Osorted(X56,X222)
         => c_List_Olinorder__class_Osorted(X56,c_List_Obutlast(X56,X222)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__butlast) ).

fof(fact_of__int__m1,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__m1) ).

fof(fact_card_Oempty,axiom,
    ! [X5] : hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oempty) ).

fof(fact_abs__minus__one,axiom,
    ! [X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Rings_Olinordered__idom(X56) )
     => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__one) ).

fof(fact_atLeast0AtMost,axiom,
    ! [X89] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X89) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_atMost__eq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(X5),X20) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(X5),X20) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X20) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_of__int__eq__iff,axiom,
    ! [X26,X84,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X84) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)
      <=> X84 = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [X89,X51,X5] :
      ( class_Nat_Osemiring__char__0(X5)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X51) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X89)
      <=> X51 = X89 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(X5),X20) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X24,X20,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)
      <=> X20 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)
      <=> X6 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_inf__top__left,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__top(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),c_Orderings_Otop__class_Otop(X56)),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__left) ).

fof(fact_sup__bot__left,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__bot(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),c_Orderings_Obot__class_Obot(X56)),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__left) ).

fof(fact_mult__1__left,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Oone__class_Oone(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_mult__1,axiom,
    ! [X60,X56] :
      ( class_Groups_Ocomm__monoid__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Oone__class_Oone(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),c_Groups_Oone__class_Oone(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_add__0__left,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X60,X56] :
      ( class_Groups_Ocomm__monoid__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),c_Groups_Ozero__class_Ozero(X56)),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_divide__self__if,axiom,
    ! [X60,X56] :
      ( class_Rings_Odivision__ring__inverse__zero(X56)
     => ( ( X60 = c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X60) = c_Groups_Ozero__class_Ozero(X56) )
        & ( X60 != c_Groups_Ozero__class_Ozero(X56)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X60) = c_Groups_Oone__class_Oone(X56) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_mod__0,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,c_Groups_Ozero__class_Ozero(X56),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).

fof(fact_mod__by__1,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,X60,c_Groups_Oone__class_Oone(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).

fof(fact_sorted__remdups,axiom,
    ! [X91,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( c_List_Olinorder__class_Osorted(X56,X91)
       => c_List_Olinorder__class_Osorted(X56,c_List_Oremdups(X56,X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remdups) ).

fof(fact_divide__zero,axiom,
    ! [X60,X56] :
      ( class_Rings_Odivision__ring__inverse__zero(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_div__by__0,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(fact_inf__bot__right,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__bot(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),c_Orderings_Obot__class_Obot(X56)) = c_Orderings_Obot__class_Obot(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).

fof(fact_sup__top__right,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__top(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),c_Orderings_Otop__class_Otop(X56)) = c_Orderings_Otop__class_Otop(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__right) ).

fof(fact_mult__zero__right,axiom,
    ! [X60,X56] :
      ( class_Rings_Omult__zero(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_listrel__sym,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => c_Relation_Osym(tc_List_Olist(X5),c_List_Olistrel(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__sym) ).

fof(fact_listrel__trans,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => c_Relation_Otrans(tc_List_Olist(X5),c_List_Olistrel(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).

fof(fact_lexord__transI,axiom,
    ! [X78,X5] :
      ( c_Relation_Otrans(X5,X78)
     => c_Relation_Otrans(tc_List_Olist(X5),c_List_Olexord(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).

fof(fact_wf__lex,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olex(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lenlex,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olenlex(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lenlex) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [X56,X221,X222] :
      ( X222 = X221
     => X222 = hAPP(hAPP(c_List_Oappend(X56),c_List_Olist_ONil(X56)),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_divide__self,axiom,
    ! [X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => ( X60 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),X60) = c_Groups_Oone__class_Oone(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_div__self,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => ( X60 != c_Groups_Ozero__class_Ozero(X56)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),X60) = c_Groups_Oone__class_Oone(X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).

fof(fact_mod__by__0,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,X60,c_Groups_Ozero__class_Ozero(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(fact_fun__left__comm,axiom,
    ! [X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => c_Finite__Set_Ofun__left__comm(X5,X5,c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm__idem__inf,axiom,
    ! [X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omax(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omin(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).

fof(fact_Domain__Id__on,axiom,
    ! [X19,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Relation_OId__on(X5,X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_Range__Id__on,axiom,
    ! [X19,X5] : hAPP(c_Relation_ORange(X5,X5),c_Relation_OId__on(X5,X19)) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).

fof(fact_power__0,axiom,
    ! [X60,X56] :
      ( class_Power_Opower(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_divide__1,axiom,
    ! [X60,X56] :
      ( class_Rings_Odivision__ring(X56)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X56),X60),c_Groups_Oone__class_Oone(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_div__by__1,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X56),X60),c_Groups_Oone__class_Oone(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(fact_inf__top__right,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__top(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),c_Orderings_Otop__class_Otop(X56)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__right) ).

fof(fact_sup__bot__right,axiom,
    ! [X55,X56] :
      ( class_Lattices_Obounded__lattice__bot(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),c_Orderings_Obot__class_Obot(X56)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__right) ).

fof(fact_mult__1__right,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Groups_Oone__class_Oone(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X60,X56] :
      ( class_Groups_Ocomm__monoid__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Groups_Oone__class_Oone(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),c_Groups_Oone__class_Oone(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_add__0__right,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X60,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X60,X56] :
      ( class_Groups_Ocomm__monoid__add(X56)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_diff__0__right,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),c_Groups_Ozero__class_Ozero(X56)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(fact_double__compl,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X55)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_abs__int__eq,axiom,
    ! [X86] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__int__eq) ).

fof(fact_of__int__int__eq,axiom,
    ! [X92] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_set__remdups,axiom,
    ! [X224,X5] : hAPP(c_List_Oset(X5),c_List_Oremdups(X5,X224)) = hAPP(c_List_Oset(X5),X224),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remdups) ).

fof(fact_mod__self,axiom,
    ! [X60,X56] :
      ( class_Divides_Osemiring__div(X56)
     => c_Divides_Odiv__class_Omod(X56,X60,X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [X223,X224,X5] :
      ( hAPP(c_List_Orev(X5),X224) = hAPP(c_List_Orev(X5),X223)
    <=> X224 = X223 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_inc__shift__def,axiom,
    ! [X93,X122] :
      ( ( X122 = X93
       => c_Random_Oinc__shift(X122,X93) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X122 != X93
       => c_Random_Oinc__shift(X122,X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X93),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inc__shift__def) ).

fof(fact_append__Nil,axiom,
    ! [X221,X56] : hAPP(hAPP(c_List_Oappend(X56),c_List_Olist_ONil(X56)),X221) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X92] : hAPP(c_Nat_OSuc,X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_sublist__nil,axiom,
    ! [X19,X5] : c_List_Osublist(X5,c_List_Olist_ONil(X5),X19) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__nil) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [X30,X5] : c_List_OtakeWhile(X5,X30,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [X55,X56] : c_List_Oremove1(X56,X55,c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_atLeastLessThan0,axiom,
    ! [X51] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).

fof(fact_power__one__right,axiom,
    ! [X60,X56] :
      ( class_Groups_Omonoid__mult(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [X55,X56] :
      ( class_Rings_Ocomm__semiring__1(X56)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_diff__self,axiom,
    ! [X60,X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X56),X60),X60) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [X123,X5] : c_List_Olist_Olist__size(X5,X123,c_List_Olist_ONil(X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).

fof(fact_sym__rtrancl,axiom,
    ! [X78,X5] :
      ( c_Relation_Osym(X5,X78)
     => c_Relation_Osym(X5,c_Transitive__Closure_Ortrancl(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__rtrancl) ).

fof(fact_acyclic__impl__antisym__rtrancl,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Oacyclic(X5,X78)
     => c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).

fof(fact_take__0,axiom,
    ! [X222,X56] : hAPP(hAPP(c_List_Otake(X56),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X222) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__0) ).

fof(fact_drop__Nil,axiom,
    ! [X92,X56] : hAPP(hAPP(c_List_Odrop(X56),X92),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Nil) ).

fof(fact_take__Nil,axiom,
    ! [X92,X56] : hAPP(hAPP(c_List_Otake(X56),X92),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Nil) ).

fof(fact_minus__equation__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = X21
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X21,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X21)
      <=> X21 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_nat__list__def,axiom,
    ! [X106] :
      ( c_List_Onat__list(X106)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X106)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__list__def) ).

fof(fact_card__atMost,axiom,
    ! [X102] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X102)) = hAPP(c_Nat_OSuc,X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atMost) ).

fof(fact_nat__of__number,axiom,
    ! [X93] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X93)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__number) ).

fof(fact_nat__number__of,axiom,
    ! [X126] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of) ).

fof(fact_nat__number__of__def,axiom,
    ! [X122] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X92] : hAPP(c_Nat_OSuc,X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_replicate__0,axiom,
    ! [X55,X56] : c_List_Oreplicate(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X55) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__0) ).

fof(fact__02,axiom,
    ! [X275,X56] : c_Lazy__Sequence_Oappend(X56,c_Lazy__Sequence_Olazy__sequence_OEmpty(X56),X275) = X275,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__02) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [X221,X56] : c_List_Osplice(X56,c_List_Olist_ONil(X56),X221) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact_splice__Nil2,axiom,
    ! [X222,X56] : c_List_Osplice(X56,X222,c_List_Olist_ONil(X56)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).

fof(fact_sgn__sgn,axiom,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => c_Groups_Osgn__class_Osgn(X56,c_Groups_Osgn__class_Osgn(X56,X60)) = c_Groups_Osgn__class_Osgn(X56,X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [X30,X5] : c_List_Olist__all(X5,X30,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_inf__idem,axiom,
    ! [X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).

fof(fact_inf_Oidem,axiom,
    ! [X60,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [X55,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__idem) ).

fof(fact_sup_Oidem,axiom,
    ! [X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oidem) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [X55,X56] :
      ( class_Lattices_Olattice(X56)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_Max_Oidem,axiom,
    ! [X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oidem) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_Min_Oidem,axiom,
    ! [X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oidem) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_times_Oidem,axiom,
    ! [X60,X56] :
      ( class_Lattices_Oab__semigroup__idem__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).

fof(fact_mult__idem,axiom,
    ! [X55,X56] :
      ( class_Lattices_Oab__semigroup__idem__mult(X56)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X55) = X55 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).

fof(fact_length__0__conv,axiom,
    ! [X224,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__0__conv) ).

fof(fact_mult__Min,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X93) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Min) ).

fof(fact_atLeast0LessThan,axiom,
    ! [X89] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [X267,X55,X56] : hAPP(c_New__DSequence_Opos__single(X56,X55),X267) = hAPP(c_Lazy__Sequence_Osingle(X56),X55),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_drop__0,axiom,
    ! [X222,X56] : hAPP(hAPP(c_List_Odrop(X56),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X222) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__0) ).

fof(fact_append__Nil2,axiom,
    ! [X222,X56] : hAPP(hAPP(c_List_Oappend(X56),X222),c_List_Olist_ONil(X56)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).

fof(fact_rev__rev__ident,axiom,
    ! [X222,X56] : hAPP(c_List_Orev(X56),hAPP(c_List_Orev(X56),X222)) = X222,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_small__lazy__int__def,axiom,
    ! [X73] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X73) = c_Lazy__Sequence_Osmall__lazy_H(X73,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X73)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__int__def) ).

fof(fact_zmod__zero,axiom,
    ! [X61] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).

fof(fact_neg__nat,axiom,
    ! [X58] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X58))
     => hAPP(c_Int_Onat,X58) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__nat) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X90),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [X90] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X90),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X89] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [X60] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_iszero__Numeral0,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_List_Omap_Oid,axiom,
    ! [X5] : hAPP(c_List_Omap(X5,X5),c_Fun_Oid(X5)) = c_Fun_Oid(tc_List_Olist(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [X5] : hAPP(c_List_Omap(X5,X5),c_COMBI(X5)) = c_Fun_Oid(tc_List_Olist(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [X24,X20] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)
    <=> X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_int__int__eq,axiom,
    ! [X89,X51] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89)
    <=> X51 = X89 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).

fof(fact_zmod__self,axiom,
    ! [X60] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X60) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(fact_rev__swap,axiom,
    ! [X223,X224,X5] :
      ( hAPP(c_List_Orev(X5),X224) = X223
    <=> X224 = hAPP(c_List_Orev(X5),X223) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).

fof(fact_zdiv__zero,axiom,
    ! [X61] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).

fof(fact_min__0L,axiom,
    ! [X92] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0L) ).

fof(fact_mult__0,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

fof(fact_diff__0__eq__0,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_distinct_Osimps_I1_J,axiom,
    ! [X56] : hBOOL(hAPP(c_List_Odistinct(X56),c_List_Olist_ONil(X56))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [X267,X55,X56] : hAPP(c_New__DSequence_Oneg__single(X56,X55),X267) = c_Lazy__Sequence_Ohb__single(X56,X55),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_remdups__remdups,axiom,
    ! [X222,X56] : c_List_Oremdups(X56,c_List_Oremdups(X56,X222)) = c_List_Oremdups(X56,X222),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__remdups) ).

fof(fact_rtrancl__idemp,axiom,
    ! [X78,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Ortrancl(X5,X78)) = c_Transitive__Closure_Ortrancl(X5,X78),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [X5] : hAPP(c_List_Oset(X5),c_List_Olist_ONil(X5)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_max__0L,axiom,
    ! [X92] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0L) ).

fof(fact_zmult__1,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X58) = X58,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(fact_nat__mult__1,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(fact_zadd__0,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58) = X58,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_conversep__eq,axiom,
    ! [X5] : c_Predicate_Oconversep(X5,X5,c_fequal) = c_fequal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).

fof(fact_not__neg__0,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__0) ).

fof(fact_not__neg__1,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__1) ).

fof(fact_zdiv__self,axiom,
    ! [X60] :
      ( X60 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X60),X60) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_number__of__Min,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).

fof(fact_min__0R,axiom,
    ! [X92] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0R) ).

fof(fact_mult__0__right,axiom,
    ! [X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)
      <=> c_Groups_Ozero__class_Ozero(X5) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_abs__eq__0,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hAPP(c_Groups_Oabs__class_Oabs(X5),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_max__0R,axiom,
    ! [X92] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0R) ).

fof(fact_zmult__1__right,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X58),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X58,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(fact_nat__mult__1__right,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_zadd__0__right,axiom,
    ! [X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X58),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X58,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_card__lessThan,axiom,
    ! [X102] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X102)) = X102,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__lessThan) ).

fof(fact_zminus__zminus,axiom,
    ! [X58] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)) = X58,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [X30,X5] : hAPP(c_List_Ofilter(X5,X30),c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_finite,axiom,
    ! [X19,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [X19,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [X26,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X26) = c_Groups_Ozero__class_Ozero(X5)
      <=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).

fof(fact_of__int__0__eq__iff,axiom,
    ! [X26,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X26)
      <=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__eq__iff) ).

fof(fact_diff__self__eq__0,axiom,
    ! [X86] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X86) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_lazy__sequence_Osize_I1_J,axiom,
    ! [X123,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X123),c_Lazy__Sequence_Olazy__sequence_OEmpty(X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).

fof(fact_number__of__eq,axiom,
    ! [X93,X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),X93) = hAPP(c_Int_Oring__1__class_Oof__int(X56),X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__eq) ).

fof(fact_com_Osimps_I5_J,axiom,
    ! [X8,X46,X11,X52] :
      ( c_Com_Ocom_OWhile(X52,X11) = c_Com_Ocom_OWhile(X46,X8)
    <=> ( X52 = X46
        & X11 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).

fof(fact_com_Osimps_I3_J,axiom,
    ! [X53,X54,X47,X48] :
      ( c_Com_Ocom_OSemi(X48,X47) = c_Com_Ocom_OSemi(X54,X53)
    <=> ( X48 = X54
        & X47 = X53 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).

fof(fact_neg__equal__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = X6
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_equal__neg__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_add__Pls__right,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),c_Int_OPls) = X93,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),c_Int_OPls) = X93,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_nat__int,axiom,
    ! [X92] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).

fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X301,X300] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X300)
        & class_Lazy__Sequence_Osmall__lazy(X301) )
     => class_Lazy__Sequence_Osmall__lazy(tc_prod(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [X301,X300] :
      ( ( class_Enum_Oenum(X300)
        & class_Enum_Oenum(X301) )
     => class_Enum_Oenum(tc_prod(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [X301,X300] :
      ( ( class_Enum_Oenum(X300)
        & class_Enum_Oenum(X301) )
     => class_Enum_Oenum(tc_sum(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [X301,X300] :
      ( ( class_Enum_Oenum(X300)
        & class_Enum_Oenum(X301) )
     => class_Enum_Oenum(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [X57,X55] :
      ( c_Nat__Transfer_Ois__nat(X55)
     => ( c_Nat__Transfer_Ois__nat(X57)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X55,X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [X301,X300] :
      ( ( class_Finite__Set_Ofinite(X300)
        & class_Finite__Set_Ofinite(X301) )
     => class_Finite__Set_Ofinite(tc_prod(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [X301,X300] :
      ( ( class_Finite__Set_Ofinite(X300)
        & class_Finite__Set_Ofinite(X301) )
     => class_Finite__Set_Ofinite(tc_sum(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [X301,X300] :
      ( ( class_Finite__Set_Ofinite(X300)
        & class_Finite__Set_Ofinite(X301) )
     => class_Finite__Set_Ofinite(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(fact_com_Osimps_I47_J,axiom,
    ! [X47,X48,X8,X46] : c_Com_Ocom_OWhile(X46,X8) != c_Com_Ocom_OSemi(X48,X47),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).

fof(fact_com_Osimps_I46_J,axiom,
    ! [X8,X46,X47,X48] : c_Com_Ocom_OSemi(X48,X47) != c_Com_Ocom_OWhile(X46,X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).

fof(fact_add__Pls,axiom,
    ! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X93) = X93,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [X224,X5] :
      ( hAPP(c_List_Orev(X5),X224) = c_List_Olist_ONil(X5)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [X224,X5] :
      ( hAPP(c_List_Orotate1(X5),X224) = c_List_Olist_ONil(X5)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [X224,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(c_List_Orev(X5),X224)
    <=> X224 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_mult__Pls,axiom,
    ! [X126] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X126) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).

fof(fact_trans__finite__psubset,axiom,
    ! [X5] : c_Relation_Otrans(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__finite__psubset) ).

fof(fact_wf__finite__psubset,axiom,
    ! [X5] : c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_transpose_Osimps_I1_J,axiom,
    ! [X56] : c_List_Otranspose(X56,c_List_Olist_ONil(tc_List_Olist(X56))) = c_List_Olist_ONil(tc_List_Olist(X56)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).

fof(fact_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Pls) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_succ__Min,axiom,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Min) ).

fof(fact_code__numeral_Onat__of__inject,axiom,
    ! [X24,X20] :
      ( hAPP(c_Code__Numeral_Onat__of,X20) = hAPP(c_Code__Numeral_Onat__of,X24)
    <=> X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [X106,X90] :
      ( hAPP(c_Code__Numeral_Onat__of,X90) = hAPP(c_Code__Numeral_Onat__of,X106)
    <=> X90 = X106 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [X51,X89] :
      ( hAPP(c_Code__Numeral_Oof__nat,X89) = hAPP(c_Code__Numeral_Oof__nat,X51)
    <=> X89 = X51 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [X24,X20] :
      ( hAPP(c_Int_ORep__Integ,X20) = hAPP(c_Int_ORep__Integ,X24)
    <=> X20 = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_Suc__inject,axiom,
    ! [X57,X55] :
      ( hAPP(c_Nat_OSuc,X55) = hAPP(c_Nat_OSuc,X57)
     => X55 = X57 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(fact_nat_Oinject,axiom,
    ! [X113,X114] :
      ( hAPP(c_Nat_OSuc,X114) = hAPP(c_Nat_OSuc,X113)
    <=> X114 = X113 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

fof(fact_sgn__0__0,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(fact_lazy__sequence_Osize_I3_J,axiom,
    ! [X56] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X56)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X56)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).

fof(fact_list_Osize_I3_J,axiom,
    ! [X56] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),c_List_Olist_ONil(X56)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_sym__Id__on,axiom,
    ! [X19,X5] : c_Relation_Osym(X5,c_Relation_OId__on(X5,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id__on) ).

fof(fact_antisym__Id__on,axiom,
    ! [X19,X5] : c_Relation_Oantisym(X5,c_Relation_OId__on(X5,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id__on) ).

fof(fact_trans__rtrancl,axiom,
    ! [X78,X5] : c_Relation_Otrans(X5,c_Transitive__Closure_Ortrancl(X5,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).

fof(fact_trans__Id__on,axiom,
    ! [X19,X5] : c_Relation_Otrans(X5,c_Relation_OId__on(X5,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).

fof(fact_wf__measures,axiom,
    ! [X263,X5] : c_Wellfounded_Owf(X5,c_List_Omeasures(X5,X263)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measures) ).

fof(fact_sorted__upto,axiom,
    ! [X94,X98] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X98,X94)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upto) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [X20,X5] : c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X20)) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [X20,X5] : c_HOL_OThe(X5,hAPP(c_fequal,X20)) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [X56] :
      ( class_Groups_Omonoid__add(X56)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X56),c_List_Olist_ONil(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_abs__zero,axiom,
    ! [X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

fof(fact_abs__one,axiom,
    ! [X56] :
      ( class_Rings_Olinordered__idom(X56)
     => hAPP(c_Groups_Oabs__class_Oabs(X56),c_Groups_Oone__class_Oone(X56)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_minus__zero,axiom,
    ! [X56] :
      ( class_Groups_Ogroup__add(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_compl__top__eq,axiom,
    ! [X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Orderings_Otop__class_Otop(X56)) = c_Orderings_Obot__class_Obot(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__top__eq) ).

fof(fact_compl__bot__eq,axiom,
    ! [X56] :
      ( class_Lattices_Oboolean__algebra(X56)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Orderings_Obot__class_Obot(X56)) = c_Orderings_Otop__class_Otop(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [X300,X301] :
      ( class_Lattices_Obounded__lattice(X301)
     => class_Lattices_Obounded__lattice(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [X300,X301] :
      ( class_Lattices_Odistrib__lattice(X301)
     => class_Lattices_Odistrib__lattice(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [X300,X301] :
      ( class_Lattices_Olattice(X301)
     => class_Lattices_Osemilattice__inf(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [X300,X301] :
      ( class_Complete__Lattice_Ocomplete__lattice(X301)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [X300,X301] :
      ( class_Lattices_Obounded__lattice(X301)
     => class_Lattices_Obounded__lattice__bot(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [X300,X301] :
      ( class_Lattices_Olattice(X301)
     => class_Lattices_Osemilattice__sup(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [X300,X301] :
      ( class_Lattices_Obounded__lattice(X301)
     => class_Lattices_Obounded__lattice__top(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [X300,X301] :
      ( class_Orderings_Otop(X301)
     => class_Orderings_Otop(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [X300,X301] :
      ( class_Lattices_Olattice(X301)
     => class_Lattices_Olattice(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X300,X301] :
      ( class_Groups_Ouminus(X301)
     => class_Groups_Ouminus(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X300,X301] :
      ( class_Lattices_Oboolean__algebra(X301)
     => class_Lattices_Oboolean__algebra(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X300,X301] :
      ( class_Orderings_Oorder(X301)
     => class_Orderings_Oorder(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X300,X301] :
      ( class_Orderings_Oord(X301)
     => class_Orderings_Oord(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X300,X301] :
      ( class_Orderings_Opreorder(X301)
     => class_Orderings_Opreorder(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [X300,X301] :
      ( class_Groups_Ominus(X301)
     => class_Groups_Ominus(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [X300,X301] :
      ( class_Orderings_Obot(X301)
     => class_Orderings_Obot(tc_fun(X300,X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(fact_equivp__implies__part__equivp,axiom,
    ! [X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => c_Equiv__Relations_Opart__equivp(X5,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).

fof(fact_wf__acyclic,axiom,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => c_Wellfounded_Oacyclic(X5,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [X58] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact__04,axiom,
    ! [X56] : c_Lazy__Sequence_Oflat(X56,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X56))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__04) ).

fof(fact_nat__of__of__nat,axiom,
    ! [X92] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X92)) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_of__nat__nat__of,axiom,
    ! [X93] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X93)) = X93,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__inverse,axiom,
    ! [X55] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X55)) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [X20] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X20)) = X20,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_iszero__def,axiom,
    ! [X26,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( c_Int_Oiszero(X5,X26)
      <=> X26 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).

fof(fact_int__eq__0__conv,axiom,
    ! [X89] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X89) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_of__int__0,axiom,
    ! [X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).

fof(fact_of__int__1,axiom,
    ! [X56] :
      ( class_Rings_Oring__1(X56)
     => hAPP(c_Int_Oring__1__class_Oof__int(X56),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).

fof(fact_of__nat__0,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__1,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).

fof(fact_int__number__of__def,axiom,
    ! [X126] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X126),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [X20,X5] :
      ( c_List_Oremdups(X5,X20) = c_List_Olist_ONil(X5)
    <=> X20 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [X20,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oremdups(X5,X20)
    <=> X20 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_sgn0,axiom,
    ! [X56] :
      ( class_Groups_Osgn__if(X56)
     => c_Groups_Osgn__class_Osgn(X56,c_Groups_Ozero__class_Ozero(X56)) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

fof(fact_max__ord__max,axiom,
    ! [X5] :
      ( class_Orderings_Oord(X5)
     => c_Orderings_Oord__class_Omax(X5) = c_Orderings_Oord_Omax(X5,c_Orderings_Oord__class_Oless__eq(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ord__max) ).

fof(fact_min__ord__min,axiom,
    ! [X5] :
      ( class_Orderings_Oord(X5)
     => c_Orderings_Oord__class_Omin(X5) = c_Orderings_Oord_Omin(X5,c_Orderings_Oord__class_Oless__eq(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ord__min) ).

fof(fact_rev_Osimps_I1_J,axiom,
    ! [X56] : hAPP(c_List_Orev(X56),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [X56] : hAPP(c_List_Otl(X56),c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
    ! [X301,X300] : class_Nat_Osize(tc_Nitpick_Opair__box(X300,X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [X301,X300] : class_Nat_Osize(tc_prod(X300,X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [X301,X300] : class_Nat_Osize(tc_sum(X300,X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).

fof(fact_number__of__Pls,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => c_Groups_Ozero__class_Ozero(X56) = hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [X56] :
      ( class_Orderings_Olinorder(X56)
     => c_List_Olinorder__class_Osorted(X56,c_List_Olist_ONil(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_sorted_ONil,axiom,
    ! [X56] :
      ( class_Orderings_Olinorder(X56)
     => c_List_Olinorder__class_Osorted(X56,c_List_Olist_ONil(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_ONil) ).

fof(fact_iszero__0,axiom,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => c_Int_Oiszero(X56,c_Groups_Ozero__class_Ozero(X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [X267,X56] : hAPP(c_New__DSequence_Opos__empty(X56),X267) = c_Lazy__Sequence_Oempty(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [X56] : c_List_Oremdups(X56,c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [X56] : c_List_Obutlast(X56,c_List_Olist_ONil(X56)) = c_List_Olist_ONil(X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [X86] : hAPP(c_Nat_OSuc,X86) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X117] : hAPP(c_Nat_OSuc,X117) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X86] : hAPP(c_Nat_OSuc,X86) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X86] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X118] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X118),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X86] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_com_Osimps_I17_J,axiom,
    ! [X8,X46] : c_Com_Ocom_OWhile(X46,X8) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).

fof(fact_com_Osimps_I13_J,axiom,
    ! [X44,X45] : c_Com_Ocom_OSemi(X45,X44) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).

fof(fact_com_Osimps_I16_J,axiom,
    ! [X8,X46] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X46,X8),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).

fof(fact_com_Osimps_I12_J,axiom,
    ! [X44,X45] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X45,X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).

fof(fact_inf__min,axiom,
    ! [X5] :
      ( ( class_Lattices_Osemilattice__inf(X5)
        & class_Orderings_Olinorder(X5) )
     => c_Lattices_Osemilattice__inf__class_Oinf(X5) = c_Orderings_Oord__class_Omin(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__min) ).

fof(fact_sup__max,axiom,
    ! [X5] :
      ( ( class_Lattices_Osemilattice__sup(X5)
        & class_Orderings_Olinorder(X5) )
     => c_Lattices_Osemilattice__sup__class_Osup(X5) = c_Orderings_Oord__class_Omax(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__max) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X92] : hAPP(c_Nat_OSuc,X92) != X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X92] : X92 != hAPP(c_Nat_OSuc,X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_id__def,axiom,
    ! [X207,X56] : hAPP(c_Fun_Oid(X56),X207) = X207,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).

fof(fact_id__apply,axiom,
    ! [X55,X56] : hAPP(c_Fun_Oid(X56),X55) = X55,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).

fof(fact_Collect__def,axiom,
    ! [X30,X5] : hAPP(c_Set_OCollect(X5),X30) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).

fof(help_c__COMBI__1,axiom,
    ! [X302,X56] : hAPP(c_COMBI(X56),X302) = X302,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(fact_one__neq__zero,axiom,
    ! [X56] :
      ( class_Rings_Ozero__neq__one(X56)
     => c_Groups_Oone__class_Oone(X56) != c_Groups_Ozero__class_Ozero(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_zero__neq__one,axiom,
    ! [X56] :
      ( class_Rings_Ozero__neq__one(X56)
     => c_Groups_Ozero__class_Ozero(X56) != c_Groups_Oone__class_Oone(X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_beyond__zero,axiom,
    ! [X93] : c_Quickcheck_Obeyond(X93,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__zero) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [X27] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).

fof(fact_wf__int__ge__less__than,axiom,
    ! [X27] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).

fof(fact_number__of__is__id,axiom,
    ! [X93] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93) = X93,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

fof(fact_nat__size,axiom,
    ! [X92] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X92) = X92,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).

fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X301] :
      ( class_Lazy__Sequence_Osmall__lazy(X301)
     => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [X301] :
      ( class_Enum_Oenum(X301)
     => class_Enum_Oenum(tc_Option_Ooption(X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [X301] :
      ( class_Finite__Set_Ofinite(X301)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(X301)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(fact_identity__equivp,axiom,
    ! [X5] : c_Equiv__Relations_Oequivp(X5,c_fequal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [X301] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [X301] : class_Nat_Osize(tc_List_Olist(X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [X301] : class_Nat_Osize(tc_Option_Ooption(X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
    ! [X301] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X301)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).

fof(conj_4,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
    & c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

fof(fact_Nitpick_OFrac__def,axiom,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_OFrac__def) ).

fof(fact_min__weak__def,axiom,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__weak__def) ).

fof(fact_max__weak__def,axiom,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__weak__def) ).

fof(fact_max__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__rpair__set) ).

fof(fact_min__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__rpair__set) ).

fof(fact_pred__nat__def,axiom,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__def) ).

fof(fact_Zero__int__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__int__def) ).

fof(fact_One__int__def,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__int__def) ).

fof(fact_type__definition__Integ,axiom,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition__Integ) ).

fof(fact_type__definition__code__numeral,axiom,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less) ).

fof(fact_int__of__def,axiom,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__def) ).

fof(fact_number__of__code__numeral__def,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).

fof(fact_Integ__def,axiom,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Integ__def) ).

fof(fact_transfer__morphism__int__nat,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__morphism__int__nat) ).

fof(fact_inj__int,axiom,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__int) ).

fof(fact_INT__greaterThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).

fof(fact_UN__atMost__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__atMost__UNIV) ).

fof(fact_UN__atLeast__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).

fof(fact_UN__lessThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__lessThan__UNIV) ).

fof(fact_transfer__morphism__nat__int,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__morphism__nat__int) ).

fof(fact_pair__less__def,axiom,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__less__def) ).

fof(fact_equiv__intrel,axiom,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__intrel) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_greaterThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__0) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).

fof(fact_atMost__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__0) ).

fof(fact_int__0__less__1,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_bin__less__0__simps_I2_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).

fof(fact_rel__simps_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).

fof(fact_rel__simps_I24_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).

fof(fact_rel__simps_I23_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).

fof(fact_rel__simps_I19_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_neg__number__of__Min,axiom,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).

fof(fact_card__UNIV__unit,axiom,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).

fof(fact_code__numeral__zero__minus__one,axiom,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).

fof(fact_eq__number__of__Pls__Min,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).

fof(fact_int__Suc0__eq__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).

fof(fact_atLeast__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__0) ).

fof(fact_lessThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__0) ).

fof(conj_1,hypothesis,
    hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

fof(fact_wf__pair__less,axiom,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).

fof(fact_max__strict__def,axiom,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__strict__def) ).

fof(fact_min__strict__def,axiom,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__strict__def) ).

fof(fact_nat__1,axiom,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1) ).

fof(fact_int__0,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).

fof(fact_int__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).

fof(fact_code__numeral_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J) ).

fof(fact_nat_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).

fof(fact_zminus__0,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

fof(fact_transfer__int__nat__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).

fof(fact_transfer__int__nat__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).

fof(fact_Int_OMin__def,axiom,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int_OMin__def) ).

fof(fact_nat__number__of__Pls,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_com_Osize_I9_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I9_J) ).

fof(fact_bool_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).

fof(fact_bool_Osize_I4_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).

fof(fact_nat__0,axiom,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).

fof(fact_zero__code__numeral__code,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).

fof(fact_zero__is__num__zero,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_semiring__norm_I113_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).

fof(fact_zero__code__numeral__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).

fof(fact_transfer__nat__int__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_one__code__numeral__def,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).

fof(fact_transfer__nat__int__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).

fof(fact_trans__less__than,axiom,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).

fof(fact_wf__pred__nat,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).

fof(fact_wf__less__than,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).

fof(fact_nat_Osize_I1_J,axiom,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).

fof(fact_code__numeral_Osize_I1_J,axiom,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I1_J) ).

fof(fact_int__0__neq__1,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).

fof(fact_bool_Osize_I1_J,axiom,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).

fof(fact_bool_Osize_I2_J,axiom,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).

fof(fact_of__int__eq__id,axiom,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__id) ).

fof(fact_com_Osize_I1_J,axiom,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).

fof(fact_bot__nat__def,axiom,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def) ).

fof(fact_inf__nat__def,axiom,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__nat__def) ).

fof(fact_sup__nat__def,axiom,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__nat__def) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).

fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).

fof(arity_Int__Oint__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(arity_Nat__Onat__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).

fof(arity_Com__Ocom__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ocom),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).

fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
    class_Nat_Osize(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).

fof(arity_Nat__Onat__Nat_Osize,axiom,
    class_Nat_Osize(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).

fof(arity_Com__Ostate__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ostate),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).

fof(arity_HOL__Obool__Nat_Osize,axiom,
    class_Nat_Osize(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).

fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).

fof(arity_HOL__Obool__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).

fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
    class_Orderings_Owellorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).

fof(arity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Nat__Onat__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).

fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).

fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).

fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
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    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).

fof(arity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).

fof(arity_Int__Oint__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).

fof(arity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).

fof(arity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_Int__Oint__Rings_Oring,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).

fof(arity_Int__Oint__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(arity_Nat__Onat__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(arity_HOL__Obool__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(arity_Nat__Onat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).

fof(arity_HOL__Obool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).

fof(fact_subtract__code__numeral__def,axiom,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_Code__Numeral_Oof__nat__code,axiom,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).

fof(fact_rel__simps_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).

fof(i_0_5193,plain,
    ! [X90,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X90) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),X5),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),tc_Int_Oint),c_COMBB(tc_fun(X5,X5),X5,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,X5),X5),tc_Int_Oint),c_HOL_OLet(X5,X5)),c_Int_Oring__1__class_Oof__int(X5)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X5)),tc_Int_Oint),c_COMBS(X5,X5,X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),tc_Int_Oint),c_COMBB(X5,tc_fun(X5,X5),X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5)))),c_Groups_Oone__class_Oone(X5))))),c_Divides_Odivmod__int(X90,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__int__num]) ).

fof(i_0_5194,plain,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X55),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(i_0_5195,plain,
    ! [X60,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Power_Opower__class_Opower(X56),X60),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).

fof(i_0_5196,plain,
    ! [X122,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(i_0_5197,plain,
    ! [X126,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).

fof(i_0_5198,plain,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(i_0_5199,plain,
    ! [X126,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).

fof(i_0_5200,plain,
    ! [X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(i_0_5201,plain,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
         => c_Divides_OnegDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),X61)))
         => c_Divides_OnegDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OnegDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(i_0_5202,plain,
    ! [X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
         => c_Divides_OposDivAlg(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
         => c_Divides_OposDivAlg(X60,X61) = hAPP(c_Divides_Oadjust(X61),c_Divides_OposDivAlg(X60,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X61))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(i_0_5203,plain,
    ! [X224,X30,X5] :
      ( c_List_OdropWhile(X5,X30,X224) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X30,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X30,X224)))) ),
    inference(fof_simplification,[status(thm)],[fact_hd__dropWhile]) ).

fof(i_0_5204,plain,
    ! [X75,X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(i_0_5205,plain,
    ! [X224,X30,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X30,X224))))
         => ~ hBOOL(hAPP(X30,X3)) )
     => c_List_OtakeWhile(X5,X30,X224) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(i_0_5206,plain,
    ! [X26,X84,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),X26))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).

fof(i_0_5207,plain,
    ! [X26,X84] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26))),c_COMBI(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(i_0_5208,plain,
    ! [X20,X78,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X78)),c_Transitive__Closure_Ortrancl(X5,X78)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X20)),c_Transitive__Closure_Otrancl(X5,X78))) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).

fof(i_0_5209,plain,
    ! [X223,X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X30,X224)),X223) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__append1]) ).

fof(i_0_5210,plain,
    ! [X78,X5] :
      ( c_Wellfounded_Oacyclic(X5,X78)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X78))) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).

fof(i_0_5211,plain,
    ! [X122,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(i_0_5212,plain,
    ! [X78,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X78)))
     => c_Wellfounded_Oacyclic(X5,X78) ),
    inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).

fof(i_0_5213,plain,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_OdropWhile(X5,X30,X224) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OdropWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(i_0_5214,plain,
    ! [X84] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X84)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X84)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X84)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__Bit1]) ).

fof(i_0_5215,plain,
    ! [X95,X96,X30] :
      ( c_List_Olist__ex(tc_Nat_Onat,X30,c_List_Oupt(X96,X95))
    <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X30),X96,X95) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__nat]) ).

fof(i_0_5216,plain,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).

fof(i_0_5217,plain,
    ! [X126,X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Int_Oring__char__0(X56) )
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(X126))) ),
    inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(i_0_5218,plain,
    ! [X223,X24,X224,X30,X5] :
      ( c_List_OdropWhile(X5,X30,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)
    <=> ( X224 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X30,X224)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))
        & ~ hBOOL(hAPP(X30,X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(i_0_5219,plain,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(i_0_5220,plain,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => hAPP(c_List_OremoveAll(X5,X20),X224) = X224 ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__id]) ).

fof(i_0_5221,plain,
    ! [X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => hAPP(c_List_OremoveAll(X5,X20),hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not]) ).

fof(i_0_5222,plain,
    ! [X92,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X92) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122))),X92) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(i_0_5223,plain,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X94)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X94),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X94)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).

fof(i_0_5224,plain,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,X94) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X94)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X94))
       => c_List_Oupt(X98,X94) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).

fof(i_0_5225,plain,
    ! [X90,X89,X30] :
      ( epred2_3(X30,X89,X90)
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X30,X89)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X88,X120] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X90))
                & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X120)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X88,X120] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X120))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X120)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5226,plain,
    ! [X90,X89,X30] :
      ( epred1_3(X30,X89,X90)
    <=> ( ( X90 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => ! [X88] :
              ( ? [X120] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X90))
                  & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X88)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X88] :
              ( ? [X120] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X120))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X89 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X88)),X120) )
             => hBOOL(hAPP(X30,X88)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5227,plain,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(i_0_5228,plain,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X122)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(i_0_5229,plain,
    ! [X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(i_0_5230,plain,
    ! [X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X122)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(i_0_5231,plain,
    ! [X57,X56] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X56),c_List_Olist_ONil(X56)),X57)),
    inference(fof_simplification,[status(thm)],[fact_member__rec_I2_J]) ).

fof(i_0_5232,plain,
    ! [X26765] : c_Divides_Oadjust(X26765) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X26765))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X26765))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(variable_rename,[status(thm)],[fact_adjust__def]) ).

fof(i_0_5233,plain,
    ! [X26187] : c_Int_Osucc(c_Int_OBit0(X26187)) = c_Int_OBit1(X26187),
    inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).

fof(i_0_5234,plain,
    ! [X26145] : c_Int_OBit0(X26145) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26145),X26145),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_5235,plain,
    ! [X26348] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26348),c_Int_OMin) = c_Int_Osucc(X26348),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(i_0_5236,plain,
    ! [X37,X1,X2,X184,X25,X23,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X23),hAPP(c_Set_Oimage(tc_prod(X25,X184),tc_prod(X5,X17),c_Product__Type_Omap__pair(X25,X5,X184,X17,X2,X1)),X37)))
     => ~ ! [X3,X38] :
            ( X23 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),hAPP(X2,X3)),hAPP(X1,X38))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25,X184)),hAPP(hAPP(c_Product__Type_OPair(X25,X184),X3),X38)),X37)) ) ),
    inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).

fof(i_0_5237,plain,
    ! [X78,X292,X293,X294,X200,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78)))
     => ( hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294) != hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292)
       => ~ ! [X49,X124] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X200),X294)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124))),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X17),tc_prod(X5,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X17),tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X49),X124)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X293),X292))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X17),X78))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).

fof(i_0_5238,plain,
    ! [X26807,X26808] :
      ( ( X26808 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26808,X26807) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( X26807 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26808,X26807) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26808)
        | X26808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X26807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26808,X26807) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26807))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26807)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26808))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26807),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X26808,X26807)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26807))))),c_Divides_Opdivmod(X26808,X26807))))
        | X26808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__pdivmod])])]) ).

fof(i_0_5239,plain,
    ! [X28117,X28118,X28119,X28120] : c_Product__Type_Oapsnd(X28120,X28119,X28118,X28117) = c_Product__Type_Omap__pair(X28118,X28118,X28120,X28119,c_Fun_Oid(X28118),X28117),
    inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).

fof(i_0_5240,plain,
    ! [X26831,X26832] :
      ( ( X26832 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26832,X26831) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( X26831 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26832,X26831) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26832)
        | X26832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X26831 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26832,X26831) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26831))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26832)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26831))),c_Divides_Opdivmod(X26832,X26831)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26831))))),c_Divides_Opdivmod(X26832,X26831))))
        | X26832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__code])])]) ).

fof(i_0_5241,plain,
    ! [X29493,X29494,X29495] : c_Nitpick_Oplus__frac(X29495,X29494,X29493) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X29495),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X29495),X29494),hAPP(c_Nitpick_Odenom(X29495),X29493))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X29495),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X29495),tc_Int_Oint),c_Nitpick_Ofrac(X29495)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29495),X29494))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X29495),X29494))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29495),X29493))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X29495),X29493)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(i_0_5242,plain,
    ! [X29518] : c_Nitpick_Odenom(X29518) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X29518,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X29518)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(i_0_5243,plain,
    ! [X29517] : c_Nitpick_Onum(X29517) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X29517,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X29517)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(i_0_5244,plain,
    ! [X29196,X29197,X29198,X29199] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29199,tc_fun(X29199,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X29199,tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_fun(X29199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29199,tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_fun(X29199,tc_HOL_Obool)),X29199),c_COMBC(X29199,tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29199,tc_prod(X29199,X29199)),tc_fun(X29199,tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),X29199),hAPP(c_COMBB(tc_prod(X29199,X29199),tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool),X29199),c_member(tc_prod(X29199,X29199)))),c_Product__Type_OPair(X29199,X29199)))),X29198)),c_fequal),X29197),X29196))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29199,X29199)),hAPP(hAPP(c_Product__Type_OPair(X29199,X29199),X29197),X29196)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool)),X29198),c_Relation_OId(X29199)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29199,X29199)),hAPP(hAPP(c_Product__Type_OPair(X29199,X29199),X29197),X29196)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool)),X29198),c_Relation_OId(X29199))))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29199,tc_fun(X29199,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X29199,tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_fun(X29199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29199,tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_fun(X29199,tc_HOL_Obool)),X29199),c_COMBC(X29199,tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29199,tc_prod(X29199,X29199)),tc_fun(X29199,tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool)),X29199),hAPP(c_COMBB(tc_prod(X29199,X29199),tc_fun(tc_fun(tc_prod(X29199,X29199),tc_HOL_Obool),tc_HOL_Obool),X29199),c_member(tc_prod(X29199,X29199)))),c_Product__Type_OPair(X29199,X29199)))),X29198)),c_fequal),X29197),X29196)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).

fof(i_0_5245,plain,
    ! [X29227] : c_Transitive__Closure_Ortrancl(X29227,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29227,X29227),tc_HOL_Obool))) = c_Relation_OId(X29227),
    inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).

fof(i_0_5246,plain,
    ! [X26605,X26606,X26607] : hAPP(c_Divides_Oadjust(X26607),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26606),X26605)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26605),X26607)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26606)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26606)),X26605))),
    inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).

fof(i_0_5247,plain,
    ! [X28939,X28940,X28941,X28942] : c_Transitive__Closure_Otrancl(X28942,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28942,X28942)),hAPP(hAPP(c_Product__Type_OPair(X28942,X28942),X28941),X28940)),X28939)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28942,X28942),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28942,X28939)),hAPP(c_Set_OCollect(tc_prod(X28942,X28942)),hAPP(c_Product__Type_Oprod_Oprod__case(X28942,X28942,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28942,tc_fun(X28942,tc_HOL_Obool),tc_fun(X28942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28942,tc_HOL_Obool),tc_fun(X28942,tc_HOL_Obool)),X28942),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28942),c_fconj),hAPP(hAPP(c_COMBC(X28942,tc_fun(tc_prod(X28942,X28942),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28942,X28942),tc_fun(tc_fun(tc_prod(X28942,X28942),tc_HOL_Obool),tc_HOL_Obool),X28942),c_member(tc_prod(X28942,X28942))),hAPP(hAPP(c_COMBC(X28942,X28942,tc_prod(X28942,X28942)),c_Product__Type_OPair(X28942,X28942)),X28941))),c_Transitive__Closure_Ortrancl(X28942,X28939))))),hAPP(hAPP(c_COMBC(X28942,tc_fun(tc_prod(X28942,X28942),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28942,X28942),tc_fun(tc_fun(tc_prod(X28942,X28942),tc_HOL_Obool),tc_HOL_Obool),X28942),c_member(tc_prod(X28942,X28942))),hAPP(c_Product__Type_OPair(X28942,X28942),X28940))),c_Transitive__Closure_Ortrancl(X28942,X28939)))))),
    inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).

fof(i_0_5248,plain,
    ! [X28959,X28960] : c_Transitive__Closure_Otrancl(X28960,X28959) = hAPP(hAPP(c_Relation_Orel__comp(X28960,X28960,X28960),X28959),c_Transitive__Closure_Ortrancl(X28960,X28959)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).

fof(i_0_5249,plain,
    ! [X26330,X26331] :
      ( ( X26330 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X26331),X26330) = c_Groups_Ozero__class_Ozero(X26331)
        | ~ class_Rings_Oring__1(X26331) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X26331),X26330) = hAPP(c_Groups_Ouminus__class_Ouminus(X26331),hAPP(c_Int_Oring__1__class_Oof__int(X26331),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26330)))
        | X26330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X26331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X26331),X26330) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X26331),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X26331,X26331)),tc_fun(tc_Int_Oint,X26331)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X26331,X26331),X26331),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X26331,X26331)),tc_fun(tc_Int_Oint,X26331)),tc_Int_Oint),c_COMBB(tc_fun(X26331,X26331),X26331,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X26331,tc_fun(tc_fun(X26331,X26331),X26331),tc_Int_Oint),c_HOL_OLet(X26331,X26331)),c_Int_Oring__1__class_Oof__int(X26331)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X26331,X26331),tc_fun(X26331,X26331)),hAPP(hAPP(c_COMBB(tc_fun(X26331,tc_fun(X26331,X26331)),tc_fun(tc_fun(X26331,X26331),tc_fun(X26331,X26331)),tc_Int_Oint),c_COMBS(X26331,X26331,X26331)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X26331,X26331),tc_fun(X26331,tc_fun(X26331,X26331))),hAPP(hAPP(c_COMBB(tc_fun(X26331,tc_fun(X26331,X26331)),tc_fun(tc_fun(X26331,X26331),tc_fun(X26331,tc_fun(X26331,X26331))),tc_Int_Oint),c_COMBB(X26331,tc_fun(X26331,X26331),X26331)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26331,tc_fun(X26331,X26331)),tc_Int_Oint),c_If(X26331)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X26331,X26331,X26331),c_Groups_Oplus__class_Oplus(X26331)),c_COMBI(X26331))))),hAPP(hAPP(c_COMBC(X26331,X26331,X26331),hAPP(hAPP(c_COMBB(X26331,tc_fun(X26331,X26331),X26331),c_Groups_Oplus__class_Oplus(X26331)),hAPP(hAPP(c_COMBS(X26331,X26331,X26331),c_Groups_Oplus__class_Oplus(X26331)),c_COMBI(X26331)))),c_Groups_Oone__class_Oone(X26331))))),c_Divides_Odivmod__int(X26330,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X26330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X26331) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5193])])]) ).

fof(i_0_5250,plain,
    ! [X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
           => ~ hBOOL(hAPP(hAPP(hAPP(X22,X3),X21),X23)) ) ),
    inference(fof_simplification,[status(thm)],[fact_SUP2__E]) ).

fof(i_0_5251,plain,
    ! [X26284,X26285,X26286] :
      ( ( X26285 = c_Groups_Ozero__class_Ozero(X26286)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26286),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26285),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26284),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X26286)))
        | ~ class_Rings_Olinordered__idom(X26286) )
      & ( X26284 = c_Groups_Ozero__class_Ozero(X26286)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26286),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26285),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26284),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X26286)))
        | ~ class_Rings_Olinordered__idom(X26286) )
      & ( X26285 != c_Groups_Ozero__class_Ozero(X26286)
        | X26284 != c_Groups_Ozero__class_Ozero(X26286)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26286),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26285),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26286),X26284),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X26286)))
        | ~ class_Rings_Olinordered__idom(X26286) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).

fof(i_0_5252,plain,
    ! [X26290,X26291,X26292] :
      ( ~ class_Rings_Olinordered__idom(X26292)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26292),hAPP(hAPP(c_Power_Opower__class_Opower(X26292),X26291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26292),X26290),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X26292))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5194])]) ).

fof(i_0_5253,plain,
    ! [X31867,X31868,X31869,X31870] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31870)),c_List_Otranspose__rel(X31870)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31870)),hAPP(hAPP(c_List_Olist_OCons(X31870),X31869),X31868)),X31867)))
      | c_List_Otranspose(X31870,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31870)),hAPP(hAPP(c_List_Olist_OCons(X31870),X31869),X31868)),X31867)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31870)),hAPP(hAPP(c_List_Olist_OCons(X31870),X31869),c_List_Oconcat(X31870,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31870),tc_List_Olist(X31870)),c_List_Olist_Olist__case(tc_List_Olist(X31870),X31870,c_List_Olist_ONil(X31870),hAPP(hAPP(c_COMBB(tc_List_Olist(X31870),tc_fun(tc_List_Olist(X31870),tc_List_Olist(X31870)),X31870),c_COMBK(tc_List_Olist(X31870),tc_List_Olist(X31870))),hAPP(hAPP(c_COMBC(X31870,tc_List_Olist(X31870),tc_List_Olist(X31870)),c_List_Olist_OCons(X31870)),c_List_Olist_ONil(X31870))))),X31867)))),c_List_Otranspose(X31870,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31870)),X31868),c_List_Oconcat(tc_List_Olist(X31870),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31870),tc_List_Olist(tc_List_Olist(X31870))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31870)),X31870,c_List_Olist_ONil(tc_List_Olist(X31870)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31870),tc_List_Olist(tc_List_Olist(X31870))),X31870),hAPP(hAPP(c_COMBC(tc_List_Olist(X31870),tc_List_Olist(tc_List_Olist(X31870)),tc_List_Olist(tc_List_Olist(X31870))),c_List_Olist_OCons(tc_List_Olist(X31870))),c_List_Olist_ONil(tc_List_Olist(X31870)))))),X31867))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).

fof(i_0_5254,plain,
    ! [X31672,X31673] : c_List_Oconcat(X31673,X31672) = hAPP(c_List_Ofoldl(tc_List_Olist(X31673),tc_List_Olist(X31673),c_List_Oappend(X31673),c_List_Olist_ONil(X31673)),X31672),
    inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).

fof(i_0_5255,plain,
    ! [X31735,X31736,X31737,X31738] : c_List_Otranspose(X31738,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31738)),hAPP(hAPP(c_List_Olist_OCons(X31738),X31737),X31736)),X31735)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31738)),hAPP(hAPP(c_List_Olist_OCons(X31738),X31737),c_List_Oconcat(X31738,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31738),tc_List_Olist(X31738)),c_List_Olist_Olist__case(tc_List_Olist(X31738),X31738,c_List_Olist_ONil(X31738),hAPP(hAPP(c_COMBB(tc_List_Olist(X31738),tc_fun(tc_List_Olist(X31738),tc_List_Olist(X31738)),X31738),c_COMBK(tc_List_Olist(X31738),tc_List_Olist(X31738))),hAPP(hAPP(c_COMBC(X31738,tc_List_Olist(X31738),tc_List_Olist(X31738)),c_List_Olist_OCons(X31738)),c_List_Olist_ONil(X31738))))),X31735)))),c_List_Otranspose(X31738,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31738)),X31736),c_List_Oconcat(tc_List_Olist(X31738),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31738),tc_List_Olist(tc_List_Olist(X31738))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31738)),X31738,c_List_Olist_ONil(tc_List_Olist(X31738)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31738),tc_List_Olist(tc_List_Olist(X31738))),X31738),hAPP(hAPP(c_COMBC(tc_List_Olist(X31738),tc_List_Olist(tc_List_Olist(X31738)),tc_List_Olist(tc_List_Olist(X31738))),c_List_Olist_OCons(tc_List_Olist(X31738))),c_List_Olist_ONil(tc_List_Olist(X31738)))))),X31735))))),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(i_0_5256,plain,
    ! [X26317,X26318,X26319] :
      ( ~ class_Rings_Olinordered__idom(X26319)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26319),X26318),c_Groups_Ozero__class_Ozero(X26319)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26319),hAPP(hAPP(c_Power_Opower__class_Opower(X26319),X26318),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26317)))),c_Groups_Ozero__class_Ozero(X26319))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).

fof(i_0_5257,plain,
    ! [X146,X78,X25,X219,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X219),hAPP(hAPP(c_Relation_Orel__comp(X5,X25,X17),X78),X146)))
     => ~ ! [X3,X38,X150] :
            ( X219 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X3),X150)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X25)),hAPP(hAPP(c_Product__Type_OPair(X5,X25),X3),X38)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25,X17)),hAPP(hAPP(c_Product__Type_OPair(X25,X17),X38),X150)),X146)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).

fof(i_0_5258,plain,
    ! [X26314,X26315,X26316] :
      ( ~ class_Rings_Olinordered__idom(X26316)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26316),c_Groups_Ozero__class_Ozero(X26316)),hAPP(hAPP(c_Power_Opower__class_Opower(X26316),X26315),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26314)))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26316),c_Groups_Ozero__class_Ozero(X26316)),X26315)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).

fof(i_0_5259,plain,
    ! [X223,X30,X224,X20,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) = hAPP(c_List_Ofilter(X5,X30),X223)
    <=> ? [X242,X247] :
          ( X223 = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X247))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X242)))
             => ~ hBOOL(hAPP(X30,X3)) )
          & hBOOL(hAPP(X30,X20))
          & X224 = hAPP(c_List_Ofilter(X5,X30),X247) ) ),
    inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(i_0_5260,plain,
    ! [X224,X20,X223,X30,X5] :
      ( hAPP(c_List_Ofilter(X5,X30),X223) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)
    <=> ? [X242,X247] :
          ( X223 = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X247))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X242)))
             => ~ hBOOL(hAPP(X30,X3)) )
          & hBOOL(hAPP(X30,X20))
          & X224 = hAPP(c_List_Ofilter(X5,X30),X247) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(i_0_5261,plain,
    ! [X26293,X26294,X26295] :
      ( ~ class_Int_Onumber__ring(X26295)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26295),X26294),X26293)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26295),hAPP(hAPP(c_Power_Opower__class_Opower(X26295),X26294),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26295),X26293),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26295),hAPP(c_Int_Onumber__class_Onumber__of(X26295),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26294)),X26293)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).

fof(i_0_5262,plain,
    ! [X26311,X26312,X26313] :
      ( ~ class_Int_Onumber__ring(X26313)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26313),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26313),X26312),X26311)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26313),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26313),hAPP(hAPP(c_Power_Opower__class_Opower(X26313),X26312),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26313),X26311),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26313),hAPP(c_Int_Onumber__class_Onumber__of(X26313),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26312)),X26311)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).

fof(i_0_5263,plain,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => c_Nitpick_Osetsum_H(X5,X17,X2,X19) = hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X19))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => c_Nitpick_Osetsum_H(X5,X17,X2,X19) = c_Groups_Ozero__class_Ozero(X17) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(i_0_5264,plain,
    ! [X26287,X26288,X26289] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26289),c_Groups_Ozero__class_Ozero(X26289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26289),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26287),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | X26288 != c_Groups_Ozero__class_Ozero(X26289)
        | X26287 != c_Groups_Ozero__class_Ozero(X26289)
        | ~ class_Rings_Olinordered__idom(X26289) )
      & ( X26288 = c_Groups_Ozero__class_Ozero(X26289)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26289),c_Groups_Ozero__class_Ozero(X26289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26289),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26287),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X26289) )
      & ( X26287 = c_Groups_Ozero__class_Ozero(X26289)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26289),c_Groups_Ozero__class_Ozero(X26289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26289),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26289),X26287),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X26289) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).

fof(i_0_5265,plain,
    ! [X31884,X31885,X31886,X31887] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31887)),X31886))),c_List_Ofoldr(tc_List_Olist(X31885),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31885)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31885))),X31884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31887)),X31886)),c_List_Ofoldr(tc_List_Olist(X31885),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31885)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31885),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31885)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31885)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X31885),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31885)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31885),tc_List_Olist(X31885),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31885)))),X31884),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).

fof(i_0_5266,plain,
    ! [X32186,X32187,X32188,X32189,X32190] : c_List_Ofoldr(X32190,X32189,X32188,X32187,X32186) = hAPP(c_List_Ofoldl(X32189,X32190,hAPP(c_COMBC(X32190,X32189,X32189),X32188),X32186),hAPP(c_List_Orev(X32190),X32187)),
    inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).

fof(i_0_5267,plain,
    ! [X31924,X31925,X31926,X31927] : hAPP(hAPP(c_List_Omap(tc_prod(X31927,tc_Nat_Onat),X31927),c_Product__Type_Ofst(X31927,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31927,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31927,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X31927,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31927,tc_Nat_Onat))),X31926)),hAPP(hAPP(c_List_Ozip(X31927,tc_Nat_Onat),X31925),c_List_Oupt(X31924,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31924),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31927)),X31925)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X31927,tc_Nat_Onat),X31927),c_Product__Type_Ofst(X31927,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31927,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31927,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X31927,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X31927,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X31927,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X31927,tc_Nat_Onat))),X31924))),X31926)),hAPP(hAPP(c_List_Ozip(X31927,tc_Nat_Onat),X31925),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31927)),X31925))))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(i_0_5268,plain,
    ! [X31951,X31952] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31952),X31951)) = c_List_Oupt(X31952,X31951),
    inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(i_0_5269,plain,
    ! [X265,X1,X5,X266] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X266,X265) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X266,X265) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X265)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X5,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X266),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X265))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X5)),c_Product__Type_Ofst(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_Random_Osimps]) ).

fof(i_0_5270,plain,
    ! [X26108,X26109] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26109)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26108)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26109)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26108)),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(i_0_5271,plain,
    ! [X26110,X26111] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26111)))),X26110) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26111)),X26110),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(i_0_5272,plain,
    ! [X31359,X31360] : hAPP(c_New__DSequence_Opos__not__seq(X31360),X31359) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X31360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X31359))),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(i_0_5273,plain,
    ! [X133,X23,X25,X17,X26,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17,X25,tc_fun(X5,tc_HOL_Obool)),X23),X133)))
     => ~ ! [X3,X38] :
            ( X133 = hAPP(hAPP(c_Product__Type_OPair(X17,X25),X3),X38)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X26),hAPP(hAPP(X23,X3),X38))) ) ),
    inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).

fof(i_0_5274,plain,
    ! [X75,X19,X20,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X75))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ~ ! [X38] :
                ( X75 = hAPP(hAPP(X2,X20),X38)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X38)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(i_0_5275,plain,
    ! [X26329] :
      ( ( X26329 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X26329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X26329,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X26329) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X26329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X26329 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X26329,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X26329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X26329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X26329 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__of__code])])]) ).

fof(i_0_5276,plain,
    ! [X26281,X26282,X26283] :
      ( ~ class_Rings_Olinordered__idom(X26283)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26283),c_Groups_Ozero__class_Ozero(X26283)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26283),hAPP(hAPP(c_Power_Opower__class_Opower(X26283),X26282),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26283),X26281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero])]) ).

fof(i_0_5277,plain,
    ! [X2,X17,X19,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X19))),hAPP(hAPP(c_COMBC(X5,X17,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17,tc_fun(X17,tc_HOL_Obool),X5),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(i_0_5278,plain,
    ! [X31724,X31725,X31726] :
      ( ( c_List_Oconcat(X31726,X31725) != c_List_Oconcat(X31726,X31724)
        | X31725 = X31724
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31725) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31724)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31726),tc_List_Olist(X31726))),esk430_3(X31724,X31725,X31726)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31726),tc_List_Olist(X31726))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31726),tc_List_Olist(X31726)),X31725),X31724)))) )
      & ( X31725 != X31724
        | c_List_Oconcat(X31726,X31725) = c_List_Oconcat(X31726,X31724)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31725) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31724)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31726),tc_List_Olist(X31726))),esk430_3(X31724,X31725,X31726)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31726),tc_List_Olist(X31726))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31726),tc_List_Olist(X31726)),X31725),X31724)))) )
      & ( c_List_Oconcat(X31726,X31725) != c_List_Oconcat(X31726,X31724)
        | X31725 = X31724
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31725) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31724)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31726),tc_List_Olist(X31726),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31726),tc_fun(tc_List_Olist(X31726),tc_Nat_Onat),tc_fun(tc_List_Olist(X31726),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31726),tc_Nat_Onat),tc_fun(tc_List_Olist(X31726),tc_HOL_Obool)),tc_List_Olist(X31726)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31726))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31726)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31726))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31726)))),esk430_3(X31724,X31725,X31726))) )
      & ( X31725 != X31724
        | c_List_Oconcat(X31726,X31725) = c_List_Oconcat(X31726,X31724)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31725) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31726))),X31724)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31726),tc_List_Olist(X31726),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31726),tc_fun(tc_List_Olist(X31726),tc_Nat_Onat),tc_fun(tc_List_Olist(X31726),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31726),tc_Nat_Onat),tc_fun(tc_List_Olist(X31726),tc_HOL_Obool)),tc_List_Olist(X31726)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31726))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31726)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31726))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31726)))),esk430_3(X31724,X31725,X31726))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__eq__concat__iff])])])]) ).

fof(i_0_5279,plain,
    ! [X31720,X31721,X31722] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31722),tc_List_Olist(X31722))),esk429_3(X31720,X31721,X31722)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31722),tc_List_Olist(X31722))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31722),tc_List_Olist(X31722)),X31721),X31720))))
        | X31721 = X31720
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31722))),X31721) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31722))),X31720)
        | c_List_Oconcat(X31722,X31721) != c_List_Oconcat(X31722,X31720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31722),tc_List_Olist(X31722),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31722),tc_fun(tc_List_Olist(X31722),tc_Nat_Onat),tc_fun(tc_List_Olist(X31722),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31722),tc_Nat_Onat),tc_fun(tc_List_Olist(X31722),tc_HOL_Obool)),tc_List_Olist(X31722)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31722))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31722)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31722))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31722)))),esk429_3(X31720,X31721,X31722)))
        | X31721 = X31720
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31722))),X31721) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31722))),X31720)
        | c_List_Oconcat(X31722,X31721) != c_List_Oconcat(X31722,X31720) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).

fof(i_0_5280,plain,
    ! [X25995,X25996,X25997,X25998,X25999] : hAPP(c_Nat_Onat_Onat__rec(X25999,X25998,X25997),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25996)),X25995)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X25999),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25996))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X25999,X25999),hAPP(hAPP(c_COMBC(tc_Int_Oint,X25999,tc_fun(X25999,X25999)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25999,tc_fun(X25999,X25999)),tc_Int_Oint),c_If(X25999)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X25999,X25998,X25997),X25995))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X25999,X25999),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X25999,X25999),tc_Int_Oint),X25997),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X25995))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25999,tc_Int_Oint),c_Nat_Onat_Onat__rec(X25999,X25998,X25997)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X25995))))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(i_0_5281,plain,
    ! [X26345] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26345),c_Int_OMin) = c_Int_Opred(X26345),
    inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).

fof(i_0_5282,plain,
    ! [X26127,X26128] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26128),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26127),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26128))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2])]) ).

fof(i_0_5283,plain,
    ! [X26327,X26328] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26328),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26327))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26328)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26328) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).

fof(i_0_5284,plain,
    ! [X26132,X26133] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26133))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26132))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26133)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26132),X26133) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).

fof(i_0_5285,plain,
    ! [X25969,X25970] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25970) != hAPP(c_Nat_OSuc,X25969)
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X25969))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X25969)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25970) = hAPP(c_Nat_OSuc,X25969) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).

fof(i_0_5286,plain,
    ! [X25971,X25972] :
      ( ( hAPP(c_Nat_OSuc,X25972) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25971)
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25971))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X25972))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25971))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X25972)))))
        | hAPP(c_Nat_OSuc,X25972) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25971) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).

fof(i_0_5287,plain,
    ! [X19,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Nitpick_Ocard_H(X5,X19) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X19))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => c_Nitpick_Ocard_H(X5,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(i_0_5288,plain,
    ! [X96,X76] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X96)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X76))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X96))))) ),
    inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).

fof(i_0_5289,plain,
    ! [X26278,X26279,X26280] :
      ( ~ class_Rings_Olinordered__semidom(X26280)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26280),hAPP(hAPP(c_Power_Opower__class_Opower(X26280),X26279),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26280),X26278),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26280),c_Groups_Ozero__class_Ozero(X26280)),X26278))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26280),X26279),X26278)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).

fof(i_0_5290,plain,
    ! [X26254,X26255,X26256] :
      ( ~ class_Rings_Olinordered__semidom(X26256)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26256),hAPP(hAPP(c_Power_Opower__class_Opower(X26256),X26255),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26256),X26254),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26256),c_Groups_Ozero__class_Ozero(X26256)),X26254))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26256),X26255),X26254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).

fof(i_0_5291,plain,
    ! [X22,X17,X27,X19,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = X22 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17,tc_HOL_Obool)),X22) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),X19))
           => hAPP(c_Set_Ovimage(X17,X5,hAPP(hAPP(c_COMBC(X17,X5,X5),hAPP(hAPP(c_COMBC(X17,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X17),c_If(X5)),hAPP(hAPP(c_COMBC(X17,tc_fun(X17,tc_HOL_Obool),tc_HOL_Obool),c_member(X17)),X22))),X23)),X27)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).

fof(i_0_5292,plain,
    ! [X26325,X26326] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26326))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26326)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26325,X26326))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).

fof(i_0_5293,plain,
    ! [X26102,X26103] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26103))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26102)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26103),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26102)),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(i_0_5294,plain,
    ! [X26296,X26297,X26298] :
      ( ~ class_Rings_Olinordered__idom(X26298)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26298),c_Groups_Ozero__class_Ozero(X26298)),hAPP(hAPP(c_Power_Opower__class_Opower(X26298),X26297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26296)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).

fof(i_0_5295,plain,
    ! [X26104,X26105] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26105))),X26104) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26105),X26104),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(i_0_5296,plain,
    ! [X26106,X26107] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26107,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26106)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26107,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26106)),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(i_0_5297,plain,
    ! [X26112,X26113] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26113),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26112)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26112)),
    inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(i_0_5298,plain,
    ! [X28892,X28893,X28894] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28894,X28894),tc_HOL_Obool)),X28893),X28892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28894,X28894),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28894,X28894,X28894),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28894,X28894),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28894,X28893)),X28892)),X28893)),X28892))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28894,X28894),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28894,X28893)),X28892)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).

fof(i_0_5299,plain,
    ! [X23,X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),X23)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X21,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X36)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),X23)),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X17),X23),hAPP(c_Finite__Set_Ocard(X5),X36)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).

fof(i_0_5300,plain,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = c_Groups_Oone__class_Oone(X17) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).

fof(i_0_5301,plain,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).

fof(i_0_5302,plain,
    ! [X25977,X25978] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25977)))
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25977))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25978)),c_Int_Onat))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25977))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25978)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25977))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).

fof(i_0_5303,plain,
    ! [X25981,X25982] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25982)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25981)))
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25981))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25982)),c_Int_Onat))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25981))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25982)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25982)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25981))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).

fof(i_0_5304,plain,
    ! [X27180,X27181,X27182,X27183,X27184,X27185,X27186] : hAPP(c_Product__Type_Oapsnd(X27186,X27185,X27184,X27183),hAPP(c_Product__Type_Oapfst(X27182,X27184,X27186,X27181),X27180)) = hAPP(c_Product__Type_Oapfst(X27182,X27184,X27185,X27181),hAPP(c_Product__Type_Oapsnd(X27186,X27185,X27182,X27183),X27180)),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(i_0_5305,plain,
    ! [X28121,X28122,X28123,X28124] : c_Product__Type_Oapfst(X28124,X28123,X28122,X28121) = c_Product__Type_Omap__pair(X28124,X28123,X28122,X28122,X28121,c_Fun_Oid(X28122)),
    inference(variable_rename,[status(thm)],[fact_apfst__def]) ).

fof(i_0_5306,plain,
    ! [X78,X75,X102,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X20),X102)),hAPP(hAPP(c_List_Oappend(X5),X20),X75))),c_List_Olexord(X5,X78)))
     => ( ! [X49] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X49),X49)),X78))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X102),X75)),c_List_Olexord(X5,X78))) ) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).

fof(i_0_5307,plain,
    ! [X26262,X26263] :
      ( ~ class_Rings_Olinordered__idom(X26263)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26263),hAPP(hAPP(c_Power_Opower__class_Opower(X26263),X26262),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X26263))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5195])]) ).

fof(i_0_5308,plain,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X20 != X26 )
       => ~ ! [X38,X99] :
              ( X89 = hAPP(c_Nat_OSuc,X99)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),X37))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X99),X37))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).

fof(i_0_5309,plain,
    ! [X106,X90] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X106))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).

fof(i_0_5310,plain,
    ! [X21,X6] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).

fof(i_0_5311,plain,
    ! [X106,X90] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X90,X106)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X106))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X106),X90)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).

fof(i_0_5312,plain,
    ! [X21,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X6,X21)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).

fof(i_0_5313,plain,
    ! [X26299,X26300,X26301] :
      ( ~ class_Groups_Omonoid__mult(X26301)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26301),X26300),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26301),X26300),hAPP(hAPP(c_Power_Opower__class_Opower(X26301),hAPP(hAPP(c_Power_Opower__class_Opower(X26301),X26300),X26299)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__odd__eq])]) ).

fof(i_0_5314,plain,
    ! [X32315,X32316,X32317] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32317),X32316))
      | ~ hBOOL(hAPP(hAPP(c_member(X32317),X32315),hAPP(c_List_Oset(X32317),X32316)))
      | c_List_OtakeWhile(X32317,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32317),c_fNot),hAPP(hAPP(c_COMBC(X32317,X32317,tc_HOL_Obool),c_fequal),X32315)),hAPP(c_List_Orev(X32317),X32316)) = hAPP(c_List_Orev(X32317),hAPP(c_List_Otl(X32317),c_List_OdropWhile(X32317,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32317),c_fNot),hAPP(hAPP(c_COMBC(X32317,X32317,tc_HOL_Obool),c_fequal),X32315)),X32316))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev])]) ).

fof(i_0_5315,plain,
    ! [X32365,X32366,X32367] : c_List_OdropWhile(X32367,X32366,X32365) = hAPP(hAPP(c_List_Odrop(X32367),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32367)),c_List_OtakeWhile(X32367,X32366,X32365))),X32365),
    inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(i_0_5316,plain,
    ! [X28450,X28451,X28452,X28453,X28454,X28455,X28456] : hAPP(c_Product__Type_Oapsnd(X28456,X28455,X28454,X28453),hAPP(c_Product__Type_Oapsnd(X28452,X28456,X28454,X28451),X28450)) = hAPP(c_Product__Type_Oapsnd(X28452,X28455,X28454,hAPP(c_Fun_Ocomp(X28456,X28455,X28452,X28453),X28451)),X28450),
    inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).

fof(i_0_5317,plain,
    ! [X28457,X28458,X28459,X28460,X28461,X28462,X28463] : hAPP(c_Product__Type_Oapfst(X28463,X28462,X28461,X28460),hAPP(c_Product__Type_Oapfst(X28459,X28463,X28461,X28458),X28457)) = hAPP(c_Product__Type_Oapfst(X28459,X28462,X28461,hAPP(c_Fun_Ocomp(X28463,X28462,X28459,X28460),X28458)),X28457),
    inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).

fof(i_0_5318,plain,
    ! [X26264,X26265,X26266] :
      ( ( X26265 = c_Groups_Ozero__class_Ozero(X26266)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26266),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26264),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X26266)
        | ~ class_Rings_Olinordered__idom(X26266) )
      & ( X26264 = c_Groups_Ozero__class_Ozero(X26266)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26266),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26264),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X26266)
        | ~ class_Rings_Olinordered__idom(X26266) )
      & ( X26265 != c_Groups_Ozero__class_Ozero(X26266)
        | X26264 != c_Groups_Ozero__class_Ozero(X26266)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26266),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X26266),X26264),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X26266)
        | ~ class_Rings_Olinordered__idom(X26266) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).

fof(i_0_5319,plain,
    ! [X31998,X31999,X32000] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X31998,X31999,X32000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))
        | c_List_Otranspose(X31999,X32000) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31999)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31999),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31999)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31999),hAPP(hAPP(c_COMBB(tc_List_Olist(X31999),tc_fun(tc_Nat_Onat,X31999),tc_Nat_Onat),c_List_Onth(X31999)),hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31998))
        | X32000 = c_List_Olist_ONil(tc_List_Olist(X31999)) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31999)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000),esk434_3(X31998,X31999,X32000))) != X31998
        | c_List_Otranspose(X31999,X32000) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31999)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31999),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31999)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31999),hAPP(hAPP(c_COMBB(tc_List_Olist(X31999),tc_fun(tc_Nat_Onat,X31999),tc_Nat_Onat),c_List_Onth(X31999)),hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31998))
        | X32000 = c_List_Olist_ONil(tc_List_Olist(X31999)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X31998,X31999,X32000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))
        | c_List_Otranspose(X31999,X32000) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31999)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31999),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31999)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31999),hAPP(hAPP(c_COMBB(tc_List_Olist(X31999),tc_fun(tc_Nat_Onat,X31999),tc_Nat_Onat),c_List_Onth(X31999)),hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31998))
        | X31998 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31999)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000),esk434_3(X31998,X31999,X32000))) != X31998
        | c_List_Otranspose(X31999,X32000) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31999)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31999),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31999)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31999)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31999),hAPP(hAPP(c_COMBB(tc_List_Olist(X31999),tc_fun(tc_Nat_Onat,X31999),tc_Nat_Onat),c_List_Onth(X31999)),hAPP(c_List_Onth(tc_List_Olist(X31999)),X32000))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31999))),X32000)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31998))
        | X31998 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__rectangle])])])]) ).

fof(i_0_5320,plain,
    ! [X26125,X26126] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26126)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26125),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26126)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26126))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26125)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26126)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5196])]) ).

fof(i_0_5321,plain,
    ! [X26921,X26922,X26923] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk267_3(X26921,X26922,X26923)),esk268_3(X26921,X26922,X26923))))
        | hBOOL(hAPP(hAPP(X26921,X26923),X26922))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26923),X26922))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk267_3(X26921,X26922,X26923)),esk268_3(X26921,X26922,X26923))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk268_3(X26921,X26922,X26923)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X26921,esk267_3(X26921,X26922,X26923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk268_3(X26921,X26922,X26923))))
        | hBOOL(hAPP(hAPP(X26921,X26923),X26922))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26923),X26922))) )
      & ( ~ hBOOL(hAPP(hAPP(X26921,esk267_3(X26921,X26922,X26923)),esk268_3(X26921,X26922,X26923)))
        | hBOOL(hAPP(hAPP(X26921,X26923),X26922))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26923),X26922))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct])])])]) ).

fof(i_0_5322,plain,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Oone__class_Oone(X17))),X36) = c_Groups_Oone__class_Oone(X17) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).

fof(i_0_5323,plain,
    ! [X21,X6,X36,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X36))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = hAPP(X21,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X36))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),hAPP(hAPP(c_COMBC(X5,X17,X17),hAPP(hAPP(c_COMBS(X5,X17,tc_fun(X17,X17)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17,tc_fun(X17,X17)),X5),c_If(X17)),hAPP(c_fequal,X6))),X21)),c_Groups_Ozero__class_Ozero(X17))),X36) = c_Groups_Ozero__class_Ozero(X17) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).

fof(i_0_5324,plain,
    ! [X26926,X26927,X26928] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk269_3(X26926,X26927,X26928)),esk270_3(X26926,X26927,X26928))))
        | hBOOL(hAPP(hAPP(X26926,X26928),X26927))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26928),X26927))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk269_3(X26926,X26927,X26928)),esk270_3(X26926,X26927,X26928)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk270_3(X26926,X26927,X26928)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X26926,esk269_3(X26926,X26927,X26928)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk270_3(X26926,X26927,X26928))))
        | hBOOL(hAPP(hAPP(X26926,X26928),X26927))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26928),X26927))) )
      & ( ~ hBOOL(hAPP(hAPP(X26926,esk269_3(X26926,X26927,X26928)),esk270_3(X26926,X26927,X26928)))
        | hBOOL(hAPP(hAPP(X26926,X26928),X26927))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26928),X26927))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct])])])]) ).

fof(i_0_5325,plain,
    ! [X78,X223,X24,X224,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223))),c_List_Olistrel(X5,X78)))
     => ~ ! [X3,X229] :
            ( X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X229)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X24)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X229),X223)),c_List_Olistrel(X5,X78))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).

fof(i_0_5326,plain,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37)))
     => ~ ! [X38] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),X37))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37))) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(i_0_5327,plain,
    ! [X29501,X29502,X29503] : c_Nitpick_Otimes__frac(X29503,X29502,X29501) = hAPP(hAPP(c_Nitpick_Ofrac(X29503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29503),X29502)),hAPP(c_Nitpick_Onum(X29503),X29501))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X29503),X29502)),hAPP(c_Nitpick_Odenom(X29503),X29501))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(i_0_5328,plain,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
     => ( ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X20 != X26 )
       => ~ ! [X38,X99] :
              ( X89 = hAPP(c_Nat_OSuc,X99)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X99),X37)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),X37)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).

fof(i_0_5329,plain,
    ! [X37,X89,X26,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X89)),X37)))
     => ~ ! [X38] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X89),X37)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X26)),X37)) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(i_0_5330,plain,
    ! [X26783,X26784] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26784))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5197])])]) ).

fof(i_0_5331,plain,
    ! [X26880,X26881] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26881),X26880)))
        | c_Divides_OnegDivAlg(X26881,X26880) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26881),X26880))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26881),X26880))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26880),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X26881,X26880) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26881),X26880))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26881),X26880))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26881),X26880)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26880),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X26881,X26880) = hAPP(c_Divides_Oadjust(X26880),c_Divides_OnegDivAlg(X26881,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26880)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26881),X26880))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).

fof(i_0_5332,plain,
    ! [X26773] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26773))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5198])])]) ).

fof(i_0_5333,plain,
    ! [X26882,X26883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26883),X26882))
        | c_Divides_OposDivAlg(X26883,X26882) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26883)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26883),X26882))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26882),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X26883,X26882) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26883)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26883),X26882))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26883),X26882))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26882),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X26883,X26882) = hAPP(c_Divides_Oadjust(X26882),c_Divides_OposDivAlg(X26883,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26882)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26883),X26882))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).

fof(i_0_5334,plain,
    ! [X26799,X26800] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26800))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5199])])]) ).

fof(i_0_5335,plain,
    ! [X26302,X26303,X26304] :
      ( ~ class_Rings_Ocomm__semiring__1(X26304)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26304),X26303),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26302))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26304),X26303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26304),hAPP(hAPP(c_Power_Opower__class_Opower(X26304),X26303),X26302)),hAPP(hAPP(c_Power_Opower__class_Opower(X26304),X26303),X26302))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).

fof(i_0_5336,plain,
    ! [X26129,X26130,X26131] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26131)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X26130))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26129))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26129),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X26130)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).

fof(i_0_5337,plain,
    ! [X25979,X25980] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25980)),hAPP(c_Nat_OSuc,X25979)))
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25980))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X25979)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25980))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X25979))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25980)),hAPP(c_Nat_OSuc,X25979))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).

fof(i_0_5338,plain,
    ! [X25983,X25984] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25984)),hAPP(c_Nat_OSuc,X25983)))
        | hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25984))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X25983)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25984))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X25983))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25984)),hAPP(c_Nat_OSuc,X25983))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).

fof(i_0_5339,plain,
    ! [X26791] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26791))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5200])])]) ).

fof(i_0_5340,plain,
    ! [X26323,X26324] :
      ( ~ class_Rings_Osemiring__1(X26324)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26323))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26324),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26323))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26324),hAPP(c_Int_Onat,X26323))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26324),hAPP(c_Int_Onat,X26323))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).

fof(i_0_5341,plain,
    ! [X26781,X26782] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26781),X26782)))
        | c_Divides_OnegDivAlg(X26781,X26782) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26781),X26782))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26782)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26781),X26782)))
        | c_Divides_OnegDivAlg(X26781,X26782) = hAPP(c_Divides_Oadjust(X26782),c_Divides_OnegDivAlg(X26781,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26782)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26782)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5201])])]) ).

fof(i_0_5342,plain,
    ! [X26779,X26780] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26780),X26779)))
        | c_Divides_OnegDivAlg(X26780,X26779) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26780),X26779)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26779),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X26780,X26779) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26780),X26779)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26780),X26779)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26779),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X26780,X26779) = hAPP(c_Divides_Oadjust(X26779),c_Divides_OnegDivAlg(X26780,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26779))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).

fof(i_0_5343,plain,
    ! [X26801,X26802] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26801),X26802))
        | c_Divides_OposDivAlg(X26801,X26802) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26801)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26802)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26801),X26802))
        | c_Divides_OposDivAlg(X26801,X26802) = hAPP(c_Divides_Oadjust(X26802),c_Divides_OposDivAlg(X26801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26802)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26802)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5202])])]) ).

fof(i_0_5344,plain,
    ! [X26792,X26793] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26793),X26792))
        | c_Divides_OposDivAlg(X26793,X26792) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26793) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26792),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X26793,X26792) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26793) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26793),X26792))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26792),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X26793,X26792) = hAPP(c_Divides_Oadjust(X26792),c_Divides_OposDivAlg(X26793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26792))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).

fof(i_0_5345,plain,
    ! [X26320,X26321] :
      ( ~ class_Rings_Oring__1(X26321)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26321),hAPP(c_Groups_Ouminus__class_Ouminus(X26321),c_Groups_Oone__class_Oone(X26321))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26320))) = hAPP(c_Groups_Ouminus__class_Ouminus(X26321),c_Groups_Oone__class_Oone(X26321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).

fof(i_0_5346,plain,
    ! [X26275,X26276,X26277] :
      ( ~ class_Rings_Oring__1(X26277)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26277),hAPP(c_Groups_Ouminus__class_Ouminus(X26277),X26276)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26275)) = hAPP(hAPP(c_Power_Opower__class_Opower(X26277),X26276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26275)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).

fof(i_0_5347,plain,
    ! [X26332,X26333] :
      ( ~ class_Int_Onumber__ring(X26333)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26333),hAPP(c_Int_Onumber__class_Onumber__of(X26333),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26332))) = hAPP(c_Int_Onumber__class_Onumber__of(X26333),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).

fof(i_0_5348,plain,
    ! [X26087] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26087))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X26087),
    inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(i_0_5349,plain,
    ! [X19,X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_OImage(X17,X5,X78),X19)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X21)),X78))
           => ~ hBOOL(hAPP(hAPP(c_member(X17),X3),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_ImageE]) ).

fof(i_0_5350,plain,
    ! [X31732,X31733,X31734] : c_Enum_On__lists(X31734,hAPP(c_Nat_OSuc,X31733),X31732) = c_List_Oconcat(tc_List_Olist(X31734),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31734),tc_List_Olist(tc_List_Olist(X31734))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31734),tc_List_Olist(X31734),tc_List_Olist(tc_List_Olist(X31734))),hAPP(hAPP(c_COMBB(tc_fun(X31734,tc_List_Olist(X31734)),tc_fun(tc_List_Olist(X31734),tc_List_Olist(tc_List_Olist(X31734))),tc_List_Olist(X31734)),c_List_Omap(X31734,tc_List_Olist(X31734))),hAPP(c_COMBC(X31734,tc_List_Olist(X31734),tc_List_Olist(X31734)),c_List_Olist_OCons(X31734)))),X31732)),c_Enum_On__lists(X31734,X31733,X31732))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(i_0_5351,plain,
    ! [X25990,X25991,X25992,X25993,X25994] : c_Nat_Onat_Onat__case(X25994,X25993,X25992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25991)),X25990)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X25994),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25991))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X25994,X25994),hAPP(hAPP(c_COMBC(tc_Int_Oint,X25994,tc_fun(X25994,X25994)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25994,tc_fun(X25994,X25994)),tc_Int_Oint),c_If(X25994)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X25994,X25993,X25992,X25990))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25994,tc_Int_Oint),X25992),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X25990)))),
    inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(i_0_5352,plain,
    ! [X26309] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26309,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26309,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26309,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26309,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod2__gr__0])]) ).

fof(i_0_5353,plain,
    ! [X26885,X26886,X26887,X26888,X26889,X26890] :
      ( ( hAPP(c_Product__Type_Oapsnd(X26890,X26889,X26888,X26887),X26886) != hAPP(c_Product__Type_Oapsnd(X26890,X26889,X26888,X26885),X26886)
        | hAPP(X26887,hAPP(c_Product__Type_Osnd(X26888,X26890),X26886)) = hAPP(X26885,hAPP(c_Product__Type_Osnd(X26888,X26890),X26886)) )
      & ( hAPP(X26887,hAPP(c_Product__Type_Osnd(X26888,X26890),X26886)) != hAPP(X26885,hAPP(c_Product__Type_Osnd(X26888,X26890),X26886))
        | hAPP(c_Product__Type_Oapsnd(X26890,X26889,X26888,X26887),X26886) = hAPP(c_Product__Type_Oapsnd(X26890,X26889,X26888,X26885),X26886) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).

fof(i_0_5354,plain,
    ! [X27141,X27142,X27143,X27144,X27145,X27146] :
      ( ( hAPP(c_Product__Type_Oapfst(X27146,X27145,X27144,X27143),X27142) != hAPP(c_Product__Type_Oapfst(X27146,X27145,X27144,X27141),X27142)
        | hAPP(X27143,hAPP(c_Product__Type_Ofst(X27146,X27144),X27142)) = hAPP(X27141,hAPP(c_Product__Type_Ofst(X27146,X27144),X27142)) )
      & ( hAPP(X27143,hAPP(c_Product__Type_Ofst(X27146,X27144),X27142)) != hAPP(X27141,hAPP(c_Product__Type_Ofst(X27146,X27144),X27142))
        | hAPP(c_Product__Type_Oapfst(X27146,X27145,X27144,X27143),X27142) = hAPP(c_Product__Type_Oapfst(X27146,X27145,X27144,X27141),X27142) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).

fof(i_0_5355,plain,
    ! [X29262] : c_Relation_OId(X29262) = hAPP(c_Set_OCollect(tc_prod(X29262,X29262)),hAPP(hAPP(c_COMBB(tc_fun(X29262,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X29262,X29262)),c_HOL_OEx(X29262)),hAPP(hAPP(c_COMBC(tc_prod(X29262,X29262),tc_fun(X29262,tc_prod(X29262,X29262)),tc_fun(X29262,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29262,X29262),tc_HOL_Obool),tc_fun(tc_fun(X29262,tc_prod(X29262,X29262)),tc_fun(X29262,tc_HOL_Obool)),tc_prod(X29262,X29262)),c_COMBB(tc_prod(X29262,X29262),tc_HOL_Obool,X29262)),c_fequal)),hAPP(hAPP(c_COMBS(X29262,X29262,tc_prod(X29262,X29262)),c_Product__Type_OPair(X29262,X29262)),c_COMBI(X29262))))),
    inference(variable_rename,[status(thm)],[fact_Id__def]) ).

fof(i_0_5356,plain,
    ! [X27128,X27129,X27130,X27131,X27132,X27133,X27134] : hAPP(c_Product__Type_Oapsnd(X27134,X27133,X27132,X27131),hAPP(c_Product__Type_Oapfst(X27130,X27132,X27134,X27129),X27128)) = hAPP(hAPP(c_Product__Type_OPair(X27132,X27133),hAPP(X27129,hAPP(c_Product__Type_Ofst(X27130,X27134),X27128))),hAPP(X27131,hAPP(c_Product__Type_Osnd(X27130,X27134),X27128))),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).

fof(i_0_5357,plain,
    ! [X27187,X27188,X27189,X27190,X27191,X27192,X27193] : hAPP(c_Product__Type_Oapfst(X27193,X27192,X27191,X27190),hAPP(c_Product__Type_Oapsnd(X27189,X27191,X27193,X27188),X27187)) = hAPP(hAPP(c_Product__Type_OPair(X27192,X27191),hAPP(X27190,hAPP(c_Product__Type_Ofst(X27193,X27189),X27187))),hAPP(X27188,hAPP(c_Product__Type_Osnd(X27193,X27189),X27187))),
    inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).

fof(i_0_5358,plain,
    ! [X26248,X26249] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26249),c_Groups_Ozero__class_Ozero(X26249)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26249),X26248),hAPP(c_Int_Onumber__class_Onumber__of(X26249),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26249),c_Groups_Ozero__class_Ozero(X26249)),X26248))
        | ~ class_Fields_Olinordered__field__inverse__zero(X26249)
        | ~ class_Int_Onumber__ring(X26249) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26249),c_Groups_Ozero__class_Ozero(X26249)),X26248))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26249),c_Groups_Ozero__class_Ozero(X26249)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26249),X26248),hAPP(c_Int_Onumber__class_Onumber__of(X26249),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X26249)
        | ~ class_Int_Onumber__ring(X26249) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_5359,plain,
    ! [X25988,X25989] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25989)),hAPP(c_Nat_OSuc,X25988)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25989))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X25988))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X25988)))),
    inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).

fof(i_0_5360,plain,
    ! [X26260,X26261] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26261),c_Groups_Ozero__class_Ozero(X26261)),hAPP(hAPP(c_Power_Opower__class_Opower(X26261),X26260),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X26260 != c_Groups_Ozero__class_Ozero(X26261)
        | ~ class_Rings_Olinordered__idom(X26261) )
      & ( X26260 = c_Groups_Ozero__class_Ozero(X26261)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26261),c_Groups_Ozero__class_Ozero(X26261)),hAPP(hAPP(c_Power_Opower__class_Opower(X26261),X26260),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X26261) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).

fof(i_0_5361,plain,
    ! [X25916,X25917] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25917)),hAPP(c_Nat_OSuc,X25916)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25917))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X25916)))),
    inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).

fof(i_0_5362,plain,
    ! [X26000,X26001,X26002,X26003] : hAPP(c_Nat_Onat_Onat__rec(X26003,X26002,X26001),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26000)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X26003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X26000))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X26003,X26003),hAPP(hAPP(c_COMBC(tc_Int_Oint,X26003,tc_fun(X26003,X26003)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26003,tc_fun(X26003,X26003)),tc_Int_Oint),c_If(X26003)),c_Nat__Numeral_Oneg)),X26002)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X26003,X26003),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X26003,X26003),tc_Int_Oint),X26001),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26003,tc_Int_Oint),c_Nat_Onat_Onat__rec(X26003,X26002,X26001)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).

fof(i_0_5363,plain,
    ! [X31739,X31740] : c_List_Oconcat(X31740,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31740),tc_List_Olist(X31740)),c_List_Olist_Olist__case(tc_List_Olist(X31740),X31740,c_List_Olist_ONil(X31740),hAPP(hAPP(c_COMBB(tc_List_Olist(X31740),tc_fun(tc_List_Olist(X31740),tc_List_Olist(X31740)),X31740),c_COMBK(tc_List_Olist(X31740),tc_List_Olist(X31740))),hAPP(hAPP(c_COMBC(X31740,tc_List_Olist(X31740),tc_List_Olist(X31740)),c_List_Olist_OCons(X31740)),c_List_Olist_ONil(X31740))))),X31739)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31740),X31740),c_List_Ohd(X31740)),hAPP(c_List_Ofilter(tc_List_Olist(X31740),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31740)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31740),tc_List_Olist(X31740),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31740)))),X31739)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(i_0_5364,plain,
    ! [X31865,X31866] : c_List_Oconcat(tc_List_Olist(X31866),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31866),tc_List_Olist(tc_List_Olist(X31866))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31866)),X31866,c_List_Olist_ONil(tc_List_Olist(X31866)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31866),tc_List_Olist(tc_List_Olist(X31866))),X31866),hAPP(hAPP(c_COMBC(tc_List_Olist(X31866),tc_List_Olist(tc_List_Olist(X31866)),tc_List_Olist(tc_List_Olist(X31866))),c_List_Olist_OCons(tc_List_Olist(X31866))),c_List_Olist_ONil(tc_List_Olist(X31866)))))),X31865)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31866),tc_List_Olist(X31866)),c_List_Otl(X31866)),hAPP(c_List_Ofilter(tc_List_Olist(X31866),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31866)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31866),tc_List_Olist(X31866),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31866)))),X31865)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(i_0_5365,plain,
    ! [X29275,X29276,X29277] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29277,X29277),tc_HOL_Obool)),c_Relation_OId(X29277)),X29276))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29277,X29277),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29277,X29277,X29277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29277,X29277),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X29277,X29275)),X29276)),X29275)),X29276))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29277,X29277),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X29277,X29275)),X29276)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).

fof(i_0_5366,plain,
    ! [X78,X224,X223,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X223)),X224)),c_List_Olistrel(X5,X78)))
     => ~ ! [X38,X230] :
            ( X224 = hAPP(hAPP(c_List_Olist_OCons(X5),X38),X230)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X38)),X78))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X223),X230)),c_List_Olistrel(X5,X78))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).

fof(i_0_5367,plain,
    ! [X26236,X26237,X26238] :
      ( ~ class_Groups_Omonoid__mult(X26238)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26238),X26237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26236)) = hAPP(hAPP(c_Power_Opower__class_Opower(X26238),hAPP(hAPP(c_Power_Opower__class_Opower(X26238),X26237),X26236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__eq])]) ).

fof(i_0_5368,plain,
    ! [X31921,X31922,X31923] : c_List_Osublist(X31923,X31922,X31921) = hAPP(hAPP(c_List_Omap(tc_prod(X31923,tc_Nat_Onat),X31923),c_Product__Type_Ofst(X31923,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31923,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31923,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X31923,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31923,tc_Nat_Onat))),X31921)),hAPP(hAPP(c_List_Ozip(X31923,tc_Nat_Onat),X31922),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31923)),X31922))))),
    inference(variable_rename,[status(thm)],[fact_sublist__def]) ).

fof(i_0_5369,plain,
    ! [X72,X33,X34,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X34),X33)),X72))
    <=> ? [X49,X50] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X34),X33) = hAPP(hAPP(c_Set_Oinsert(X5),X49),X50)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X49,X50),X72))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X49),X50)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(i_0_5370,plain,
    ! [X29509,X29510] : c_Nitpick_Ouminus__frac(X29510,X29509) = c_Nitpick_OAbs__Frac(X29510,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29510),X29509))),hAPP(c_Nitpick_Odenom(X29510),X29509))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(i_0_5371,plain,
    ! [X26891,X26892,X26893,X26894,X26895] : hAPP(c_Product__Type_Osnd(X26895,X26894),hAPP(c_Product__Type_Oapsnd(X26893,X26894,X26895,X26892),X26891)) = hAPP(X26892,hAPP(c_Product__Type_Osnd(X26895,X26893),X26891)),
    inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).

fof(i_0_5372,plain,
    ! [X27147,X27148,X27149,X27150,X27151] : hAPP(c_Product__Type_Ofst(X27151,X27150),hAPP(c_Product__Type_Oapfst(X27149,X27151,X27150,X27148),X27147)) = hAPP(X27148,hAPP(c_Product__Type_Ofst(X27149,X27150),X27147)),
    inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).

fof(i_0_5373,plain,
    ! [X26981,X26982,X26983,X26984,X26985] : hAPP(c_Product__Type_Ofst(X26985,X26984),hAPP(c_Product__Type_Oapsnd(X26983,X26984,X26985,X26982),X26981)) = hAPP(c_Product__Type_Ofst(X26985,X26983),X26981),
    inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).

fof(i_0_5374,plain,
    ! [X27152,X27153,X27154,X27155,X27156] : hAPP(c_Product__Type_Osnd(X27156,X27155),hAPP(c_Product__Type_Oapfst(X27154,X27156,X27155,X27153),X27152)) = hAPP(c_Product__Type_Osnd(X27154,X27155),X27152),
    inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).

fof(i_0_5375,plain,
    ! [X25973,X25974,X25975,X25976] : c_Nat_Onat_Onat__case(X25976,X25975,X25974,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25973)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X25976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25973))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X25976,X25976),hAPP(hAPP(c_COMBC(tc_Int_Oint,X25976,tc_fun(X25976,X25976)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25976,tc_fun(X25976,X25976)),tc_Int_Oint),c_If(X25976)),c_Nat__Numeral_Oneg)),X25975)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25976,tc_Int_Oint),X25974),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).

fof(i_0_5376,plain,
    ! [X25986,X25987] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25987)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25986)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25986))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X25987))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25987)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).

fof(i_0_5377,plain,
    ! [X25918,X25919] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25919)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25918)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25918))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25919)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).

fof(i_0_5378,plain,
    ! [X26322] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26322))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26322),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero])]) ).

fof(i_0_5379,plain,
    ! [X26250,X26251] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X26251)
      | ~ class_Int_Onumber__ring(X26251)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26251),c_Groups_Ozero__class_Ozero(X26251)),X26250))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26251),c_Groups_Ozero__class_Ozero(X26251)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26251),X26250),hAPP(c_Int_Onumber__class_Onumber__of(X26251),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero])]) ).

fof(i_0_5380,plain,
    ! [X26272,X26273,X26274] :
      ( ~ class_Rings_Ocomm__semiring__1(X26274)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26274),X26273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26274),hAPP(hAPP(c_Power_Opower__class_Opower(X26274),X26273),X26272)),hAPP(hAPP(c_Power_Opower__class_Opower(X26274),X26273),X26272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).

fof(i_0_5381,plain,
    ! [X26310] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X26310))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26310),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__2__gt__zero])]) ).

fof(i_0_5382,plain,
    ! [X26085,X26086] :
      ( ~ class_Groups_Omonoid__mult(X26086)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26086),X26085),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26086),X26085),X26085)),X26085) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).

fof(i_0_5383,plain,
    ! [X26252,X26253] :
      ( ~ class_Rings_Olinordered__idom(X26253)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26253),c_Groups_Ozero__class_Ozero(X26253)),hAPP(hAPP(c_Power_Opower__class_Opower(X26253),X26252),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power2])]) ).

fof(i_0_5384,plain,
    ! [X26305,X26306] :
      ( ~ class_Rings_Oring__1(X26306)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26306),hAPP(c_Groups_Ouminus__class_Ouminus(X26306),c_Groups_Oone__class_Oone(X26306))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26305)) = c_Groups_Oone__class_Oone(X26306) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).

fof(i_0_5385,plain,
    ! [X26378,X26379] :
      ( ~ class_Int_Onumber__ring(X26379)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26379),hAPP(c_Int_Onumber__class_Onumber__of(X26379),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26378)) = c_Groups_Oone__class_Oone(X26379) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).

fof(i_0_5386,plain,
    ! [X75,X167] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X167),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X167),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X167)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of]) ).

fof(i_0_5387,plain,
    ! [X32350,X32351,X32352,X32353,X32354] : c_List_OdropWhile(X32354,X32353,hAPP(hAPP(c_List_Omap(X32352,X32354),X32351),X32350)) = hAPP(hAPP(c_List_Omap(X32352,X32354),X32351),c_List_OdropWhile(X32352,hAPP(c_Fun_Ocomp(X32354,tc_HOL_Obool,X32352,X32353),X32351),X32350)),
    inference(variable_rename,[status(thm)],[fact_dropWhile__map]) ).

fof(i_0_5388,plain,
    ! [X26,X147] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X147))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X147)) = hAPP(c_Int_Onat,X26) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X147))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X147)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X147)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    inference(fof_simplification,[status(thm)],[fact_diff__nat__eq__if]) ).

fof(i_0_5389,plain,
    ! [X32318,X32319,X32320] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32320),X32319))
      | ~ hBOOL(hAPP(hAPP(c_member(X32320),X32318),hAPP(c_List_Oset(X32320),X32319)))
      | c_List_OdropWhile(X32320,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32320),c_fNot),hAPP(hAPP(c_COMBC(X32320,X32320,tc_HOL_Obool),c_fequal),X32318)),hAPP(c_List_Orev(X32320),X32319)) = hAPP(hAPP(c_List_Olist_OCons(X32320),X32318),hAPP(c_List_Orev(X32320),c_List_OtakeWhile(X32320,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32320),c_fNot),hAPP(hAPP(c_COMBC(X32320,X32320,tc_HOL_Obool),c_fequal),X32318)),X32319))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev])]) ).

fof(i_0_5390,plain,
    ! [X33870,X33871,X33872,X33875] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33872,X33872)),hAPP(hAPP(c_Product__Type_OPair(X33872,X33872),hAPP(X33871,hAPP(c_Nat_OSuc,esk547_3(X33870,X33871,X33872)))),hAPP(X33871,esk547_3(X33870,X33871,X33872)))),c_Transitive__Closure_Ortrancl(X33872,X33870)))
      | ~ c_Wellfounded_Owf(X33872,c_Transitive__Closure_Otrancl(X33872,X33870))
      | hAPP(X33871,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk548_3(X33870,X33871,X33872)),X33875)) = hAPP(X33871,esk548_3(X33870,X33871,X33872)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__weak__decr__stable])])])]) ).

fof(i_0_5391,plain,
    ! [X6,X20,X19,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X21,X19),X20))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X20)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(i_0_5392,plain,
    ! [X31728,X31729,X31730,X31731] : c_List_Oconcat(X31731,hAPP(hAPP(c_List_Omap(X31730,tc_List_Olist(X31731)),hAPP(hAPP(c_COMBC(X31730,tc_List_Olist(X31731),tc_List_Olist(X31731)),hAPP(hAPP(c_COMBB(X31731,tc_fun(tc_List_Olist(X31731),tc_List_Olist(X31731)),X31730),c_List_Olist_OCons(X31731)),X31729)),c_List_Olist_ONil(X31731))),X31728)) = hAPP(hAPP(c_List_Omap(X31730,X31731),X31729),X31728),
    inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).

fof(i_0_5393,plain,
    ! [X29514,X29515,X29516] :
      ( ( ~ c_Nitpick_Oless__eq__frac(X29516,X29515,X29514)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29516),c_Nitpick_Oplus__frac(X29516,X29515,c_Nitpick_Ouminus__frac(X29516,X29514)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29516),c_Nitpick_Oplus__frac(X29516,X29515,c_Nitpick_Ouminus__frac(X29516,X29514)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__eq__frac(X29516,X29515,X29514) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).

fof(i_0_5394,plain,
    ! [X29511,X29512,X29513] :
      ( ( ~ c_Nitpick_Oless__frac(X29513,X29512,X29511)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29513),c_Nitpick_Oplus__frac(X29513,X29512,c_Nitpick_Ouminus__frac(X29513,X29511)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29513),c_Nitpick_Oplus__frac(X29513,X29512,c_Nitpick_Ouminus__frac(X29513,X29511)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__frac(X29513,X29512,X29511) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).

fof(i_0_5395,plain,
    ! [X26257,X26258,X26259] :
      ( ~ class_Rings_Olinordered__semidom(X26259)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26259),X26258),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X26259),X26257),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26259),c_Groups_Ozero__class_Ozero(X26259)),X26258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26259),c_Groups_Ozero__class_Ozero(X26259)),X26257))
      | X26258 = X26257 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).

fof(i_0_5396,plain,
    ! [X26269] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | X26269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X26269 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])]) ).

fof(i_0_5397,plain,
    ! [X26244] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26244))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26244),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(variable_rename,[status(thm)],[fact_div2__Suc__Suc]) ).

fof(i_0_5398,plain,
    ! [X26239,X26240] :
      ( ~ class_Rings_Olinordered__idom(X26240)
      | hAPP(c_Groups_Oabs__class_Oabs(X26240),hAPP(hAPP(c_Power_Opower__class_Opower(X26240),X26239),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X26240),X26239),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power2])]) ).

fof(i_0_5399,plain,
    ! [X29504,X29505,X29506] :
      ( ~ class_Rings_Oinverse(X29506)
      | ~ class_Rings_Oring__1(X29506)
      | c_Nitpick_Oof__frac(X29505,X29506,X29504) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X29506),hAPP(c_Int_Oring__1__class_Oof__int(X29506),hAPP(c_Nitpick_Onum(X29505),X29504))),hAPP(c_Int_Oring__1__class_Oof__int(X29506),hAPP(c_Nitpick_Odenom(X29505),X29504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).

fof(i_0_5400,plain,
    ! [X78,X220,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),X220),hAPP(c_Relation_Oconverse(X17,X5),X78)))
     => ~ ! [X3,X38] :
            ( X220 = hAPP(hAPP(c_Product__Type_OPair(X5,X17),X38),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X38)),X78)) ) ),
    inference(fof_simplification,[status(thm)],[fact_converseE]) ).

fof(i_0_5401,plain,
    ! [X2,X89,X51,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X51)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X89),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(i_0_5402,plain,
    ! [X26,X24,X19,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X21,X19),X24))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X19))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X26,hAPP(hAPP(c_Set_Oinsert(X5),X21),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X24))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(i_0_5403,plain,
    ! [X24,X26,X2,X17,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,X19),X24))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X17,X2,X26,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),hAPP(hAPP(X2,X20),X24))) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(i_0_5404,plain,
    ! [X29436,X29437,X29438,X29439] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29439,X29439)),hAPP(hAPP(c_Product__Type_OPair(X29439,X29439),X29438),esk362_4(X29436,X29437,X29438,X29439))),X29436))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29439,X29439)),hAPP(hAPP(c_Product__Type_OPair(X29439,X29439),X29438),X29437)),c_Transitive__Closure_Otrancl(X29439,X29436))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29439,X29439)),hAPP(hAPP(c_Product__Type_OPair(X29439,X29439),esk362_4(X29436,X29437,X29438,X29439)),X29437)),c_Transitive__Closure_Ortrancl(X29439,X29436)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29439,X29439)),hAPP(hAPP(c_Product__Type_OPair(X29439,X29439),X29438),X29437)),c_Transitive__Closure_Otrancl(X29439,X29436))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).

fof(i_0_5405,plain,
    ! [X29431,X29432,X29433,X29434] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29434,X29434)),hAPP(hAPP(c_Product__Type_OPair(X29434,X29434),X29433),esk361_4(X29431,X29432,X29433,X29434))),c_Transitive__Closure_Ortrancl(X29434,X29431)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29434,X29434)),hAPP(hAPP(c_Product__Type_OPair(X29434,X29434),X29433),X29432)),c_Transitive__Closure_Otrancl(X29434,X29431))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29434,X29434)),hAPP(hAPP(c_Product__Type_OPair(X29434,X29434),esk361_4(X29431,X29432,X29433,X29434)),X29432)),X29431))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29434,X29434)),hAPP(hAPP(c_Product__Type_OPair(X29434,X29434),X29433),X29432)),c_Transitive__Closure_Otrancl(X29434,X29431))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).

fof(i_0_5406,plain,
    ! [X27135,X27136,X27137,X27138,X27139,X27140] : hAPP(c_Product__Type_Oapfst(X27140,X27139,X27138,X27137),hAPP(hAPP(c_Product__Type_OPair(X27140,X27138),X27136),X27135)) = hAPP(hAPP(c_Product__Type_OPair(X27139,X27138),hAPP(X27137,X27136)),X27135),
    inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).

fof(i_0_5407,plain,
    ! [X26809,X26810,X26811,X26812,X26813,X26814] : hAPP(c_Product__Type_Oapsnd(X26814,X26813,X26812,X26811),hAPP(hAPP(c_Product__Type_OPair(X26812,X26814),X26810),X26809)) = hAPP(hAPP(c_Product__Type_OPair(X26812,X26813),X26810),hAPP(X26811,X26809)),
    inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).

fof(i_0_5408,plain,
    ! [X224,X20,X30,X5] :
      ( c_List_Olist__ex1(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224))
    <=> ( ( hBOOL(hAPP(X30,X20))
         => c_List_Olist__all(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30))),hAPP(c_fequal,X20)),X224) )
        & ( ~ hBOOL(hAPP(X30,X20))
         => c_List_Olist__ex1(X5,X30,X224) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(i_0_5409,plain,
    ! [X31882,X31883] : c_List_Ofoldr(tc_List_Olist(X31883),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31883)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31883))),c_List_Otranspose(X31883,X31882),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31883))),hAPP(c_List_Ofilter(tc_List_Olist(X31883),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31883)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31883),tc_List_Olist(X31883),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31883)))),X31882)),
    inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).

fof(i_0_5410,plain,
    ! [X32368,X32369,X32370,X32371] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32370)),c_List_OdropWhile(X32370,X32369,X32368))))
      | hAPP(hAPP(c_List_Onth(X32370),c_List_OdropWhile(X32370,X32369,X32368)),X32371) = hAPP(hAPP(c_List_Onth(X32370),X32368),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32370)),c_List_OtakeWhile(X32370,X32369,X32368)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])]) ).

fof(i_0_5411,plain,
    ! [X26245,X26246] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26246)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26245))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26246),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26245))),
    inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(i_0_5412,plain,
    ! [X26241,X26242] :
      ( ~ class_Rings_Olinordered__idom(X26242)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26242),hAPP(c_Groups_Oabs__class_Oabs(X26242),X26241)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X26242),X26241),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__abs])]) ).

fof(i_0_5413,plain,
    ! [X26232,X26233] :
      ( ~ class_Rings_Oring__1(X26233)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26233),hAPP(c_Groups_Ouminus__class_Ouminus(X26233),X26232)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X26233),X26232),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__minus])]) ).

fof(i_0_5414,plain,
    ! [X26243] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26243)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26243,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[fact_mod2__Suc__Suc]) ).

fof(i_0_5415,plain,
    ! [X30,X19,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X18),X19))
       => ( hBOOL(hAPP(X30,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X49,X42] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X42))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X49),X19))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X49),X42))
                   => ( hBOOL(hAPP(X30,X42))
                     => hBOOL(hAPP(X30,hAPP(hAPP(c_Set_Oinsert(X5),X49),X42))) ) ) ) )
           => hBOOL(hAPP(X30,X18)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).

fof(i_0_5416,plain,
    ! [X26217,X26218] :
      ( ~ class_Int_Onumber__ring(X26218)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26218),hAPP(c_Int_Onumber__class_Onumber__of(X26218),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26218),X26217),X26217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).

fof(i_0_5417,plain,
    ! [X2,X30,X224,X5,X17] :
      ( class_Groups_Omonoid__add(X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
           => ( ~ hBOOL(hAPP(X30,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X17) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),hAPP(c_List_Ofilter(X5,X30),X224))) = hAPP(c_List_Omonoid__add__class_Olistsum(X17),hAPP(hAPP(c_List_Omap(X5,X17),X2),X224)) ) ),
    inference(fof_simplification,[status(thm)],[fact_listsum__map__filter]) ).

fof(i_0_5418,plain,
    ! [X26234] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26234),X26234),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).

fof(i_0_5419,plain,
    ! [X26229] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26229) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26229)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(i_0_5420,plain,
    ! [X32330,X32331,X32332] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32332)),c_List_OdropWhile(X32332,X32331,X32330))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32332)),X32330))),
    inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).

fof(i_0_5421,plain,
    ! [X20,X19,X18,X1,X26,X2,X17,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X17,X2,X26,X1,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X17),X20),X19)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X18,X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_5422,plain,
    ! [X78,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Relation_ORange(X17,X5),X78)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X5)),hAPP(hAPP(c_Product__Type_OPair(X17,X5),X3),X21)),X78)) ),
    inference(fof_simplification,[status(thm)],[fact_RangeE]) ).

fof(i_0_5423,plain,
    ! [X28905,X28906,X28907,X28908,X28909] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28908),X28907)),c_Transitive__Closure_Otrancl(X28909,X28906)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28907),X28905)),c_Transitive__Closure_Otrancl(X28909,X28906)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28908),X28905)),c_Transitive__Closure_Otrancl(X28909,X28906))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).

fof(i_0_5424,plain,
    ! [X29166,X29167,X29168,X29169] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29169,X29169)),hAPP(hAPP(c_Product__Type_OPair(X29169,X29169),X29168),X29167)),hAPP(c_Relation_Oconverse(X29169,X29169),c_Transitive__Closure_Otrancl(X29169,X29166))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29169,X29169)),hAPP(hAPP(c_Product__Type_OPair(X29169,X29169),X29168),X29167)),c_Transitive__Closure_Otrancl(X29169,hAPP(c_Relation_Oconverse(X29169,X29169),X29166)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).

fof(i_0_5425,plain,
    ! [X29170,X29171,X29172,X29173] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29173,X29173)),hAPP(hAPP(c_Product__Type_OPair(X29173,X29173),X29172),X29171)),c_Transitive__Closure_Otrancl(X29173,hAPP(c_Relation_Oconverse(X29173,X29173),X29170))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29173,X29173)),hAPP(hAPP(c_Product__Type_OPair(X29173,X29173),X29172),X29171)),hAPP(c_Relation_Oconverse(X29173,X29173),c_Transitive__Closure_Otrancl(X29173,X29170)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).

fof(i_0_5426,plain,
    ! [X20,X19,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X19),X20))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(i_0_5427,plain,
    ! [X32324,X32325,X32326] :
      ( c_List_OdropWhile(X32326,X32325,X32324) = c_List_Olist_ONil(X32326)
      | ~ hBOOL(hAPP(X32325,hAPP(c_List_Ohd(X32326),c_List_OdropWhile(X32326,X32325,X32324)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5203])]) ).

fof(i_0_5428,plain,
    ! [X26270,X26271] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X26271),X26270),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X26271)
        | X26270 = c_Groups_Oone__class_Oone(X26271)
        | X26270 = hAPP(c_Groups_Ouminus__class_Ouminus(X26271),c_Groups_Oone__class_Oone(X26271))
        | ~ class_Rings_Oring__1__no__zero__divisors(X26271) )
      & ( X26270 != c_Groups_Oone__class_Oone(X26271)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26271),X26270),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X26271)
        | ~ class_Rings_Oring__1__no__zero__divisors(X26271) )
      & ( X26270 != hAPP(c_Groups_Ouminus__class_Ouminus(X26271),c_Groups_Oone__class_Oone(X26271))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26271),X26270),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X26271)
        | ~ class_Rings_Oring__1__no__zero__divisors(X26271) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).

fof(i_0_5429,plain,
    ! [X26222,X26223] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X26223),X26222),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X26223)
        | X26222 = c_Groups_Ozero__class_Ozero(X26223)
        | ~ class_Rings_Oring__1__no__zero__divisors(X26223) )
      & ( X26222 != c_Groups_Ozero__class_Ozero(X26223)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26223),X26222),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X26223)
        | ~ class_Rings_Oring__1__no__zero__divisors(X26223) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).

fof(i_0_5430,plain,
    ! [X31632,X31633,X31634,X31635] : hAPP(c_List_OremoveAll(X31635,X31634),hAPP(hAPP(c_List_Oappend(X31635),X31633),X31632)) = hAPP(hAPP(c_List_Oappend(X31635),hAPP(c_List_OremoveAll(X31635,X31634),X31633)),hAPP(c_List_OremoveAll(X31635,X31634),X31632)),
    inference(variable_rename,[status(thm)],[fact_removeAll__append]) ).

fof(i_0_5431,plain,
    ! [X31821,X31822] : c_List_OremoveAll(X31822,X31821) = c_List_Ofilter(X31822,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31822),c_fNot),hAPP(c_fequal,X31821))),
    inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(i_0_5432,plain,
    ! [X32217,X32218,X32219] : hAPP(c_List_Orotate(X32219,X32218),hAPP(c_List_Orev(X32219),X32217)) = hAPP(c_List_Orev(X32219),hAPP(c_List_Orotate(X32219,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32219)),X32217)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X32218,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32219)),X32217)))),X32217)),
    inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).

fof(i_0_5433,plain,
    ! [X30766,X30767] : c_List_Orotate(X30767,X30766) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X30767),tc_List_Olist(X30767)),X30766),c_List_Orotate1(X30767)),
    inference(variable_rename,[status(thm)],[fact_rotate__def]) ).

fof(i_0_5434,plain,
    ! [X29010,X29011,X29012,X29013,X29014] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29014,X29014)),hAPP(hAPP(c_Product__Type_OPair(X29014,X29014),X29013),X29012)),c_Transitive__Closure_Ortrancl(X29014,X29011)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29014,X29014)),hAPP(hAPP(c_Product__Type_OPair(X29014,X29014),X29012),X29010)),c_Transitive__Closure_Otrancl(X29014,X29011)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29014,X29014)),hAPP(hAPP(c_Product__Type_OPair(X29014,X29014),X29013),X29010)),c_Transitive__Closure_Otrancl(X29014,X29011))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).

fof(i_0_5435,plain,
    ! [X29015,X29016,X29017,X29018,X29019] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29019,X29019)),hAPP(hAPP(c_Product__Type_OPair(X29019,X29019),X29018),X29017)),c_Transitive__Closure_Otrancl(X29019,X29016)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29019,X29019)),hAPP(hAPP(c_Product__Type_OPair(X29019,X29019),X29017),X29015)),c_Transitive__Closure_Ortrancl(X29019,X29016)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29019,X29019)),hAPP(hAPP(c_Product__Type_OPair(X29019,X29019),X29018),X29015)),c_Transitive__Closure_Otrancl(X29019,X29016))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).

fof(i_0_5436,plain,
    ! [X28915,X28916,X28917,X28918,X28919] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28919,X28919)),hAPP(hAPP(c_Product__Type_OPair(X28919,X28919),X28918),X28917)),X28916))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28919,X28919)),hAPP(hAPP(c_Product__Type_OPair(X28919,X28919),X28917),X28915)),c_Transitive__Closure_Otrancl(X28919,X28916)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28919,X28919)),hAPP(hAPP(c_Product__Type_OPair(X28919,X28919),X28918),X28915)),c_Transitive__Closure_Otrancl(X28919,X28916))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).

fof(i_0_5437,plain,
    ! [X28910,X28911,X28912,X28913,X28914] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28914)),hAPP(hAPP(c_Product__Type_OPair(X28914,X28914),X28913),X28912)),c_Transitive__Closure_Otrancl(X28914,X28911)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28914)),hAPP(hAPP(c_Product__Type_OPair(X28914,X28914),X28912),X28910)),X28911))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28914)),hAPP(hAPP(c_Product__Type_OPair(X28914,X28914),X28913),X28910)),c_Transitive__Closure_Otrancl(X28914,X28911))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).

fof(i_0_5438,plain,
    ! [X5,X6,X30] :
      ( ( hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X30)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X30)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).

fof(i_0_5439,plain,
    ! [X31907,X31908,X31909,X31910,X31911,X31912,X31913] : c_List_Ofoldr(X31913,X31912,X31911,hAPP(hAPP(c_List_Omap(X31910,X31913),X31909),X31908),X31907) = c_List_Ofoldr(X31910,X31912,hAPP(c_Fun_Ocomp(X31913,tc_fun(X31912,X31912),X31910,X31911),X31909),X31908,X31907),
    inference(variable_rename,[status(thm)],[fact_foldr__map]) ).

fof(i_0_5440,plain,
    ! [X24,X2,X17,X19,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Set_Oimage(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24)),X19) = hAPP(hAPP(c_Set_Oinsert(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Set_Oimage(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24)),X19) = hAPP(c_Set_Oimage(X5,X17,X2),X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).

fof(i_0_5441,plain,
    ! [X28931,X28932,X28933] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28933,X28933),tc_HOL_Obool)),X28932),hAPP(hAPP(c_Product__Type_OSigma(X28933,X28933),X28931),hAPP(c_COMBK(tc_fun(X28933,tc_HOL_Obool),X28933),X28931))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28933,X28933),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28933,X28932)),hAPP(hAPP(c_Product__Type_OSigma(X28933,X28933),X28931),hAPP(c_COMBK(tc_fun(X28933,tc_HOL_Obool),X28933),X28931)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).

fof(i_0_5442,plain,
    ! [X26036,X26037,X26038] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26037)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26038),hAPP(c_Int_Onumber__class_Onumber__of(X26038),X26036)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26037))) = hAPP(hAPP(c_HOL_OLet(X26038,X26038),hAPP(hAPP(c_Power_Opower__class_Opower(X26038),hAPP(c_Int_Onumber__class_Onumber__of(X26038),X26036)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26037))),hAPP(hAPP(c_COMBS(X26038,X26038,X26038),hAPP(hAPP(c_COMBB(X26038,tc_fun(X26038,X26038),X26038),c_Groups_Otimes__class_Otimes(X26038)),hAPP(c_Groups_Otimes__class_Otimes(X26038),hAPP(c_Int_Onumber__class_Onumber__of(X26038),X26036)))),c_COMBI(X26038)))
        | ~ class_Int_Onumber__ring(X26038) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26037)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26038),hAPP(c_Int_Onumber__class_Onumber__of(X26038),X26036)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26037))) = c_Groups_Oone__class_Oone(X26038)
        | ~ class_Int_Onumber__ring(X26038) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5204])])]) ).

fof(i_0_5443,plain,
    ! [X21,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X21)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X21) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
            & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X21)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(i_0_5444,plain,
    ! [X31898,X31899,X31900,X31901,X31902,X31903] : c_List_Ofoldr(X31903,X31902,X31901,hAPP(hAPP(c_List_Oappend(X31903),X31900),X31899),X31898) = c_List_Ofoldr(X31903,X31902,X31901,X31900,c_List_Ofoldr(X31903,X31902,X31901,X31899,X31898)),
    inference(variable_rename,[status(thm)],[fact_foldr__append]) ).

fof(i_0_5445,plain,
    ! [X22,X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),X22)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).

fof(i_0_5446,plain,
    ! [X24,X78,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X24),X24)),c_List_Olexord(X5,X78))) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).

fof(i_0_5447,plain,
    ! [X26202,X26203] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X26203)),c_Int_OBit1(X26202)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X26203)),X26202)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(i_0_5448,plain,
    ! [X19,X6,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X19))
    <=> ( c_Fun_Oinj__on(X5,X17,X2,X19)
        & ~ hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X17,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).

fof(i_0_5449,plain,
    ! [X28031,X28032] : c_Product__Type_Oapfst(X28032,X28032,X28031,c_Fun_Oid(X28032)) = c_Fun_Oid(tc_prod(X28032,X28031)),
    inference(variable_rename,[status(thm)],[fact_apfst__id]) ).

fof(i_0_5450,plain,
    ! [X28029,X28030] : c_Product__Type_Oapsnd(X28030,X28030,X28029,c_Fun_Oid(X28030)) = c_Fun_Oid(tc_prod(X28029,X28030)),
    inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).

fof(i_0_5451,plain,
    ! [X29256,X29257] : c_Transitive__Closure_Otrancl(X29257,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29257,X29257),tc_HOL_Obool)),X29256),c_Relation_OId(X29257))) = c_Transitive__Closure_Ortrancl(X29257,X29256),
    inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).

fof(i_0_5452,plain,
    ! [X22,X20,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X22)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).

fof(i_0_5453,plain,
    ! [X26082,X26083] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X26083),X26082) != c_Groups_Oone__class_Oone(X26083)
        | c_Int_Oiszero(X26083,hAPP(c_Int_Onumber__class_Onumber__of(X26083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26082),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Int_Onumber__ring(X26083) )
      & ( ~ c_Int_Oiszero(X26083,hAPP(c_Int_Onumber__class_Onumber__of(X26083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26082),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X26083),X26082) = c_Groups_Oone__class_Oone(X26083)
        | ~ class_Int_Onumber__ring(X26083) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).

fof(i_0_5454,plain,
    ! [X26080,X26081] :
      ( ( c_Groups_Oone__class_Oone(X26081) != hAPP(c_Int_Onumber__class_Onumber__of(X26081),X26080)
        | c_Int_Oiszero(X26081,hAPP(c_Int_Onumber__class_Onumber__of(X26081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26080))))
        | ~ class_Int_Onumber__ring(X26081) )
      & ( ~ c_Int_Oiszero(X26081,hAPP(c_Int_Onumber__class_Onumber__of(X26081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26080))))
        | c_Groups_Oone__class_Oone(X26081) = hAPP(c_Int_Onumber__class_Onumber__of(X26081),X26080)
        | ~ class_Int_Onumber__ring(X26081) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).

fof(i_0_5455,plain,
    ! [X6,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X21) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X21) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X21)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(i_0_5456,plain,
    ! [X32382,X32383,X32384] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32384),esk446_3(X32382,X32383,X32384)),hAPP(c_List_Oset(X32384),c_List_OdropWhile(X32384,X32383,X32382))))
        | c_List_OtakeWhile(X32384,X32383,X32382) = hAPP(c_List_Ofilter(X32384,X32383),X32382) )
      & ( hBOOL(hAPP(X32383,esk446_3(X32382,X32383,X32384)))
        | c_List_OtakeWhile(X32384,X32383,X32382) = hAPP(c_List_Ofilter(X32384,X32383),X32382) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5205])])])]) ).

fof(i_0_5457,plain,
    ! [X29029,X29030,X29031,X29032,X29033] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29033,X29033)),hAPP(hAPP(c_Product__Type_OPair(X29033,X29033),X29032),X29031)),X29030))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29033,X29033)),hAPP(hAPP(c_Product__Type_OPair(X29033,X29033),X29031),X29029)),c_Transitive__Closure_Ortrancl(X29033,X29030)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29033,X29033)),hAPP(hAPP(c_Product__Type_OPair(X29033,X29033),X29032),X29029)),c_Transitive__Closure_Otrancl(X29033,X29030))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).

fof(i_0_5458,plain,
    ! [X29020,X29021,X29022,X29023,X29024] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29024,X29024)),hAPP(hAPP(c_Product__Type_OPair(X29024,X29024),X29023),X29022)),c_Transitive__Closure_Ortrancl(X29024,X29021)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29024,X29024)),hAPP(hAPP(c_Product__Type_OPair(X29024,X29024),X29022),X29020)),X29021))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29024,X29024)),hAPP(hAPP(c_Product__Type_OPair(X29024,X29024),X29023),X29020)),c_Transitive__Closure_Otrancl(X29024,X29021))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).

fof(i_0_5459,plain,
    ! [X26122,X26123,X26124] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26123)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26124),X26122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26123))) = hAPP(hAPP(c_HOL_OLet(X26124,X26124),hAPP(hAPP(c_Power_Opower__class_Opower(X26124),X26122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26123))),hAPP(hAPP(c_COMBS(X26124,X26124,X26124),hAPP(hAPP(c_COMBB(X26124,tc_fun(X26124,X26124),X26124),c_Groups_Otimes__class_Otimes(X26124)),hAPP(c_Groups_Otimes__class_Otimes(X26124),X26122))),c_COMBI(X26124)))
        | ~ class_Int_Onumber__ring(X26124) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26123)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X26124),X26122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26123))) = c_Groups_Oone__class_Oone(X26124)
        | ~ class_Int_Onumber__ring(X26124) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5206])])]) ).

fof(i_0_5460,plain,
    ! [X26267,X26268] :
      ( ~ class_Groups_Omonoid__mult(X26268)
      | ~ class_Int_Onumber(X26268)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26268),hAPP(c_Int_Onumber__class_Onumber__of(X26268),X26267)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26268),hAPP(c_Int_Onumber__class_Onumber__of(X26268),X26267)),hAPP(c_Int_Onumber__class_Onumber__of(X26268),X26267)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).

fof(i_0_5461,plain,
    ! [X28920,X28921,X28922,X28923,X28924] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28924,X28924)),hAPP(hAPP(c_Product__Type_OPair(X28924,X28924),X28923),X28922)),X28921))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28924,X28924)),hAPP(hAPP(c_Product__Type_OPair(X28924,X28924),X28922),X28920)),X28921))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28924,X28924)),hAPP(hAPP(c_Product__Type_OPair(X28924,X28924),X28923),X28920)),c_Transitive__Closure_Otrancl(X28924,X28921))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).

fof(i_0_5462,plain,
    ! [X78,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X17),X78)))
     => ~ ! [X38] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X38)),X78)) ),
    inference(fof_simplification,[status(thm)],[fact_DomainE]) ).

fof(i_0_5463,plain,
    ! [X26247] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26247),X26247)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X26247,
    inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).

fof(i_0_5464,plain,
    ! [X26219,X26220] :
      ( ~ class_Int_Onumber__ring(X26220)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26220),X26219),hAPP(c_Int_Onumber__class_Onumber__of(X26220),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26220),X26219),X26219) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

fof(i_0_5465,plain,
    ! [X26227,X26228] :
      ( ~ class_Groups_Omonoid__mult(X26228)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26228),X26227),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26228),X26227),X26227) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).

fof(i_0_5466,plain,
    ! [X26225,X26226] :
      ( ~ class_Rings_Ocomm__semiring__1(X26226)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26226),X26225),X26225) = hAPP(hAPP(c_Power_Opower__class_Opower(X26226),X26225),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])]) ).

fof(i_0_5467,plain,
    ! [X6,X23,X21,X22,X19,X25,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_fun(X25,tc_HOL_Obool))),X19),X22),X21),X23))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X22,X6),X21),X23))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).

fof(i_0_5468,plain,
    ! [X26235] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26235),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26235),X26235),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).

fof(i_0_5469,plain,
    ! [X26230] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26230),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X26230)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(i_0_5470,plain,
    ! [X26224] :
      ( ~ class_Rings_Osemiring__1(X26224)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26224),c_Groups_Ozero__class_Ozero(X26224)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X26224) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).

fof(i_0_5471,plain,
    ! [X26231] :
      ( ~ class_Rings_Osemiring__1(X26231)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26231),c_Groups_Oone__class_Oone(X26231)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X26231) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

fof(i_0_5472,plain,
    ! [X75,X2,X17,X224,X24,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_List_Oset(X5),X224)))
     => hAPP(hAPP(c_List_Omap(X5,X17),c_Fun_Ofun__upd(X5,X17,X2,X24,X75)),X224) = hAPP(hAPP(c_List_Omap(X5,X17),X2),X224) ),
    inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).

fof(i_0_5473,plain,
    ! [X26039,X26040] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26040)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26039),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26040))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26039),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26040))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26039))),c_COMBI(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26040)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26039),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26040))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5207])]) ).

fof(i_0_5474,plain,
    ! [X28925,X28926,X28927,X28928] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28928,X28928)),X28927),c_Transitive__Closure_Otrancl(X28928,X28926)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28928,X28928),tc_HOL_Obool)),X28926),X28925))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28928,X28928)),X28927),c_Transitive__Closure_Otrancl(X28928,X28925))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).

fof(i_0_5475,plain,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X55),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X57),X57))),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(i_0_5476,plain,
    ! [X28890,X28891] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28891,X28891),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28891,X28890)),hAPP(hAPP(c_Product__Type_OSigma(X28891,X28891),hAPP(c_Relation_OField(X28891),X28890)),hAPP(c_COMBK(tc_fun(X28891,tc_HOL_Obool),X28891),hAPP(c_Relation_OField(X28891),X28890))))),
    inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(i_0_5477,plain,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => ( ~ hBOOL(hAPP(hAPP(X19,X20),X24))
       => hBOOL(hAPP(hAPP(X22,X20),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup2E]) ).

fof(i_0_5478,plain,
    ! [X29034,X29035,X29036,X29037] :
      ( ( X29036 != X29035
        | X29036 = X29035
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Ortrancl(X29037,X29034))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Otrancl(X29037,X29034)))
        | X29036 = X29035
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Ortrancl(X29037,X29034))) )
      & ( X29036 != X29035
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Ortrancl(X29037,X29034))) )
      & ( X29036 = X29035
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Otrancl(X29037,X29034)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29037,X29037)),hAPP(hAPP(c_Product__Type_OPair(X29037,X29037),X29036),X29035)),c_Transitive__Closure_Ortrancl(X29037,X29034))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).

fof(i_0_5479,plain,
    ! [X28949,X28950,X28951,X28952] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28952,X28952)),hAPP(hAPP(c_Product__Type_OPair(X28952,X28952),X28951),X28950)),c_Transitive__Closure_Otrancl(X28952,X28949)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28952,X28952)),hAPP(hAPP(c_Product__Type_OPair(X28952,X28952),X28951),X28950)),c_Transitive__Closure_Ortrancl(X28952,X28949))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).

fof(i_0_5480,plain,
    ! [X24,X20,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24))
     => ~ ( hBOOL(hAPP(hAPP(X19,X20),X24))
         => ~ hBOOL(hAPP(hAPP(X22,X20),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf2E]) ).

fof(i_0_5481,plain,
    ! [X26051,X26052] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26052)),c_Int_OBit1(X26051)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26052),X26051)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26052),X26051))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26052)),c_Int_OBit1(X26051))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_5482,plain,
    ! [X26049,X26050] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26050)),c_Int_OBit1(X26049)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26050),X26049)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26050),X26049))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26050)),c_Int_OBit1(X26049))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_5483,plain,
    ! [X26045,X26046] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26046)),c_Int_OBit1(X26045)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26046),X26045)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26046),X26045))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26046)),c_Int_OBit1(X26045))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_5484,plain,
    ! [X26043,X26044] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26044)),c_Int_OBit1(X26043)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26044),X26043)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26044),X26043))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26044)),c_Int_OBit1(X26043))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_5485,plain,
    ! [X31610,X31611,X31612] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31612),X31611))
      | hBOOL(hAPP(c_List_Odistinct(X31612),hAPP(c_List_OremoveAll(X31612,X31610),X31611))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__removeAll])]) ).

fof(i_0_5486,plain,
    ! [X31599,X31600,X31601,X31602,X31603] :
      ( ~ c_Fun_Oinj__on(X31603,X31602,X31601,hAPP(hAPP(c_Set_Oinsert(X31603),X31600),hAPP(c_List_Oset(X31603),X31599)))
      | hAPP(hAPP(c_List_Omap(X31603,X31602),X31601),hAPP(c_List_OremoveAll(X31603,X31600),X31599)) = hAPP(c_List_OremoveAll(X31602,hAPP(X31601,X31600)),hAPP(hAPP(c_List_Omap(X31603,X31602),X31601),X31599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])]) ).

fof(i_0_5487,plain,
    ! [X29074,X29075,X29076] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29076,X29076),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X29076,X29076),X29075)),c_Transitive__Closure_Ortrancl(X29076,X29075)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29076,X29076),tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29076,X29076)),hAPP(hAPP(c_Product__Type_OPair(X29076,X29076),X29074),X29074)),c_Transitive__Closure_Otrancl(X29076,X29075))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5208])]) ).

fof(i_0_5488,plain,
    ! [X32355,X32356,X32357,X32358,X32359] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32359),X32358),hAPP(c_List_Oset(X32359),X32357)))
      | hBOOL(hAPP(X32356,X32358))
      | c_List_OdropWhile(X32359,X32356,hAPP(hAPP(c_List_Oappend(X32359),X32357),X32355)) = hAPP(hAPP(c_List_Oappend(X32359),c_List_OdropWhile(X32359,X32356,X32357)),X32355) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5209])]) ).

fof(i_0_5489,plain,
    ! [X32500,X32501,X32502,X32503] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32503),esk458_4(X32500,X32501,X32502,X32503)),hAPP(c_List_Oset(X32503),X32502)))
        | c_List_OdropWhile(X32503,X32501,hAPP(hAPP(c_List_Oappend(X32503),X32502),X32500)) = c_List_OdropWhile(X32503,X32501,X32500) )
      & ( ~ hBOOL(hAPP(X32501,esk458_4(X32500,X32501,X32502,X32503)))
        | c_List_OdropWhile(X32503,X32501,hAPP(hAPP(c_List_Oappend(X32503),X32502),X32500)) = c_List_OdropWhile(X32503,X32501,X32500) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__append2])])])]) ).

fof(i_0_5490,plain,
    ! [X31654,X31655,X31656,X31657,X31658] :
      ( ~ c_Fun_Oinj__on(X31658,X31657,X31656,c_Orderings_Otop__class_Otop(tc_fun(X31658,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(X31658,X31657),X31656),hAPP(c_List_OremoveAll(X31658,X31655),X31654)) = hAPP(c_List_OremoveAll(X31657,hAPP(X31656,X31655)),hAPP(hAPP(c_List_Omap(X31658,X31657),X31656),X31654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj])]) ).

fof(i_0_5491,plain,
    ! [X224,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
     => ~ hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X30,X224))))) ),
    inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(i_0_5492,plain,
    ! [X31919,X31920] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31920))),c_List_Otranspose(X31920,X31919)) = c_List_Ofoldr(tc_List_Olist(X31920),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31920)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31920))),X31919,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__transpose]) ).

fof(i_0_5493,plain,
    ! [X29361,X29362,X29363,X29365,X29366,X29367,X29368] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk346_3(X29361,X29362,X29363)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29363,X29363)),X29362),c_Transitive__Closure_Otrancl(X29363,X29361))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29363,X29363)),X29362),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29363,X29363),tc_HOL_Obool),esk346_3(X29361,X29362,X29363)),X29361)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29363,X29363)),X29362),c_Transitive__Closure_Otrancl(X29363,X29361))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29368))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29367,X29367)),X29366),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29367,X29367),tc_HOL_Obool),X29368),X29365)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29367,X29367)),X29366),c_Transitive__Closure_Otrancl(X29367,X29365))) ) ),
    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_trancl__power])])])])])]) ).

fof(i_0_5494,plain,
    ! [X31715,X31716,X31717] : c_List_Oconcat(X31717,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X31717)),X31716),X31715)) = hAPP(hAPP(c_List_Oappend(X31717),c_List_Oconcat(X31717,X31716)),c_List_Oconcat(X31717,X31715)),
    inference(variable_rename,[status(thm)],[fact_concat__append]) ).

fof(i_0_5495,plain,
    ! [X96,X6,X224,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X224))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X224)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X224),X96)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X224),X96),X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).

fof(i_0_5496,plain,
    ! [X19,X2,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X17,X5,X2),X19))),hAPP(c_Finite__Set_Ocard(X17),X19)))
     => ~ c_Fun_Oinj__on(X17,X5,X2,X19) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_5497,plain,
    ! [X29025,X29026,X29027,X29028] :
      ( ( X29027 != X29026
        | X29027 = X29026
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29028,X29028)),hAPP(hAPP(c_Product__Type_OPair(X29028,X29028),X29027),X29026)),c_Transitive__Closure_Ortrancl(X29028,X29025))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29028,X29028)),hAPP(hAPP(c_Product__Type_OPair(X29028,X29028),X29027),X29026)),c_Transitive__Closure_Otrancl(X29028,X29025)))
        | X29027 = X29026
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29028,X29028)),hAPP(hAPP(c_Product__Type_OPair(X29028,X29028),X29027),X29026)),c_Transitive__Closure_Ortrancl(X29028,X29025))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).

fof(i_0_5498,plain,
    ! [X30,X224,X5,X89] :
      ( ! [X88] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X89))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
           => hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X88))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)))
         => ~ hBOOL(hAPP(X30,hAPP(hAPP(c_List_Onth(X5),X224),X89))) )
       => c_List_OtakeWhile(X5,X30,X224) = hAPP(hAPP(c_List_Otake(X5),X89),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(i_0_5499,plain,
    ! [X28886,X28887,X28888,X28889] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28889,X28889)),hAPP(hAPP(c_Product__Type_OPair(X28889,X28889),X28888),X28887)),X28886))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28889,X28889)),hAPP(hAPP(c_Product__Type_OPair(X28889,X28889),X28888),X28887)),c_Transitive__Closure_Otrancl(X28889,X28886))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).

fof(i_0_5500,plain,
    ! [X84,X23,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(i_0_5501,plain,
    ! [X84,X23,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(i_0_5502,plain,
    ! [X23,X21,X84,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(i_0_5503,plain,
    ! [X23,X21,X84,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(i_0_5504,plain,
    ! [X20,X24,X19,X2,X17,X5] :
      ( c_Fun_Oinj__on(X5,X17,X2,X19)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_Set_Oimage(X5,X17,X2),X19)))
       => c_Fun_Oinj__on(X5,X17,c_Fun_Ofun__upd(X5,X17,X2,X20,X24),X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(i_0_5505,plain,
    ! [X32440,X32441] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk453_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk452_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk454_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk452_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( esk453_2(X32440,X32441) != esk454_2(X32440,X32441)
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk452_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32441,tc_HOL_Obool)),hAPP(c_List_Oset(X32441),esk453_2(X32440,X32441))),hAPP(c_List_Oset(X32441),esk454_2(X32440,X32441))) != c_Orderings_Obot__class_Obot(tc_fun(X32441,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk452_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk453_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32441),esk452_2(X32440,X32441)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32441)),esk454_2(X32440,X32441)),hAPP(c_List_Oset(tc_List_Olist(X32441)),X32440)))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32441),esk452_2(X32440,X32441)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( esk453_2(X32440,X32441) != esk454_2(X32440,X32441)
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32441),esk452_2(X32440,X32441)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32441,tc_HOL_Obool)),hAPP(c_List_Oset(X32441),esk453_2(X32440,X32441))),hAPP(c_List_Oset(X32441),esk454_2(X32440,X32441))) != c_Orderings_Obot__class_Obot(tc_fun(X32441,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X32441),c_List_Oconcat(X32441,X32440)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32441),esk452_2(X32440,X32441)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32441)),X32440)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__concat])])])]) ).

fof(i_0_5506,plain,
    ! [X5,X6,X30] :
      ( ( hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X30)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X30,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X30)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).

fof(i_0_5507,plain,
    ! [X30800,X30801,X30802] : hAPP(c_List_Orotate(X30802,X30801),X30800) = hAPP(hAPP(c_List_Oappend(X30802),hAPP(hAPP(c_List_Odrop(X30802),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30801,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30802)),X30800))),X30800)),hAPP(hAPP(c_List_Otake(X30802),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30801,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30802)),X30800))),X30800)),
    inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).

fof(i_0_5508,plain,
    ! [X28880,X28881,X28882,X28883,X28884] :
      ( ( ~ c_Wellfounded_Oacyclic(X28881,X28880)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28881,X28881)),hAPP(hAPP(c_Product__Type_OPair(X28881,X28881),X28882),X28882)),c_Transitive__Closure_Otrancl(X28881,X28880))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28884,X28884)),hAPP(hAPP(c_Product__Type_OPair(X28884,X28884),esk340_2(X28883,X28884)),esk340_2(X28883,X28884))),c_Transitive__Closure_Otrancl(X28884,X28883)))
        | c_Wellfounded_Oacyclic(X28884,X28883) ) ),
    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_5210])])])])]) ).

fof(i_0_5509,plain,
    ! [X223,X224,X24,X20,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X20),X24)),hAPP(c_List_Oset(tc_prod(X5,X17)),hAPP(hAPP(c_List_Ozip(X5,X17),X224),X223))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
         => ~ hBOOL(hAPP(hAPP(c_member(X17),X24),hAPP(c_List_Oset(X17),X223))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).

fof(i_0_5510,plain,
    ! [X31628,X31629,X31630,X31631] :
      ( ( X31631 != X31630
        | hAPP(c_List_OremoveAll(X31629,X31631),hAPP(hAPP(c_List_Olist_OCons(X31629),X31630),X31628)) = hAPP(c_List_OremoveAll(X31629,X31631),X31628) )
      & ( X31631 = X31630
        | hAPP(c_List_OremoveAll(X31629,X31631),hAPP(hAPP(c_List_Olist_OCons(X31629),X31630),X31628)) = hAPP(hAPP(c_List_Olist_OCons(X31629),X31630),hAPP(c_List_OremoveAll(X31629,X31631),X31628)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J])]) ).

fof(i_0_5511,plain,
    ! [X78,X20,X24,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),X78))
    <=> ( c_Wellfounded_Oacyclic(X5,X78)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).

fof(i_0_5512,plain,
    ! [X78,X20,X24,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X20)),X78))
    <=> ( c_Wellfounded_Owf(X5,X78)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X78))) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).

fof(i_0_5513,plain,
    ! [X28929,X28930] : c_Transitive__Closure_Otrancl(X28930,X28929) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28930,X28930),tc_HOL_Obool)),X28929),hAPP(hAPP(c_Relation_Orel__comp(X28930,X28930,X28930),c_Transitive__Closure_Otrancl(X28930,X28929)),X28929)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).

fof(i_0_5514,plain,
    ! [X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
    <=> ! [X218] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X218))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X218))
              & ! [X38] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X3)),X78))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X38),X218)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).

fof(i_0_5515,plain,
    ! [X26169,X26170] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26170)),c_Int_OBit0(X26169)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26170),X26169)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26170),X26169))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26170)),c_Int_OBit0(X26169))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_5516,plain,
    ! [X26167,X26168] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26168)),c_Int_OBit0(X26167)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26168),X26167)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26168),X26167))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26168)),c_Int_OBit0(X26167))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_5517,plain,
    ! [X26194,X26195] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26195)),c_Int_OBit0(X26194)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26195),X26194)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26195),X26194))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26195)),c_Int_OBit0(X26194))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_5518,plain,
    ! [X26192,X26193] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26193)),c_Int_OBit0(X26192)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26193),X26192)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26193),X26192))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26193)),c_Int_OBit0(X26192))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_5519,plain,
    ! [X25198,X25199] : c_Nitpick_Oint__lcm(X25199,X25198) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25199)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25198)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(i_0_5520,plain,
    ! [X25216,X25217] : c_Nitpick_Onat__lcm(X25217,X25216) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25217),X25216)),c_Nitpick_Onat__gcd(X25217,X25216)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(i_0_5521,plain,
    ! [X31892,X31893,X31894,X31895,X31896,X31897] : c_List_Ofoldr(X31897,X31896,X31895,hAPP(hAPP(c_List_Olist_OCons(X31897),X31894),X31893),X31892) = hAPP(hAPP(X31895,X31894),c_List_Ofoldr(X31897,X31896,X31895,X31893,X31892)),
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(i_0_5522,plain,
    ! [X20,X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X20)),X78))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X6)),X78)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).

fof(i_0_5523,plain,
    ! [X20,X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X20)),X78))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X6)),X78)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).

fof(i_0_5524,plain,
    ! [X191,X89,X51] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X51,X89),X191))
    <=> ( X51 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X191)),X89)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191))
        & ( X89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X191) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X89 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)),X89)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X89))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X191)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(i_0_5525,plain,
    ! [X6,X84,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(i_0_5526,plain,
    ! [X6,X84,X21,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(i_0_5527,plain,
    ! [X26065] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X26065)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26065))),
    inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).

fof(i_0_5528,plain,
    ! [X30,X34,X187] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X34)))
     => ( ! [X121,X88] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X121),X88)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X88))
               => hBOOL(hAPP(hAPP(X30,X121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X88),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X30,X121),X88)) ) )
       => hBOOL(hAPP(hAPP(X30,X187),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct]) ).

fof(i_0_5529,plain,
    ! [X28844,X28845] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X28845),X28844)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28845),X28844)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28845),X28844))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X28845),X28844)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq])]) ).

fof(i_0_5530,plain,
    ! [X78,X19,X40,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X40),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X19),X78)))
     => ~ ! [X3] :
            ( X40 = hAPP(c_Relation_OImage(X5,X5,X78),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_quotientE]) ).

fof(i_0_5531,plain,
    ! [X26825,X26826] :
      ( ( X26826 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Divides_Odivmod__nat(X26825,X26826) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26825),X26826))
        | c_Divides_Odivmod__nat(X26825,X26826) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26825) )
      & ( X26826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26825),X26826))
        | c_Divides_Odivmod__nat(X26825,X26826) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26825),X26826),X26826)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).

fof(i_0_5532,plain,
    ! [X26861,X26862] : c_Divides_Odivmod__nat(X26862,X26861) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X26862,X26861)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).

fof(i_0_5533,plain,
    ! [X26060] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26060)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26060),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26060),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26060)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J])]) ).

fof(i_0_5534,plain,
    ! [X248,X249,X250,X251,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X251),X250) = hAPP(hAPP(c_List_Oappend(X5),X249),X248)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)))
         => ( X251 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),X249)
            & X250 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),X249)),X248) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)),X251) = X249
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X249)),X251)),X250) = X248 ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(i_0_5535,plain,
    ! [X26340] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26340)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26340),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26340),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26340)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).

fof(i_0_5536,plain,
    ! [X26062] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26062)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26062),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26062),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X26062)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_5537,plain,
    ! [X26075] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26075)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26075),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26075),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26075)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_5538,plain,
    ! [X26338] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26338)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26338),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26338),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X26338)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).

fof(i_0_5539,plain,
    ! [X26064] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26064))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26064))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26064)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26064)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).

fof(i_0_5540,plain,
    ! [X31662,X31663] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31663)),c_List_Oremdups(X31663,c_List_Oconcat(X31663,X31662))) = hAPP(c_Finite__Set_Ocard(X31663),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31663),tc_fun(X31663,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31663)),X31662)),c_List_Oset(X31663))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__concat]) ).

fof(i_0_5541,plain,
    ! [X26094,X26095] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26095),c_Groups_Oone__class_Oone(X26095)),hAPP(c_Int_Onumber__class_Onumber__of(X26095),X26094)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X26094))
        | ~ class_Int_Onumber__ring(X26095)
        | ~ class_Rings_Olinordered__idom(X26095) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X26094))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26095),c_Groups_Oone__class_Oone(X26095)),hAPP(c_Int_Onumber__class_Onumber__of(X26095),X26094)))
        | ~ class_Int_Onumber__ring(X26095)
        | ~ class_Rings_Olinordered__idom(X26095) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_5542,plain,
    ! [X26088,X26089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26089),c_Groups_Oone__class_Oone(X26089)),hAPP(c_Int_Onumber__class_Onumber__of(X26089),X26088)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X26088))
        | ~ class_Int_Onumber__ring(X26089)
        | ~ class_Rings_Olinordered__idom(X26089) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X26088))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26089),c_Groups_Oone__class_Oone(X26089)),hAPP(c_Int_Onumber__class_Onumber__of(X26089),X26088)))
        | ~ class_Int_Onumber__ring(X26089)
        | ~ class_Rings_Olinordered__idom(X26089) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_5543,plain,
    ! [X84,X21,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(i_0_5544,plain,
    ! [X84,X21,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84))),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(i_0_5545,plain,
    ! [X17,X5,X19,X24,X20,X22] :
      ( ( ~ hBOOL(hAPP(hAPP(X22,X20),X24))
       => hBOOL(hAPP(hAPP(X19,X20),X24)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X19),X22),X20),X24)) ),
    inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).

fof(i_0_5546,plain,
    ! [X37,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),c_Wellfounded_Oacc(X5,X37)))
     => ~ ! [X150] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X150),X20)),X37))
           => hBOOL(hAPP(hAPP(c_member(X5),X150),c_Wellfounded_Oacc(X5,X37))) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).

fof(i_0_5547,plain,
    ! [X21,X19,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X21,X19) = X21 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X21,X19) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).

fof(i_0_5548,plain,
    ! [X26307,X26308] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26308)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26307))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26308))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26308)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26308)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26307))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26308))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26307)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26308)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5211])]) ).

fof(i_0_5549,plain,
    ! [X29396,X29397] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29397,X29397)),hAPP(hAPP(c_Product__Type_OPair(X29397,X29397),esk353_2(X29396,X29397)),esk353_2(X29396,X29397))),c_Transitive__Closure_Otrancl(X29397,X29396)))
      | c_Wellfounded_Oacyclic(X29397,X29396) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5212])])]) ).

fof(i_0_5550,plain,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X224)),c_List_Olistrel1(X5,X78))),
    inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(i_0_5551,plain,
    ! [X78,X223,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X223)),c_List_Olex(X5,X78))),
    inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).

fof(i_0_5552,plain,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X78))),
    inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(i_0_5553,plain,
    ! [X78,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X20),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X78))),
    inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).

fof(i_0_5554,plain,
    ! [X78,X224,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X224),c_List_Olist_ONil(X5))),c_List_Olex(X5,X78))),
    inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(i_0_5555,plain,
    ! [X31916,X31917,X31918] :
      ( ~ class_Groups_Omonoid__add(X31918)
      | hAPP(c_List_Ofoldl(X31918,X31918,c_Groups_Oplus__class_Oplus(X31918),X31917),X31916) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31918),X31917),c_List_Ofoldr(X31918,X31918,c_Groups_Oplus__class_Oplus(X31918),X31916,c_Groups_Ozero__class_Ozero(X31918))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).

fof(i_0_5556,plain,
    ! [X29223,X29224,X29225] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29225,X29225)),hAPP(hAPP(c_Product__Type_OPair(X29225,X29225),X29224),X29223)),c_Relation_OId(X29225)))
        | X29224 = X29223 )
      & ( X29224 != X29223
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29225,X29225)),hAPP(hAPP(c_Product__Type_OPair(X29225,X29225),X29224),X29223)),c_Relation_OId(X29225))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).

fof(i_0_5557,plain,
    ! [X30,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
     => ( hBOOL(hAPP(X30,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X42] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X42))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X42))
               => ( hBOOL(hAPP(X30,X42))
                 => hBOOL(hAPP(X30,hAPP(hAPP(c_Set_Oinsert(X5),X3),X42))) ) ) )
         => hBOOL(hAPP(X30,X18)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__induct]) ).

fof(i_0_5558,plain,
    ! [X26221] :
      ( ~ class_Int_Onumber__ring(X26221)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26221),c_Groups_Oone__class_Oone(X26221)),c_Groups_Oone__class_Oone(X26221)) = hAPP(c_Int_Onumber__class_Onumber__of(X26221),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])]) ).

fof(i_0_5559,plain,
    ! [X31659,X31660,X31661] : hAPP(c_List_Oset(X31661),hAPP(c_List_OremoveAll(X31661,X31660),X31659)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31661,tc_HOL_Obool)),hAPP(c_List_Oset(X31661),X31659)),hAPP(hAPP(c_Set_Oinsert(X31661),X31660),c_Orderings_Obot__class_Obot(tc_fun(X31661,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_set__removeAll]) ).

fof(i_0_5560,plain,
    ! [X1,X2,X17,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X1,X6) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X2,X6) ) ),
    inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).

fof(i_0_5561,plain,
    ! [X26805,X26806] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26806),X26805))
      | c_Divides_Odivmod__nat(X26805,X26806) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26805),X26806)),X26806))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26805),X26806),X26806)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).

fof(i_0_5562,plain,
    ! [X32191,X32192,X32193,X32194,X32195] : hAPP(c_List_Ofoldl(X32195,X32194,X32193,X32192),X32191) = c_List_Ofoldr(X32194,X32195,hAPP(c_COMBC(X32195,X32194,X32195),X32193),hAPP(c_List_Orev(X32194),X32191),X32192),
    inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).

fof(i_0_5563,plain,
    ! [X1,X2,X17,X19,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(c_Fun_Ooverride__on(X5,X17,X2,X1,X19),X6) = hAPP(X2,X6) ),
    inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).

fof(i_0_5564,plain,
    ! [X32347,X32348,X32349] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32349),X32348))
      | hBOOL(hAPP(c_List_Odistinct(X32349),c_List_OdropWhile(X32349,X32347,X32348))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).

fof(i_0_5565,plain,
    ! [X1,X19,X18,X26,X2,X17,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X17,X2,X26,X18)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
         => hAPP(hAPP(X18,X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X17,X2),X1),X26),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
         => hAPP(hAPP(X18,X1),X19) = X26 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(i_0_5566,plain,
    ! [X26970,X26971,X26972,X26973] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26973,X26973)),hAPP(hAPP(c_Product__Type_OPair(X26973,X26973),X26972),X26971)),hAPP(c_Wellfounded_Omeasure(X26973),X26970)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X26970,X26972)),hAPP(X26970,X26971))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X26970,X26972)),hAPP(X26970,X26971)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26973,X26973)),hAPP(hAPP(c_Product__Type_OPair(X26973,X26973),X26972),X26971)),hAPP(c_Wellfounded_Omeasure(X26973),X26970))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_5567,plain,
    ! [X27207] : c_Wellfounded_Omeasure(X27207) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X27207),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[fact_measure__def]) ).

fof(i_0_5568,plain,
    ! [X22,X19,X21,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X17),X6),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X17),X19),X22)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => ~ hBOOL(hAPP(hAPP(c_member(X17),X21),hAPP(X22,X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).

fof(i_0_5569,plain,
    ! [X31702,X31703,X31704,X31705] : hAPP(hAPP(c_List_Omap(X31705,X31704),X31703),c_List_Oconcat(X31705,X31702)) = c_List_Oconcat(X31704,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31705),tc_List_Olist(X31704)),hAPP(c_List_Omap(X31705,X31704),X31703)),X31702)),
    inference(variable_rename,[status(thm)],[fact_map__concat]) ).

fof(i_0_5570,plain,
    ! [X26173,X26174] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X26174)),c_Int_OBit0(X26173)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26174),X26173)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_5571,plain,
    ! [X26178,X26179] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X26179)),c_Int_OBit0(X26178)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26179),X26178)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(i_0_5572,plain,
    ! [X224,X17,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),hAPP(c_Set_Oimage(X17,X5,X2),hAPP(c_List_Oset(X17),X224))))
       => c_List_Olinorder__class_Oinsort__insert__key(X17,X5,X2,X20,X224) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(i_0_5573,plain,
    ! [X29278,X29279,X29280] :
      ( ( ~ c_Relation_Ototal__on(X29280,X29279,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29280,X29280),tc_HOL_Obool)),X29278),c_Relation_OId(X29280)))
        | c_Relation_Ototal__on(X29280,X29279,X29278) )
      & ( ~ c_Relation_Ototal__on(X29280,X29279,X29278)
        | c_Relation_Ototal__on(X29280,X29279,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29280,X29280),tc_HOL_Obool)),X29278),c_Relation_OId(X29280))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).

fof(i_0_5574,plain,
    ! [X26100,X26101] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X26101))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26100)),X26101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26101),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred])]) ).

fof(i_0_5575,plain,
    ! [X26200,X26201] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X26201)),X26200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26201),X26200))),X26200),
    inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).

fof(i_0_5576,plain,
    ! [X26213] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26213))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26213))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X26213))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26213))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).

fof(i_0_5577,plain,
    ! [X26204,X26205] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X26205)),c_Int_OBit1(X26204)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26205),c_Int_Osucc(X26204))),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(i_0_5578,plain,
    ! [X26198,X26199] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26199)),c_Int_OBit1(X26198)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26199),X26198)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26199),X26198))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26199)),c_Int_OBit1(X26198))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_5579,plain,
    ! [X26196,X26197] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26197)),c_Int_OBit1(X26196)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26197),X26196)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26197),X26196))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26197)),c_Int_OBit1(X26196))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_5580,plain,
    ! [X26163,X26164] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26164)),c_Int_OBit1(X26163)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26164),X26163)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26164),X26163))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26164)),c_Int_OBit1(X26163))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_5581,plain,
    ! [X26161,X26162] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26162)),c_Int_OBit1(X26161)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26162),X26161)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26162),X26161))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26162)),c_Int_OBit1(X26161))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_5582,plain,
    ! [X33369,X33370] :
      ( ( ~ c_Relation_Oantisym(X33370,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33370,X33370),tc_HOL_Obool)),X33369),c_Relation_OId(X33370)))
        | c_Relation_Oantisym(X33370,X33369) )
      & ( ~ c_Relation_Oantisym(X33370,X33369)
        | c_Relation_Oantisym(X33370,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33370,X33370),tc_HOL_Obool)),X33369),c_Relation_OId(X33370))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__reflcl])]) ).

fof(i_0_5583,plain,
    ! [X32341,X32342,X32343,X32344] :
      ( ( ~ hBOOL(hAPP(X32344,X32343))
        | c_List_OdropWhile(X32342,X32344,hAPP(hAPP(c_List_Olist_OCons(X32342),X32343),X32341)) = c_List_OdropWhile(X32342,X32344,X32341) )
      & ( hBOOL(hAPP(X32344,X32343))
        | c_List_OdropWhile(X32342,X32344,hAPP(hAPP(c_List_Olist_OCons(X32342),X32343),X32341)) = hAPP(hAPP(c_List_Olist_OCons(X32342),X32343),X32341) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5213])]) ).

fof(i_0_5584,plain,
    ! [X26121] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26121)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26121)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26121)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X26121)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26121)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5214])]) ).

fof(i_0_5585,plain,
    ! [X28903,X28904] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28904,X28904)),c_Transitive__Closure_Otrancl(X28904,X28903)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28904,X28904)),X28903)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28904,X28904)),X28903))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28904,X28904)),c_Transitive__Closure_Otrancl(X28904,X28903))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).

fof(i_0_5586,plain,
    ! [X22,X6,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X22))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).

fof(i_0_5587,plain,
    ! [X32149,X32150] : hAPP(c_List_Orev(X32150),c_List_Oconcat(X32150,X32149)) = c_List_Oconcat(X32150,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32150),tc_List_Olist(X32150)),c_List_Orev(X32150)),hAPP(c_List_Orev(tc_List_Olist(X32150)),X32149))),
    inference(variable_rename,[status(thm)],[fact_rev__concat]) ).

fof(i_0_5588,plain,
    ! [X26,X1,X6,X19,X5,X17] :
      ( class_Groups_Oab__semigroup__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),X26),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),X26),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).

fof(i_0_5589,plain,
    ! [X31741,X31742,X31743] : hAPP(c_List_Ofilter(X31743,X31742),c_List_Oconcat(X31743,X31741)) = c_List_Oconcat(X31743,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31743),tc_List_Olist(X31743)),c_List_Ofilter(X31743,X31742)),X31741)),
    inference(variable_rename,[status(thm)],[fact_filter__concat]) ).

fof(i_0_5590,plain,
    ! [X24,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
    inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).

fof(i_0_5591,plain,
    ! [X6,X23,X21,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

fof(i_0_5592,plain,
    ! [X6,X23,X21,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).

fof(i_0_5593,plain,
    ! [X30742,X30743,X30744] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30744),hAPP(c_List_Orotate(X30744,X30743),X30742)))
        | hBOOL(hAPP(c_List_Odistinct(X30744),X30742)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30744),X30742))
        | hBOOL(hAPP(c_List_Odistinct(X30744),hAPP(c_List_Orotate(X30744,X30743),X30742))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).

fof(i_0_5594,plain,
    ! [X33953,X33954,X33955] :
      ( ( ~ c_List_Olist__ex(tc_Nat_Onat,X33955,c_List_Oupt(X33954,X33953))
        | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X33955),X33954,X33953) )
      & ( c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X33955),X33954,X33953)
        | c_List_Olist__ex(tc_Nat_Onat,X33955,c_List_Oupt(X33954,X33953)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5215])]) ).

fof(i_0_5595,plain,
    ! [X24,X37,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_Relation_ODomain(X5,X5),X37)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X24)),c_Transitive__Closure_Ortrancl(X5,X37)))
      <=> X20 = X24 ) ),
    inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(i_0_5596,plain,
    ! [X26171,X26172] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X26172)),c_Int_OBit1(X26171)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26172),X26171)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_5597,plain,
    ! [X1,X19,X18,X26,X2,X17,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X17,X2,X26,X18)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17),X19))
       => hAPP(hAPP(X18,X1),X19) = X26 ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(i_0_5598,plain,
    ! [X26119,X26120] :
      ( ~ class_Int_Onumber__ring(X26120)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26120),hAPP(c_Int_Onumber__class_Onumber__of(X26120),X26119)),c_Groups_Oone__class_Oone(X26120)) = hAPP(c_Int_Onumber__class_Onumber__of(X26120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26119),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J])]) ).

fof(i_0_5599,plain,
    ! [X224,X20,X2,X5,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X224)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).

fof(i_0_5600,plain,
    ! [X26117,X26118] :
      ( ~ class_Int_Onumber__ring(X26118)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26118),c_Groups_Oone__class_Oone(X26118)),hAPP(c_Int_Onumber__class_Onumber__of(X26118),X26117)) = hAPP(c_Int_Onumber__class_Onumber__of(X26118),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26117))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).

fof(i_0_5601,plain,
    ! [X28895,X28896,X28897] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28897,X28897)),X28896),X28895))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28897,X28897)),X28896),c_Transitive__Closure_Otrancl(X28897,X28895))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).

fof(i_0_5602,plain,
    ! [X31687,X31688,X31689] : c_List_Oconcat(X31689,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31689)),X31688),X31687)) = hAPP(hAPP(c_List_Oappend(X31689),X31688),c_List_Oconcat(X31689,X31687)),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(i_0_5603,plain,
    ! [X26096,X26097] :
      ( ~ class_Int_Onumber__ring(X26097)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26097),c_Groups_Oone__class_Oone(X26097)),hAPP(c_Int_Onumber__class_Onumber__of(X26097),X26096)) = hAPP(c_Int_Onumber__class_Onumber__of(X26097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X26096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_5604,plain,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X27))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X27)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X27)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(i_0_5605,plain,
    ! [X31962,X31963] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31962)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31962)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31962))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31962)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31963),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31962)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5216])]) ).

fof(i_0_5606,plain,
    ! [X18,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X20),X18))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X20),X18)))
           => ! [X63] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X63),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X20),X18)))
               => ( X3 != X63
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X63) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X20),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).

fof(i_0_5607,plain,
    ! [X29254,X29255] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29255,X29255),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X29255,X29254)),c_Relation_OId(X29255)) = c_Transitive__Closure_Ortrancl(X29255,X29254),
    inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).

fof(i_0_5608,plain,
    ! [X55,X221,X222,X56,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92),X55) = hAPP(hAPP(c_List_Oappend(X56),hAPP(hAPP(c_List_Olist__update(X56,X222),X92),X55)),X221) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Olist__update(X56,hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92),X55) = hAPP(hAPP(c_List_Oappend(X56),X222),hAPP(hAPP(c_List_Olist__update(X56,X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).

fof(i_0_5609,plain,
    ! [X23,X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).

fof(i_0_5610,plain,
    ! [X23,X21,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X21),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X21)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).

fof(i_0_5611,plain,
    ! [X33035,X33036,X33037,X33038,X33039,X33040] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33040,X33039,X33038,X33037,c_Lazy__Sequence_Olazy__sequence_OInsert(X33039,X33036,X33035)) = hAPP(hAPP(X33037,X33036),X33035),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(i_0_5612,plain,
    ! [X33029,X33030,X33031,X33032,X33033] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33033,X33032,X33031,X33030,X33029) = c_Option_Ooption_Ooption__case(X33033,tc_prod(X33032,tc_Lazy__Sequence_Olazy__sequence(X33032)),X33031,hAPP(c_Product__Type_Oprod_Oprod__case(X33032,tc_Lazy__Sequence_Olazy__sequence(X33032),X33033),X33030),hAPP(c_Lazy__Sequence_Oyield(X33032),X33029)),
    inference(variable_rename,[status(thm)],[fact_seq__case]) ).

fof(i_0_5613,plain,
    ! [X26068,X26069] :
      ( ~ class_Int_Onumber__ring(X26069)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26069),hAPP(c_Int_Onumber__class_Onumber__of(X26069),c_Int_OBit1(c_Int_OPls))),X26068) = X26068 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).

fof(i_0_5614,plain,
    ! [X95,X96,X30] :
      ( c_List_Olist__ex(tc_Int_Oint,X30,c_List_Oupto(X96,X95))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X30),X96,X95) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__int]) ).

fof(i_0_5615,plain,
    ! [X30745,X30746,X30747] : c_List_Orotate(X30747,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30746),X30745)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X30747),tc_List_Olist(X30747),tc_List_Olist(X30747),c_List_Orotate(X30747,X30746)),c_List_Orotate(X30747,X30745)),
    inference(variable_rename,[status(thm)],[fact_rotate__add]) ).

fof(i_0_5616,plain,
    ! [X27,X23,X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X27)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X27)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(i_0_5617,plain,
    ! [X26092,X26093] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26093),hAPP(c_Int_Onumber__class_Onumber__of(X26093),X26092)),c_Groups_Oone__class_Oone(X26093)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26092),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X26093)
        | ~ class_Rings_Olinordered__idom(X26093) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26092),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26093),hAPP(c_Int_Onumber__class_Onumber__of(X26093),X26092)),c_Groups_Oone__class_Oone(X26093)))
        | ~ class_Int_Onumber__ring(X26093)
        | ~ class_Rings_Olinordered__idom(X26093) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_5618,plain,
    ! [X26090,X26091] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26091),hAPP(c_Int_Onumber__class_Onumber__of(X26091),X26090)),c_Groups_Oone__class_Oone(X26091)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26090),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X26091)
        | ~ class_Rings_Olinordered__idom(X26091) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26090),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26091),hAPP(c_Int_Onumber__class_Onumber__of(X26091),X26090)),c_Groups_Oone__class_Oone(X26091)))
        | ~ class_Int_Onumber__ring(X26091)
        | ~ class_Rings_Olinordered__idom(X26091) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_5619,plain,
    ! [X29441,X29442] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29442,X29442)),X29441),c_Relation_OId(X29442)))
      | X29441 = hAPP(hAPP(c_Product__Type_OPair(X29442,X29442),esk363_2(X29441,X29442)),esk363_2(X29441,X29442)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).

fof(i_0_5620,plain,
    ! [X26361] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X26361)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X26361)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(i_0_5621,plain,
    ! [X29200,X29201] : hBOOL(hAPP(hAPP(c_member(tc_prod(X29201,X29201)),hAPP(hAPP(c_Product__Type_OPair(X29201,X29201),X29200),X29200)),c_Relation_OId(X29201))),
    inference(variable_rename,[status(thm)],[fact_IdI]) ).

fof(i_0_5622,plain,
    ! [X31669,X31670,X31671] : hAPP(c_List_Ofoldl(tc_List_Olist(X31671),tc_List_Olist(X31671),c_List_Oappend(X31671),X31670),X31669) = hAPP(hAPP(c_List_Oappend(X31671),X31670),c_List_Oconcat(X31671,X31669)),
    inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).

fof(i_0_5623,plain,
    ! [X26176,X26177] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X26177)),c_Int_OBit1(X26176)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26177),X26176)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(i_0_5624,plain,
    ! [X224,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X20,X224) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X20),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).

fof(i_0_5625,plain,
    ! [X78,X5] :
      ( c_Relation_Oirrefl(X5,X78)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X78)) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).

fof(i_0_5626,plain,
    ! [X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X78)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).

fof(i_0_5627,plain,
    ! [X6,X78,X5] :
      ( c_Wellfounded_Owf(X5,X78)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X78)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).

fof(i_0_5628,plain,
    ! [X29258,X29259] : c_Transitive__Closure_Ortrancl(X29259,X29258) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29259,X29259),tc_HOL_Obool)),c_Relation_OId(X29259)),hAPP(hAPP(c_Relation_Orel__comp(X29259,X29259,X29259),c_Transitive__Closure_Ortrancl(X29259,X29258)),X29258)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).

fof(i_0_5629,plain,
    ! [X6,X22,X19,X17,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17,tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(X22,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X17),X6),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INT__E]) ).

fof(i_0_5630,plain,
    ! [X26341] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X26341)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26341)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26341))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X26341))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).

fof(i_0_5631,plain,
    ! [X26339] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X26339)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X26339)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X26339))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X26339))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).

fof(i_0_5632,plain,
    ! [X26074] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X26074)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26074)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26074))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X26074))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_5633,plain,
    ! [X26061] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X26061)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26061)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26061))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X26061))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_5634,plain,
    ! [X26214,X26215,X26216] :
      ( ~ class_Int_Onumber__ring(X26216)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26216),hAPP(c_Int_Onumber__class_Onumber__of(X26216),X26215)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X26214))) = hAPP(hAPP(c_HOL_OLet(X26216,X26216),hAPP(hAPP(c_Power_Opower__class_Opower(X26216),hAPP(c_Int_Onumber__class_Onumber__of(X26216),X26215)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26214))),hAPP(hAPP(c_COMBS(X26216,X26216,X26216),c_Groups_Otimes__class_Otimes(X26216)),c_COMBI(X26216))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).

fof(i_0_5635,plain,
    ! [X20,X24,X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X23)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X24))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X24)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).

fof(i_0_5636,plain,
    ! [X31914,X31915] :
      ( ~ class_Groups_Omonoid__add(X31915)
      | hAPP(c_List_Ofoldl(X31915,X31915,c_Groups_Oplus__class_Oplus(X31915),c_Groups_Ozero__class_Ozero(X31915)),X31914) = c_List_Ofoldr(X31915,X31915,c_Groups_Oplus__class_Oplus(X31915),X31914,c_Groups_Ozero__class_Ozero(X31915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).

fof(i_0_5637,plain,
    ! [X31993,X31994,X31995,X31996,X31997] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31996),X31995)))
      | hAPP(hAPP(c_List_Onth(X31994),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31994),X31993),c_List_Oupt(X31995,X31996))),X31997) = hAPP(X31993,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31995),X31997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).

fof(i_0_5638,plain,
    ! [X30749,X30750,X30751,X30752] : hAPP(c_List_Orotate(X30752,X30751),hAPP(c_List_Orotate(X30752,X30750),X30749)) = hAPP(c_List_Orotate(X30752,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30751),X30750)),X30749),
    inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).

fof(i_0_5639,plain,
    ! [X31904,X31905,X31906] :
      ( ~ class_Groups_Oab__semigroup__add(X31906)
      | c_List_Ofoldr(X31906,X31906,c_Groups_Oplus__class_Oplus(X31906),X31905,X31904) = hAPP(c_List_Ofoldl(X31906,X31906,c_Groups_Oplus__class_Oplus(X31906),X31904),X31905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).

fof(i_0_5640,plain,
    ! [X33145,X33146,X33147,X33148] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33148,X33147,X33146,X33145,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33147)) = X33146,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I4_J]) ).

fof(i_0_5641,plain,
    ! [X30774,X30775,X30776] : hAPP(c_List_Orotate(X30776,X30775),X30774) = hAPP(c_List_Orotate(X30776,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30775,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30776)),X30774))),X30774),
    inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).

fof(i_0_5642,plain,
    ! [X26041,X26042] :
      ( ~ class_Int_Onumber__ring(X26042)
      | ~ class_Int_Oring__char__0(X26042)
      | ~ c_Int_Oiszero(X26042,hAPP(c_Int_Onumber__class_Onumber__of(X26042),c_Int_OBit1(X26041))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5217])]) ).

fof(i_0_5643,plain,
    ! [X26184] : c_Int_Opred(c_Int_OBit0(X26184)) = c_Int_OBit1(c_Int_Opred(X26184)),
    inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).

fof(i_0_5644,plain,
    ! [X6,X2,X19,X5,X17] :
      ( class_Fields_Ofield(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X17)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).

fof(i_0_5645,plain,
    ! [X29260,X29261] : c_Relation_Orefl__on(X29261,c_Orderings_Otop__class_Otop(tc_fun(X29261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29261,X29261),tc_HOL_Obool)),X29260),c_Relation_OId(X29261))),
    inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).

fof(i_0_5646,plain,
    ! [X32321,X32322,X32323] : hAPP(hAPP(c_List_Oappend(X32323),c_List_OtakeWhile(X32323,X32322,X32321)),c_List_OdropWhile(X32323,X32322,X32321)) = X32321,
    inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(i_0_5647,plain,
    ! [X2,X6,X19,X5,X17] :
      ( class_Groups_Oab__group__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).

fof(i_0_5648,plain,
    ! [X31708,X31709] : hAPP(c_List_Oset(X31709),c_List_Oconcat(X31709,X31708)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31709),tc_fun(X31709,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31709)),X31708)),c_List_Oset(X31709)),
    inference(variable_rename,[status(thm)],[fact_set__concat]) ).

fof(i_0_5649,plain,
    ! [X31706,X31707] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31707)),c_List_Oconcat(X31707,X31706)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31707),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31707))),X31706)),
    inference(variable_rename,[status(thm)],[fact_length__concat]) ).

fof(i_0_5650,plain,
    ! [X6,X21,X22,X19,X17,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X17,tc_HOL_Obool)),X19),X22),X21))
     => ( ~ hBOOL(hAPP(hAPP(X22,X6),X21))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).

fof(i_0_5651,plain,
    ! [X33346,X33347] :
      ( ~ c_Relation_Otrans(X33347,X33346)
      | ~ c_Relation_Oantisym(X33347,X33346)
      | c_Relation_Otrans(X33347,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X33347,X33347),tc_HOL_Obool)),X33346),c_Relation_OId(X33347))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__diff__Id])]) ).

fof(i_0_5652,plain,
    ! [X32231,X32232,X32233] :
      ( ( X32232 != c_List_Olist_ONil(X32233)
        | c_List_Ofoldr(X32233,X32233,c_Orderings_Oord__class_Omax(X32233),X32232,X32231) = X32231
        | ~ c_List_Olinorder__class_Osorted(X32233,hAPP(c_List_Orev(X32233),X32232))
        | ~ class_Orderings_Olinorder(X32233) )
      & ( X32232 = c_List_Olist_ONil(X32233)
        | c_List_Ofoldr(X32233,X32233,c_Orderings_Oord__class_Omax(X32233),X32232,X32231) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X32233),hAPP(hAPP(c_List_Onth(X32233),X32232),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32231)
        | ~ c_List_Olinorder__class_Osorted(X32233,hAPP(c_List_Orev(X32233),X32232))
        | ~ class_Orderings_Olinorder(X32233) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).

fof(i_0_5653,plain,
    ! [X33265,X33266] :
      ( ~ c_Relation_Otrans(X33266,X33265)
      | c_Relation_Otrans(X33266,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33266,X33266),tc_HOL_Obool)),X33265),c_Relation_OId(X33266))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__reflclI])]) ).

fof(i_0_5654,plain,
    ! [X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X30),X224))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224))) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).

fof(i_0_5655,plain,
    ! [X29229,X29230] : c_Transitive__Closure_Ortrancl(X29230,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29230,X29230),tc_HOL_Obool)),X29229),c_Relation_OId(X29230))) = c_Transitive__Closure_Ortrancl(X29230,X29229),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(i_0_5656,plain,
    ! [X29234,X29235] : c_Transitive__Closure_Ortrancl(X29235,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29235,X29235),tc_HOL_Obool)),X29234),c_Relation_OId(X29235))) = c_Transitive__Closure_Ortrancl(X29235,X29234),
    inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(i_0_5657,plain,
    ! [X32360,X32361,X32362,X32363,X32364] :
      ( ( X32362 = hAPP(hAPP(c_List_Oappend(X32364),c_List_OtakeWhile(X32364,X32363,X32362)),hAPP(hAPP(c_List_Olist_OCons(X32364),X32361),X32360))
        | c_List_OdropWhile(X32364,X32363,X32362) != hAPP(hAPP(c_List_Olist_OCons(X32364),X32361),X32360) )
      & ( ~ hBOOL(hAPP(X32363,X32361))
        | c_List_OdropWhile(X32364,X32363,X32362) != hAPP(hAPP(c_List_Olist_OCons(X32364),X32361),X32360) )
      & ( X32362 != hAPP(hAPP(c_List_Oappend(X32364),c_List_OtakeWhile(X32364,X32363,X32362)),hAPP(hAPP(c_List_Olist_OCons(X32364),X32361),X32360))
        | hBOOL(hAPP(X32363,X32361))
        | c_List_OdropWhile(X32364,X32363,X32362) = hAPP(hAPP(c_List_Olist_OCons(X32364),X32361),X32360) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5218])])]) ).

fof(i_0_5658,plain,
    ! [X29263,X29264] : c_Relation_Oirrefl(X29264,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29264,X29264),tc_HOL_Obool)),X29263),c_Relation_OId(X29264))),
    inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(i_0_5659,plain,
    ! [X26055] :
      ( ~ class_Int_Onumber__ring(X26055)
      | ~ c_Int_Oiszero(X26055,hAPP(c_Int_Onumber__class_Onumber__of(X26055),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5219])]) ).

fof(i_0_5660,plain,
    ! [X119,X107,X61,X60] :
      ( X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X107)),X119)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X119))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X61)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X119))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X60,X61),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X119))) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).

fof(i_0_5661,plain,
    ! [X26367] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X26367)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X26367)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(i_0_5662,plain,
    ! [X2,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(i_0_5663,plain,
    ! [X29144,X29145] :
      ( ~ c_Wellfounded_Owf(X29145,hAPP(c_Relation_Oconverse(X29145,X29145),X29144))
      | c_Wellfounded_Owf(X29145,hAPP(c_Relation_Oconverse(X29145,X29145),c_Transitive__Closure_Otrancl(X29145,X29144))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).

fof(i_0_5664,plain,
    ! [X31690,X31691,X31692,X31693,X31694] :
      ( ( c_List_Oconcat(X31691,X31690) != c_List_Olist_ONil(X31691)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31691)),X31692),hAPP(c_List_Oset(tc_List_Olist(X31691)),X31690)))
        | X31692 = c_List_Olist_ONil(X31691) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31694)),esk427_2(X31693,X31694)),hAPP(c_List_Oset(tc_List_Olist(X31694)),X31693)))
        | c_List_Oconcat(X31694,X31693) = c_List_Olist_ONil(X31694) )
      & ( esk427_2(X31693,X31694) != c_List_Olist_ONil(X31694)
        | c_List_Oconcat(X31694,X31693) = c_List_Olist_ONil(X31694) ) ),
    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_concat__eq__Nil__conv])])])])])]) ).

fof(i_0_5665,plain,
    ! [X31696,X31697,X31698,X31699,X31700] :
      ( ( c_List_Olist_ONil(X31697) != c_List_Oconcat(X31697,X31696)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31697)),X31698),hAPP(c_List_Oset(tc_List_Olist(X31697)),X31696)))
        | X31698 = c_List_Olist_ONil(X31697) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31700)),esk428_2(X31699,X31700)),hAPP(c_List_Oset(tc_List_Olist(X31700)),X31699)))
        | c_List_Olist_ONil(X31700) = c_List_Oconcat(X31700,X31699) )
      & ( esk428_2(X31699,X31700) != c_List_Olist_ONil(X31700)
        | c_List_Olist_ONil(X31700) = c_List_Oconcat(X31700,X31699) ) ),
    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_Nil__eq__concat__conv])])])])])]) ).

fof(i_0_5666,plain,
    ! [X31936,X31937,X31938] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31938),X31937))
      | c_List_Oupt(X31938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31937),X31936)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31938,X31937)),c_List_Oupt(X31937,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31937),X31936))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).

fof(i_0_5667,plain,
    ! [X2,X51,X89,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(c_Nat_OSuc,X89))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X51,X89))),hAPP(X2,hAPP(c_Nat_OSuc,X89))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(i_0_5668,plain,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnE]) ).

fof(i_0_5669,plain,
    ! [X32333,X32334,X32335,X32336,X32337,X32338,X32339] :
      ( ( c_List_OdropWhile(X32335,X32334,X32333) != c_List_Olist_ONil(X32335)
        | ~ hBOOL(hAPP(hAPP(c_member(X32335),X32336),hAPP(c_List_Oset(X32335),X32333)))
        | hBOOL(hAPP(X32334,X32336)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32339),esk442_3(X32337,X32338,X32339)),hAPP(c_List_Oset(X32339),X32337)))
        | c_List_OdropWhile(X32339,X32338,X32337) = c_List_Olist_ONil(X32339) )
      & ( ~ hBOOL(hAPP(X32338,esk442_3(X32337,X32338,X32339)))
        | c_List_OdropWhile(X32339,X32338,X32337) = c_List_Olist_ONil(X32339) ) ),
    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_dropWhile__eq__Nil__conv])])])])])]) ).

fof(i_0_5670,plain,
    ! [X31643,X31644,X31645] :
      ( hBOOL(hAPP(hAPP(c_member(X31645),X31644),hAPP(c_List_Oset(X31645),X31643)))
      | hAPP(c_List_OremoveAll(X31645,X31644),X31643) = X31643 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5220])]) ).

fof(i_0_5671,plain,
    ! [X20,X19,X18,X2,X17,X5] :
      ( c_Finite__Set_Ofolding(X5,X17,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Fun_Ocomp(X17,X17,X17,hAPP(X18,X19)),hAPP(X2,X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).

fof(i_0_5672,plain,
    ! [X32327,X32328,X32329] :
      ( ~ class_Orderings_Olinorder(X32329)
      | ~ c_List_Olinorder__class_Osorted(X32329,X32328)
      | c_List_Olinorder__class_Osorted(X32329,c_List_OdropWhile(X32329,X32327,X32328)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile])]) ).

fof(i_0_5673,plain,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X230,X262] :
          ( X224 = hAPP(hAPP(c_List_Oappend(X5),X230),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X262))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X262))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(i_0_5674,plain,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
    <=> ? [X230] :
          ( ? [X262] : X224 = hAPP(hAPP(c_List_Oappend(X5),X230),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X262))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X230))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(i_0_5675,plain,
    ! [X26188] : c_Int_Osucc(c_Int_OBit1(X26188)) = c_Int_OBit0(c_Int_Osucc(X26188)),
    inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).

fof(i_0_5676,plain,
    ! [X26206,X26207,X26208] :
      ( ~ class_Int_Onumber__ring(X26208)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X26208),X26207),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X26206))) = hAPP(hAPP(c_HOL_OLet(X26208,X26208),hAPP(hAPP(c_Power_Opower__class_Opower(X26208),X26207),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26206))),hAPP(hAPP(c_COMBS(X26208,X26208,X26208),c_Groups_Otimes__class_Otimes(X26208)),c_COMBI(X26208))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).

fof(i_0_5677,plain,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).

fof(i_0_5678,plain,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ),
    inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).

fof(i_0_5679,plain,
    ! [X31817,X31818,X31819,X31820] :
      ( hBOOL(hAPP(X31820,X31819))
      | hAPP(c_List_OremoveAll(X31818,X31819),hAPP(c_List_Ofilter(X31818,X31820),X31817)) = hAPP(c_List_Ofilter(X31818,X31820),X31817) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5221])]) ).

fof(i_0_5680,plain,
    ! [X32312,X32313] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X32313),X32312) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X32313)),c_List_Oembed__list(X32312))),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(i_0_5681,plain,
    ! [X32291] : c_List_Oreturn__list(X32291) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X32291),
    inference(variable_rename,[status(thm)],[fact_return__list__def]) ).

fof(i_0_5682,plain,
    ! [X32314] : c_List_Oembed__list(X32314) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X32314),
    inference(variable_rename,[status(thm)],[fact_embed__list__def]) ).

fof(i_0_5683,plain,
    ! [X90,X19,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(c_Nat_OSuc,X90)
    <=> ? [X124,X125] :
          ( X19 = hAPP(hAPP(c_Set_Oinsert(X5),X124),X125)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X124),X125))
          & hAPP(c_Finite__Set_Ocard(X5),X125) = X90
          & ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X125 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).

fof(i_0_5684,plain,
    ! [X31646,X31647,X31648] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31648),X31647))
      | c_List_Oremove1(X31648,X31646,X31647) = hAPP(c_List_OremoveAll(X31648,X31646),X31647) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])]) ).

fof(i_0_5685,plain,
    ! [X31948,X31949,X31950] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31950),X31949)),X31948))
      | hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X31949),c_List_Oupt(X31950,X31948)) = c_List_Oupt(X31950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31950),X31949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).

fof(i_0_5686,plain,
    ! [X31026,X31027,X31028,X31029,X31030] : hAPP(c_List_Orotate(X31030,X31029),hAPP(hAPP(c_List_Omap(X31028,X31030),X31027),X31026)) = hAPP(hAPP(c_List_Omap(X31028,X31030),X31027),hAPP(c_List_Orotate(X31028,X31029),X31026)),
    inference(variable_rename,[status(thm)],[fact_rotate__map]) ).

fof(i_0_5687,plain,
    ! [X29140,X29141] : c_Transitive__Closure_Otrancl(X29141,hAPP(c_Relation_Oconverse(X29141,X29141),X29140)) = hAPP(c_Relation_Oconverse(X29141,X29141),c_Transitive__Closure_Otrancl(X29141,X29140)),
    inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).

fof(i_0_5688,plain,
    ! [X223,X17,X24,X20,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X20)),hAPP(X2,X24)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) = hAPP(hAPP(c_List_Olist_OCons(X17),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X20)),hAPP(X2,X24)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),hAPP(hAPP(c_List_Olist_OCons(X17),X24),X223)) = hAPP(hAPP(c_List_Olist_OCons(X17),X24),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17,X5,X2),X20),X223)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(i_0_5689,plain,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).

fof(i_0_5690,plain,
    ! [X22,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_5691,plain,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_IntE]) ).

fof(i_0_5692,plain,
    ! [X95,X96] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X96),X95)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),X95))
         => c_List_Oupto(X96,X95) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X96),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),X95)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),X95))
         => c_List_Oupto(X96,X95) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).

fof(i_0_5693,plain,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(i_0_5694,plain,
    ! [X96,X27] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X27),X96)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X96))
         => c_Lazy__Sequence_Osmall__lazy_H(X27,X96) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X96))
         => c_Lazy__Sequence_Osmall__lazy_H(X27,X96) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X96),c_Lazy__Sequence_Osmall__lazy_H(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opsimps]) ).

fof(i_0_5695,plain,
    ! [X24,X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X24,X224)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).

fof(i_0_5696,plain,
    ! [X111,X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X224,X111)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).

fof(i_0_5697,plain,
    ! [X31975,X31976,X31977] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31977),X31976)),X31975))
      | hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X31977,X31975)),X31976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31977),X31976) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).

fof(i_0_5698,plain,
    ! [X26209,X26210] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26210),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X26209))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26210),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26209))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_zpower__number__of__even]) ).

fof(i_0_5699,plain,
    ! [X1,X2,X5,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X17)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X17)),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_5700,plain,
    ! [X222,X55,X56,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55)))
       => hAPP(c_Random_Opick(X56,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X56)),X55),X222)),X98) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X56),X55) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55)))
       => hAPP(c_Random_Opick(X56,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X56)),X55),X222)),X98) = hAPP(c_Random_Opick(X56,X222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X56),X55))) ) ),
    inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).

fof(i_0_5701,plain,
    ! [X62,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X19),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X62)))
     => ~ ! [X152] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X19),X152))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X152),X62)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnionE]) ).

fof(i_0_5702,plain,
    ! [X26143,X26144] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26144)),c_Int_OBit0(X26143)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26144),X26143)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26144),X26143))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26144)),c_Int_OBit0(X26143))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_5703,plain,
    ! [X26141,X26142] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26142)),c_Int_OBit0(X26141)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26142),X26141)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26142),X26141))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26142)),c_Int_OBit0(X26141))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_5704,plain,
    ! [X26156,X26157] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26157)),c_Int_OBit0(X26156)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26157),X26156)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26157),X26156))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26157)),c_Int_OBit0(X26156))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_5705,plain,
    ! [X26154,X26155] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26155)),c_Int_OBit0(X26154)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26155),X26154)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26155),X26154))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26155)),c_Int_OBit0(X26154))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_5706,plain,
    ! [X31623,X31624] : hAPP(c_List_OremoveAll(X31624,X31623),c_List_Olist_ONil(X31624)) = c_List_Olist_ONil(X31624),
    inference(variable_rename,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(i_0_5707,plain,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X19)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(i_0_5708,plain,
    ! [X26098,X26099] :
      ( ~ class_Int_Onumber__ring(X26099)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26099),hAPP(c_Int_Onumber__class_Onumber__of(X26099),X26098)),c_Groups_Oone__class_Oone(X26099)) = hAPP(c_Int_Onumber__class_Onumber__of(X26099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26098),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_5709,plain,
    ! [X84,X75,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X84)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X75))) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_5710,plain,
    ! [X24,X20,X17,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X17,tc_HOL_Obool))),X20),X24)),
    inference(fof_simplification,[status(thm)],[fact_bot2E]) ).

fof(i_0_5711,plain,
    ! [X57,X151,X142,X143] :
      ( X143 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X142),X151)),X57)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X57))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X57),X142)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X142),X57))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X142 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X143,X142) = X57 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(i_0_5712,plain,
    ! [X31888,X31889,X31890,X31891] : c_List_Ofoldr(X31891,X31890,X31889,c_List_Olist_ONil(X31891),X31888) = X31888,
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(i_0_5713,plain,
    ! [X32428,X32429,X32430,X32431] : c_List_Oconcat(X32431,hAPP(hAPP(c_List_Omap(X32430,tc_List_Olist(X32431)),X32429),X32428)) = c_List_Omaps(X32430,X32431,X32429,X32428),
    inference(variable_rename,[status(thm)],[fact_concat__map__maps]) ).

fof(i_0_5714,plain,
    ! [X32424,X32425,X32426,X32427] : c_List_Omaps(X32427,X32426,X32425,X32424) = c_List_Oconcat(X32426,hAPP(hAPP(c_List_Omap(X32427,tc_List_Olist(X32426)),X32425),X32424)),
    inference(variable_rename,[status(thm)],[fact_maps__def]) ).

fof(i_0_5715,plain,
    ! [X141,X57,X142,X143] :
      ( X143 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X142),X57)),X141)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X142)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X142),X141))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X141),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X142 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X143),X142) = X57 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(i_0_5716,plain,
    ! [X30780,X30781,X30782] : hAPP(c_List_Orotate(X30782,hAPP(c_Nat_OSuc,X30781)),X30780) = hAPP(c_List_Orotate1(X30782),hAPP(c_List_Orotate(X30782,X30781),X30780)),
    inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).

fof(i_0_5717,plain,
    ! [X26,X20,X19,X2,X17,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X17,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),X26),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X17,X2),hAPP(hAPP(X2,X20),X26)),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(i_0_5718,plain,
    ! [X31964,X31965,X31966,X31967] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31967),X31966))
        | c_List_Oupt(X31967,X31966) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31965),X31964) )
      & ( X31967 = X31965
        | c_List_Oupt(X31967,X31966) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31965),X31964) )
      & ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31967),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31966) = X31964
        | c_List_Oupt(X31967,X31966) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31965),X31964) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31967),X31966))
        | X31967 != X31965
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31967),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31966) != X31964
        | c_List_Oupt(X31967,X31966) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31965),X31964) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])]) ).

fof(i_0_5719,plain,
    ! [X2,X51,X89,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89))),hAPP(X2,X89)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(i_0_5720,plain,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => ( ~ hBOOL(hAPP(X19,X20))
       => hBOOL(hAPP(X22,X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup1E]) ).

fof(i_0_5721,plain,
    ! [X26183] : c_Int_Opred(c_Int_OBit1(X26183)) = c_Int_OBit0(X26183),
    inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).

fof(i_0_5722,plain,
    ! [X93,X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X93) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X166))),X93) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(i_0_5723,plain,
    ! [X28898] : c_Transitive__Closure_Otrancl(X28898,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28898,X28898),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28898,X28898),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).

fof(i_0_5724,plain,
    ! [X31985,X31986,X31987,X31988] :
      ( ~ class_Groups_Ocomm__monoid__add(X31988)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31988),X31987),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31986,X31985))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31988),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31988),X31987),c_List_Oupt(X31986,X31985))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).

fof(i_0_5725,plain,
    ! [X31989,X31990,X31991,X31992] :
      ( ~ class_Groups_Ocomm__monoid__add(X31992)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31992),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31992),X31991),c_List_Oupt(X31990,X31989))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31992),X31991),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31990,X31989))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).

fof(i_0_5726,plain,
    ! [X20,X22,X19,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20))
     => ~ ( hBOOL(hAPP(X19,X20))
         => ~ hBOOL(hAPP(X22,X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf1E]) ).

fof(i_0_5727,plain,
    ! [X30763,X30764,X30765] : hAPP(c_List_Orotate1(X30765),hAPP(c_List_Orotate(X30765,X30764),X30763)) = hAPP(c_List_Orotate(X30765,X30764),hAPP(c_List_Orotate1(X30765),X30763)),
    inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(i_0_5728,plain,
    ! [X26066,X26067] :
      ( ~ class_Int_Onumber__ring(X26067)
      | hAPP(c_Int_Onumber__class_Onumber__of(X26067),c_Int_OBit1(X26066)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26067),c_Groups_Oone__class_Oone(X26067)),hAPP(c_Int_Onumber__class_Onumber__of(X26067),X26066))),hAPP(c_Int_Onumber__class_Onumber__of(X26067),X26066)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_5729,plain,
    ! [X22,X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ) ),
    inference(fof_simplification,[status(thm)],[fact_DiffI]) ).

fof(i_0_5730,plain,
    ! [X33165,X33166,X33167,X33168] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X33168,X33167,X33166,c_Code__Numeral_OSuc__code__numeral(X33165)) = hAPP(hAPP(X33166,X33165),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X33168,X33167,X33166,X33165)),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(i_0_5731,plain,
    ! [X31340] : c_Code__Numeral_OSuc__code__numeral(X31340) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X31340))),
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(i_0_5732,plain,
    ! [X19,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Finite__Set_Ocard(X5),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_5733,plain,
    ! [X29215,X29216,X29217] : hAPP(hAPP(c_Relation_Orel__comp(X29217,X29217,X29216),c_Relation_OId(X29217)),X29215) = X29215,
    inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).

fof(i_0_5734,plain,
    ! [X26078,X26079] :
      ( ~ class_Fields_Ofield(X26079)
      | ~ class_Int_Onumber__ring(X26079)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26079),X26078),hAPP(c_Int_Onumber__class_Onumber__of(X26079),c_Int_OBit1(c_Int_OPls))) = X26078 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_5735,plain,
    ! [X26076,X26077] :
      ( ~ class_Fields_Ofield(X26077)
      | ~ class_Int_Onumber__ring(X26077)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26077),X26076),hAPP(c_Int_Onumber__class_Onumber__of(X26077),c_Int_OBit1(c_Int_OPls))) = X26076 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_5736,plain,
    ! [X55,X61,X60,X56] :
      ( class_Lattices_Osemilattice__sup(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X56),X60),X61)),X55))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__supE]) ).

fof(i_0_5737,plain,
    ! [X55,X61,X60,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),hAPP(hAPP(c_Orderings_Oord__class_Omax(X56),X60),X61)),X55))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X60),X55))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X61),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(i_0_5738,plain,
    ! [X26070,X26071] :
      ( ~ class_Int_Onumber__ring(X26071)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26071),X26070),hAPP(c_Int_Onumber__class_Onumber__of(X26071),c_Int_OBit1(c_Int_OPls))) = X26070 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).

fof(i_0_5739,plain,
    ! [X33050,X33051,X33052,X33053] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33053),hAPP(hAPP(c_List_Olist_OCons(X33053),X33052),X33051)),X33050))
        | X33052 = X33050
        | hBOOL(hAPP(hAPP(c_List_Omember(X33053),X33051),X33050)) )
      & ( X33052 != X33050
        | hBOOL(hAPP(hAPP(c_List_Omember(X33053),hAPP(hAPP(c_List_Olist_OCons(X33053),X33052),X33051)),X33050)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33053),X33051),X33050))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33053),hAPP(hAPP(c_List_Olist_OCons(X33053),X33052),X33051)),X33050)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_member__rec_I1_J])])]) ).

fof(i_0_5740,plain,
    ! [X33054] : c_List_Omember(X33054) = c_List_Oset(X33054),
    inference(variable_rename,[status(thm)],[fact_member__set]) ).

fof(i_0_5741,plain,
    ! [X30728,X30729,X30730] :
      ( X30730 = c_List_Olist_ONil(X30729)
      | hAPP(c_List_Ohd(X30729),hAPP(c_List_Orotate(X30729,X30728),X30730)) = hAPP(hAPP(c_List_Onth(X30729),X30730),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30728,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30729)),X30730))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).

fof(i_0_5742,plain,
    ! [X93,X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)),X93)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X166))),X93) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(i_0_5743,plain,
    ! [X30789,X30790,X30791] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30791)),X30790)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate(X30791,X30789),X30790) = X30790 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).

fof(i_0_5744,plain,
    ! [X22,X62,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).

fof(i_0_5745,plain,
    ! [X19,X22,X23,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X22))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22))) ),
    inference(fof_simplification,[status(thm)],[fact_UnCI]) ).

fof(i_0_5746,plain,
    ! [X60,X56] :
      ( class_Rings_Olinordered__ring(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X56),X60),X60)),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_5747,plain,
    ! [X26158] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26158)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26158),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26158),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26158)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J])]) ).

fof(i_0_5748,plain,
    ! [X26180,X26181] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26181))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26180))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26181)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26180)),
    inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(i_0_5749,plain,
    ! [X92,X93,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X93)),X92))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X92)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_5750,plain,
    ! [X26166] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26166)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26166),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26166),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26166)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_5751,plain,
    ! [X26359] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26359)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26359),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26359),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X26359)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).

fof(i_0_5752,plain,
    ! [X26342] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26342)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26342),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26342),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26342)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).

fof(i_0_5753,plain,
    ! [X26160] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26160)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26160),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26160),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X26160)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_5754,plain,
    ! [X26182] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26182))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26182))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26182)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X26182)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).

fof(i_0_5755,plain,
    ! [X29213,X29214] : hAPP(c_Relation_OImage(X29214,X29214,c_Relation_OId(X29214)),X29213) = X29213,
    inference(variable_rename,[status(thm)],[fact_Image__Id]) ).

fof(i_0_5756,plain,
    ! [X19,X22,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),X22) = hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).

fof(i_0_5757,plain,
    ! [X25935,X25936] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25936),X25935))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X25936)),X25935)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X25936)),X25935))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25936),X25935)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).

fof(i_0_5758,plain,
    ! [X26366] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X26366)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X26366)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(i_0_5759,plain,
    ! [X25912,X25913] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25913)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25913)),X25912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25912) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25913)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25913)),X25912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X25913))),X25912) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5222])]) ).

fof(i_0_5760,plain,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__if]) ).

fof(i_0_5761,plain,
    ! [X86,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X92) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)),X92)) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__geq]) ).

fof(i_0_5762,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X92))))),
    inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).

fof(i_0_5763,plain,
    ! [X29231,X29232] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29232,X29232),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X29232,X29231)),c_Relation_OId(X29232)) = c_Transitive__Closure_Ortrancl(X29232,X29231),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(i_0_5764,plain,
    ! [X31934,X31935] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31935),X31934))
        | c_List_Oupt(X31935,hAPP(c_Nat_OSuc,X31934)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31935,X31934)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31934),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31935),X31934))
        | c_List_Oupt(X31935,hAPP(c_Nat_OSuc,X31934)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5223])]) ).

fof(i_0_5765,plain,
    ! [X31932,X31933] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31933),X31932))
      | c_List_Oupt(X31933,hAPP(c_Nat_OSuc,X31932)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31933,X31932)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31932),c_List_Olist_ONil(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])]) ).

fof(i_0_5766,plain,
    ! [X22,X19,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).

fof(i_0_5767,plain,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Otimes__class_Otimes(X17)),X1),c_Groups_Oone__class_Oone(X17)),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = c_Groups_Oone__class_Oone(X17) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).

fof(i_0_5768,plain,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17,X5,c_Groups_Oplus__class_Oplus(X17)),X1),c_Groups_Ozero__class_Ozero(X17)),X19) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = c_Groups_Ozero__class_Ozero(X17) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).

fof(i_0_5769,plain,
    ! [X221,X222,X56,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92) = hAPP(hAPP(c_List_Onth(X56),X222),X92) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222)))
       => hAPP(hAPP(c_List_Onth(X56),hAPP(hAPP(c_List_Oappend(X56),X222),X221)),X92) = hAPP(hAPP(c_List_Onth(X56),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X56)),X222))) ) ),
    inference(fof_simplification,[status(thm)],[fact_nth__append]) ).

fof(i_0_5770,plain,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).

fof(i_0_5771,plain,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplD]) ).

fof(i_0_5772,plain,
    ! [X19,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplE]) ).

fof(i_0_5773,plain,
    ! [X26189] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X26189)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X26189)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__Bit0]) ).

fof(i_0_5774,plain,
    ! [X122,X103,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Orderings_Oord(X161) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X122) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X103) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).

fof(i_0_5775,plain,
    ! [X122,X103,X161] :
      ( ( class_Int_Onumber(X161)
        & class_Orderings_Oord(X161) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X103) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X161),hAPP(c_Int_Onumber__class_Onumber__of(X161),X103)),hAPP(c_Int_Onumber__class_Onumber__of(X161),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X161),X122) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).

fof(i_0_5776,plain,
    ! [X94,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X94)),X98)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_5777,plain,
    ! [X98,X94] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X98)),X98)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_5778,plain,
    ! [X223,X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremove1(X5,X20,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X20,X224)),X223) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremove1(X5,X20,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = hAPP(hAPP(c_List_Oappend(X5),X224),c_List_Oremove1(X5,X20,X223)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).

fof(i_0_5779,plain,
    ! [X25968] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25968))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25968) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25968) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25968)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).

fof(i_0_5780,plain,
    ! [X20,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X20)),
    inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).

fof(i_0_5781,plain,
    ! [X26047,X26048] :
      ( ( c_Int_OBit1(X26048) != c_Int_OBit1(X26047)
        | X26048 = X26047 )
      & ( X26048 != X26047
        | c_Int_OBit1(X26048) = c_Int_OBit1(X26047) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_5782,plain,
    ! [X32943,X32944] : c_List_Oconcat(X32944,c_List_Oreplicate(tc_List_Olist(X32944),X32943,c_List_Olist_ONil(X32944))) = c_List_Olist_ONil(X32944),
    inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial]) ).

fof(i_0_5783,plain,
    ! [X21,X6,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X21)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X21))
            & ~ hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X121] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X121)
              & ~ hBOOL(hAPP(X30,X121)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(i_0_5784,plain,
    ! [X224,X20,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X224)) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(i_0_5785,plain,
    ! [X30753,X30754,X30755] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30755)),hAPP(c_List_Orotate(X30755,X30754),X30753)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30755)),X30753),
    inference(variable_rename,[status(thm)],[fact_length__rotate]) ).

fof(i_0_5786,plain,
    ! [X32345,X32346] : c_List_OdropWhile(X32346,X32345,c_List_Olist_ONil(X32346)) = c_List_Olist_ONil(X32346),
    inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(i_0_5787,plain,
    ! [X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X19 ),
    inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(i_0_5788,plain,
    ! [X2,X6,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).

fof(i_0_5789,plain,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).

fof(i_0_5790,plain,
    ! [X2,X6,X18,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X18))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X18))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X18)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X18)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).

fof(i_0_5791,plain,
    ! [X1,X20,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17),hAPP(X1,X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).

fof(i_0_5792,plain,
    ! [X31955,X31956,X31957] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X31957),c_List_Oupt(X31956,X31955)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31956),X31957),X31955),
    inference(variable_rename,[status(thm)],[fact_drop__upt]) ).

fof(i_0_5793,plain,
    ! [X224,X30,X5] :
      ( hAPP(c_List_Ofilter(X5,X30),X224) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
         => ~ hBOOL(hAPP(X30,X3)) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).

fof(i_0_5794,plain,
    ! [X86,X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)))),
    inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).

fof(i_0_5795,plain,
    ! [X30756,X30757,X30758] : hAPP(c_List_Oset(X30758),hAPP(c_List_Orotate(X30758,X30757),X30756)) = hAPP(c_List_Oset(X30758),X30756),
    inference(variable_rename,[status(thm)],[fact_set__rotate]) ).

fof(i_0_5796,plain,
    ! [X5,X19,X20,X22] :
      ( ( ~ hBOOL(hAPP(X22,X20))
       => hBOOL(hAPP(X19,X20)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X22),X20)) ),
    inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).

fof(i_0_5797,plain,
    ! [X255,X256,X224,X30,X5] :
      ( c_List_Opartition(X5,X30,X224) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X256),X255)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X256)))
           => hBOOL(hAPP(X30,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X255)))
           => ~ hBOOL(hAPP(X30,X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_partition__P]) ).

fof(i_0_5798,plain,
    ! [X28899,X28900] : hAPP(c_Relation_ODomain(X28900,X28900),c_Transitive__Closure_Otrancl(X28900,X28899)) = hAPP(c_Relation_ODomain(X28900,X28900),X28899),
    inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).

fof(i_0_5799,plain,
    ! [X28901,X28902] : hAPP(c_Relation_ORange(X28902,X28902),c_Transitive__Closure_Otrancl(X28902,X28901)) = hAPP(c_Relation_ORange(X28902,X28902),X28901),
    inference(variable_rename,[status(thm)],[fact_trancl__range]) ).

fof(i_0_5800,plain,
    ! [X167,X75] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),X167))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X75),c_Int_OPls)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_5801,plain,
    ! [X58,X57,X55] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X55),X57))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X57),X55)) )
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X57),X58))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X58),X57)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X55),X58))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X58),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).

fof(i_0_5802,plain,
    ! [X26146,X26147] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X26147)),c_Int_OBit0(X26146)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26147),X26146)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_5803,plain,
    ! [X26152,X26153] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X26153)),c_Int_OBit0(X26152)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26153),X26152)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(i_0_5804,plain,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(i_0_5805,plain,
    ! [X20] :
      ~ ! [X38] :
          ( X20 = hAPP(c_Int_OAbs__Integ,X38)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg)) ),
    inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(i_0_5806,plain,
    ! [X31941,X31942] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31942),X31941))
      | c_List_Oupt(X31942,X31941) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31942),c_List_Oupt(hAPP(c_Nat_OSuc,X31942),X31941)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).

fof(i_0_5807,plain,
    ! [X31939,X31940] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31940),X31939))
        | c_List_Oupt(X31940,X31939) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31940),c_List_Oupt(hAPP(c_Nat_OSuc,X31940),X31939)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31940),X31939))
        | c_List_Oupt(X31940,X31939) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5224])]) ).

fof(i_0_5808,plain,
    ! [X224,X2,X5,X20,X30,X17] :
      ( class_Orderings_Olinorder(X17)
     => ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X17,X2),X20),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).

fof(i_0_5809,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(i_0_5810,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(i_0_5811,plain,
    ! [X19,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).

fof(i_0_5812,plain,
    ! [X6,X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).

fof(i_0_5813,plain,
    ! [X26190,X26191] :
      ( ~ class_Int_Onumber__ring(X26191)
      | hAPP(c_Int_Onumber__class_Onumber__of(X26191),c_Int_OBit0(X26190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26191),c_Groups_Ozero__class_Ozero(X26191)),hAPP(c_Int_Onumber__class_Onumber__of(X26191),X26190))),hAPP(c_Int_Onumber__class_Onumber__of(X26191),X26190)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_5814,plain,
    ! [X31983,X31984] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31984),hAPP(c_List_Onth(X31984),X31983)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31984)),X31983))) = X31983,
    inference(variable_rename,[status(thm)],[fact_map__nth]) ).

fof(i_0_5815,plain,
    ! [X61,X60,X55,X56] :
      ( class_Lattices_Osemilattice__inf(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X56),X60),X61)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__infE]) ).

fof(i_0_5816,plain,
    ! [X61,X60,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),hAPP(hAPP(c_Orderings_Oord__class_Omin(X56),X60),X61)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X60))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X61)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(i_0_5817,plain,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X20,X224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X20,X224)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).

fof(i_0_5818,plain,
    ! [X22,X62,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X62))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)),X62) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X62) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(i_0_5819,plain,
    ! [X26388,X26389] :
      ( ( X26389 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X26389,X26388) = X26388 )
      & ( X26389 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X26389,X26388) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X26389),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X26388)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).

fof(i_0_5820,plain,
    ! [X31338,X31339] : c_Code__Numeral_Onat__of__aux(X31339,X31338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31339)),X31338),
    inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).

fof(i_0_5821,plain,
    ! [X33402,X33403] :
      ( ~ c_Relation_Osym(X33403,X33402)
      | c_Relation_Osym(X33403,c_Transitive__Closure_Otrancl(X33403,X33402)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trancl])]) ).

fof(i_0_5822,plain,
    ! [X28864,X28865] :
      ( ~ c_Wellfounded_Owf(X28865,X28864)
      | c_Wellfounded_Owf(X28865,c_Transitive__Closure_Otrancl(X28865,X28864)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).

fof(i_0_5823,plain,
    ! [X29218,X29219,X29220] : hAPP(hAPP(c_Relation_Orel__comp(X29220,X29219,X29219),X29218),c_Relation_OId(X29219)) = X29218,
    inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).

fof(i_0_5824,plain,
    ! [X28957,X28958] : c_Transitive__Closure_Otrancl(X28958,X28957) = hAPP(hAPP(c_Relation_Orel__comp(X28958,X28958,X28958),c_Transitive__Closure_Ortrancl(X28958,X28957)),X28957),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).

fof(i_0_5825,plain,
    ! [X28953,X28954] : c_Transitive__Closure_Ortrancl(X28954,c_Transitive__Closure_Otrancl(X28954,X28953)) = c_Transitive__Closure_Ortrancl(X28954,X28953),
    inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(i_0_5826,plain,
    ! [X31686] : c_List_Oconcat(X31686,c_List_Olist_ONil(tc_List_Olist(X31686))) = c_List_Olist_ONil(X31686),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(i_0_5827,plain,
    ! [X21,X6] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).

fof(i_0_5828,plain,
    ! [X21,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).

fof(i_0_5829,plain,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(i_0_5830,plain,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(i_0_5831,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(i_0_5832,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X20),X19) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(i_0_5833,plain,
    ! [X33237,X33238] : c_Relation_Otrans(X33238,c_Transitive__Closure_Otrancl(X33238,X33237)),
    inference(variable_rename,[status(thm)],[fact_trans__trancl]) ).

fof(i_0_5834,plain,
    ! [X167,X75] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X75) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X167)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X75) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X167)))
             => X75 = X167 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).

fof(i_0_5835,plain,
    ! [X55,X56] :
      ( ( class_Int_Onumber__ring(X56)
        & class_Rings_Olinordered__idom(X56) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),hAPP(c_Int_Onumber__class_Onumber__of(X56),X55)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X55) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).

fof(i_0_5836,plain,
    ! [X29202] : hAPP(c_Relation_Oconverse(X29202,X29202),c_Relation_OId(X29202)) = c_Relation_OId(X29202),
    inference(variable_rename,[status(thm)],[fact_converse__Id]) ).

fof(i_0_5837,plain,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).

fof(i_0_5838,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(i_0_5839,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(i_0_5840,plain,
    ! [X26150,X26151] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X26151)),X26150) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26151),X26150)),
    inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).

fof(i_0_5841,plain,
    ! [X223,X30,X224,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),X223)) = c_List_OtakeWhile(X5,X30,X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__append1]) ).

fof(i_0_5842,plain,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).

fof(i_0_5843,plain,
    ! [X126,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126))) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(i_0_5844,plain,
    ! [X20,X19,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).

fof(i_0_5845,plain,
    ! [X6,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X6))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X21)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).

fof(i_0_5846,plain,
    ! [X25931,X25932] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25932))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25931),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X25932))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).

fof(i_0_5847,plain,
    ! [X89,X30] :
      ( ~ hBOOL(hAPP(X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X30,X89))
       => ? [X97] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X89))
            & ! [X88] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X97))
               => ~ hBOOL(hAPP(X30,X88)) )
            & hBOOL(hAPP(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_5848,plain,
    ! [X31978,X31979] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X31979,X31978) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31979),hAPP(c_Nat_OSuc,X31978))),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(i_0_5849,plain,
    ! [X26343] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X26343)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26343)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26343))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X26343))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).

fof(i_0_5850,plain,
    ! [X26358] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X26358)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26358)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X26358))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X26358))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).

fof(i_0_5851,plain,
    ! [X26165] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X26165)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X26165)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X26165))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X26165))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_5852,plain,
    ! [X26159] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X26159)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26159)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26159))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X26159))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_5853,plain,
    ! [X22,X19,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X22) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(i_0_5854,plain,
    ! [X30786,X30787,X30788] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30788,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30787)),X30786)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Orotate(X30787,X30788),X30786) = X30786 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).

fof(i_0_5855,plain,
    ! [X30760,X30761,X30762] :
      ( ( hAPP(c_List_Orotate(X30762,X30761),X30760) != c_List_Olist_ONil(X30762)
        | X30760 = c_List_Olist_ONil(X30762) )
      & ( X30760 != c_List_Olist_ONil(X30762)
        | hAPP(c_List_Orotate(X30762,X30761),X30760) = c_List_Olist_ONil(X30762) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).

fof(i_0_5856,plain,
    ! [X96,X95] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X95),X96))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X95),X96))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X96,X95) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X96),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),X95)) ) ),
    inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).

fof(i_0_5857,plain,
    ! [X26211,X26212] :
      ( ~ class_Int_Onumber__ring(X26212)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26212),c_Groups_Oone__class_Oone(X26212)),c_Groups_Oone__class_Oone(X26212))),hAPP(c_Int_Onumber__class_Onumber__of(X26212),X26211)) = hAPP(c_Int_Onumber__class_Onumber__of(X26212),c_Int_OBit0(X26211)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).

fof(i_0_5858,plain,
    ! [X21,X22,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X22))
       => X6 = X21 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X21),X22))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_5859,plain,
    ! [X26063] : c_Int_OBit1(X26063) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26063)),X26063),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_5860,plain,
    ! [X29527,X29528,X29529,X29530,X29531,X29532] : hAPP(hAPP(c_Product__Type_Ointernal__split(X29532,X29531,X29530),X29529),hAPP(hAPP(c_Product__Type_OPair(X29532,X29531),X29528),X29527)) = hAPP(hAPP(X29529,X29528),X29527),
    inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).

fof(i_0_5861,plain,
    ! [X29519,X29520,X29521] : c_Product__Type_Ointernal__split(X29521,X29520,X29519) = c_Product__Type_Oprod_Oprod__case(X29521,X29520,X29519),
    inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).

fof(i_0_5862,plain,
    ! [X32965,X32966,X32967] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32967),hAPP(c_COMBK(X32967,tc_Nat_Onat),X32966)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32965)) = c_List_Oreplicate(X32967,X32965,X32966),
    inference(variable_rename,[status(thm)],[fact_map__replicate__trivial]) ).

fof(i_0_5863,plain,
    ! [X19,X23,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19))) ),
    inference(fof_simplification,[status(thm)],[fact_ComplI]) ).

fof(i_0_5864,plain,
    ! [X17,X19,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hAPP(c_Set_Ovimage(X17,X5,hAPP(c_COMBK(X5,X17),X23)),X19) = c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19))
       => hAPP(c_Set_Ovimage(X17,X5,hAPP(c_COMBK(X5,X17),X23)),X19) = c_Orderings_Obot__class_Obot(tc_fun(X17,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).

fof(i_0_5865,plain,
    ! [X20,X19,X18,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(X2,X20),hAPP(X18,X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(i_0_5866,plain,
    ! [X31970,X31971] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X31971,X31970)) = c_List_Oupt(hAPP(c_Nat_OSuc,X31971),hAPP(c_Nat_OSuc,X31970)),
    inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).

fof(i_0_5867,plain,
    ! [X61,X60] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = c_Divides_OposDivAlg(X60,X61) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => ( ( X60 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X60,X61) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
              & ( X60 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X60,X61) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X60))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = c_Divides_OnegDivAlg(X60,X61) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))
           => c_Divides_Odivmod__int(X60,X61) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).

fof(i_0_5868,plain,
    ! [X106,X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Oappend(X5),X224),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X106))) = c_List_OtakeWhile(X5,X30,X224) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).

fof(i_0_5869,plain,
    ! [X29233] : c_Relation_Orefl__on(X29233,c_Orderings_Otop__class_Otop(tc_fun(X29233,tc_HOL_Obool)),c_Relation_OId(X29233)),
    inference(variable_rename,[status(thm)],[fact_refl__Id]) ).

fof(i_0_5870,plain,
    ! [X26072] :
      ( ~ class_Int_Onumber__ring(X26072)
      | hAPP(c_Int_Onumber__class_Onumber__of(X26072),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X26072) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_5871,plain,
    ! [X26073] :
      ( ~ class_Int_Onumber__ring(X26073)
      | c_Groups_Oone__class_Oone(X26073) = hAPP(c_Int_Onumber__class_Onumber__of(X26073),c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_5872,plain,
    ! [X89,X51] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X89)),X51)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_5873,plain,
    ! [X60,X56] :
      ( class_Groups_Oordered__ab__group__add__abs(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Groups_Oabs__class_Oabs(X56),X60)),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).

fof(i_0_5874,plain,
    ! [X86,X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),X86)),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(i_0_5875,plain,
    ! [X26185,X26186] :
      ( ( ~ c_Int_Oiszero(X26186,hAPP(c_Int_Onumber__class_Onumber__of(X26186),c_Int_OBit0(X26185)))
        | c_Int_Oiszero(X26186,hAPP(c_Int_Onumber__class_Onumber__of(X26186),X26185))
        | ~ class_Int_Onumber__ring(X26186)
        | ~ class_Int_Oring__char__0(X26186) )
      & ( ~ c_Int_Oiszero(X26186,hAPP(c_Int_Onumber__class_Onumber__of(X26186),X26185))
        | c_Int_Oiszero(X26186,hAPP(c_Int_Onumber__class_Onumber__of(X26186),c_Int_OBit0(X26185)))
        | ~ class_Int_Onumber__ring(X26186)
        | ~ class_Int_Oring__char__0(X26186) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).

fof(i_0_5876,plain,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X166),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X166),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X122),X166)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_5877,plain,
    ! [X92,X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),X92) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)),X92)) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).

fof(i_0_5878,plain,
    ! [X26175] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X26175)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X26175)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(i_0_5879,plain,
    ! [X119,X91,X93] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Random_Ominus__shift(X119,X93,X91) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X119),X93)),X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Random_Ominus__shift(X119,X93,X91) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X93),X91) ) ),
    inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).

fof(i_0_5880,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,c_Divides_Odiv__class_Omod(tc_Int_Oint,X89,X90)))
    <=> epred2_3(X30,X89,X90) ),
    inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5225]) ).

fof(i_0_5881,plain,
    ! [X94,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
       => c_List_Oupto(X98,X94) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X98),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)),X94)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X94))
       => c_List_Oupto(X98,X94) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).

fof(i_0_5882,plain,
    ! [X26134,X26135] : c_Int_OBit0(X26135) != c_Int_OBit1(X26134),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_5883,plain,
    ! [X26136,X26137] : c_Int_OBit1(X26137) != c_Int_OBit0(X26136),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_5884,plain,
    ! [X26820,X26821] : c_Divides_Odivmod__nat(X26821,X26820) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26821),X26820)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26821,X26820)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(i_0_5885,plain,
    ! [X27326,X27327,X27328,X27329] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X27329,X27328,X27327,c_Code__Numeral_OSuc__code__numeral(X27326)) = hAPP(X27327,X27326),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(i_0_5886,plain,
    ! [X31980,X31981] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X31981,X31980) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31981),X31980)),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(i_0_5887,plain,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_Oremdups(X5,X224) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Oremdups(X5,X224)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(i_0_5888,plain,
    ! [X93,X56] :
      ( class_Rings_Oring__1(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X56),X93) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X56),X93) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onat,X93)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).

fof(i_0_5889,plain,
    ! [X98,X73] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X73,X98) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X73,X98) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X98),c_Lazy__Sequence_Osmall__lazy_H(X73,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps]) ).

fof(i_0_5890,plain,
    ! [X29226] : hAPP(c_Relation_ODomain(X29226,X29226),c_Relation_OId(X29226)) = c_Orderings_Otop__class_Otop(tc_fun(X29226,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).

fof(i_0_5891,plain,
    ! [X29228] : hAPP(c_Relation_ORange(X29228,X29228),c_Relation_OId(X29228)) = c_Orderings_Otop__class_Otop(tc_fun(X29228,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__Id]) ).

fof(i_0_5892,plain,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X20),c_Big__Operators_Olattice__class_OInf__fin(X5,X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(i_0_5893,plain,
    ! [X20,X19,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X20),c_Big__Operators_Olattice__class_OSup__fin(X5,X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(i_0_5894,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X20),c_Big__Operators_Olinorder__class_OMin(X5,X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).

fof(i_0_5895,plain,
    ! [X20,X19,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X20),c_Big__Operators_Olinorder__class_OMax(X5,X19)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).

fof(i_0_5896,plain,
    ! [X33950,X33951,X33952] :
      ( ( ~ c_List_Olist__all(tc_Nat_Onat,X33952,c_List_Oupt(X33951,X33950))
        | c_List_Oall__interval__nat(X33952,X33951,X33950) )
      & ( ~ c_List_Oall__interval__nat(X33952,X33951,X33950)
        | c_List_Olist__all(tc_Nat_Onat,X33952,c_List_Oupt(X33951,X33950)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__nat])]) ).

fof(i_0_5897,plain,
    ! [X28955,X28956] : c_Transitive__Closure_Otrancl(X28956,c_Transitive__Closure_Ortrancl(X28956,X28955)) = c_Transitive__Closure_Ortrancl(X28956,X28955),
    inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(i_0_5898,plain,
    ! [X20,X5,X19] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)),X19) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_Olist_ONil(X5)),X19) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).

fof(i_0_5899,plain,
    ! [X33057,X33058,X33059] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33059),X33058),X33057))
        | hBOOL(hAPP(hAPP(c_member(X33059),X33057),hAPP(c_List_Oset(X33059),X33058))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33059),X33057),hAPP(c_List_Oset(X33059),X33058)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33059),X33058),X33057)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_List_Omember__def])]) ).

fof(i_0_5900,plain,
    ! [X33047,X33048,X33049] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33049),X33048),hAPP(c_List_Oset(X33049),X33047)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33049),X33047),X33048)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33049),X33047),X33048))
        | hBOOL(hAPP(hAPP(c_member(X33049),X33048),hAPP(c_List_Oset(X33049),X33047))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__member])]) ).

fof(i_0_5901,plain,
    ! [X166] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166))) ) ),
    inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(i_0_5902,plain,
    ! [X29212] : c_Relation_Osingle__valued(X29212,X29212,c_Relation_OId(X29212)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).

fof(i_0_5903,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_5904,plain,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_5905,axiom,
    ! [X90,X89,X30] :
      ( hBOOL(hAPP(X30,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X89),X90)))
    <=> epred1_3(X30,X89,X90) ),
    inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5226]) ).

fof(i_0_5906,plain,
    ! [X22,X19,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X22))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X20),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X20),X22)
        <=> X19 = X22 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_5907,plain,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Finite__Set_Ocard(X5),X19) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X19)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_5908,plain,
    ! [X31968,X31969] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31969),X31968))
      | c_List_Olast(tc_Nat_Onat,c_List_Oupt(X31969,X31968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31968),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])]) ).

fof(i_0_5909,plain,
    ! [X27090] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X27090)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X27090,
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(i_0_5910,plain,
    ! [X89,X51] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X89))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X51))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_5911,plain,
    ! [X31958,X31959] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X31959,X31958))),
    inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).

fof(i_0_5912,plain,
    ! [X29326,X29327] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29327,X29327),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29326) = c_Relation_OId(X29327),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(i_0_5913,plain,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),c_List_OtakeWhile(X5,X30,X224)) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => c_List_OtakeWhile(X5,X30,hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(i_0_5914,plain,
    ! [X93] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).

fof(i_0_5915,plain,
    ! [X26337] :
      ( ( c_Int_OMin != c_Int_OBit1(X26337)
        | c_Int_OMin = X26337 )
      & ( c_Int_OMin != X26337
        | c_Int_OMin = c_Int_OBit1(X26337) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).

fof(i_0_5916,plain,
    ! [X26336] :
      ( ( c_Int_OBit1(X26336) != c_Int_OMin
        | X26336 = c_Int_OMin )
      & ( X26336 != c_Int_OMin
        | c_Int_OBit1(X26336) = c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).

fof(i_0_5917,plain,
    ! [X26053] : c_Int_OBit1(X26053) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_5918,plain,
    ! [X26054] : c_Int_OPls != c_Int_OBit1(X26054),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_5919,plain,
    ! [X33398] : c_Relation_Osym(X33398,c_Relation_OId(X33398)),
    inference(variable_rename,[status(thm)],[fact_sym__Id]) ).

fof(i_0_5920,plain,
    ! [X33351] : c_Relation_Oantisym(X33351,c_Relation_OId(X33351)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id]) ).

fof(i_0_5921,plain,
    ! [X33233] : c_Relation_Otrans(X33233,c_Relation_OId(X33233)),
    inference(variable_rename,[status(thm)],[fact_trans__Id]) ).

fof(i_0_5922,plain,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X122) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(X56) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(i_0_5923,plain,
    ! [X20,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_5924,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_5925,plain,
    ! [X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(i_0_5926,plain,
    ! [X224,X20,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oinsert(X5,X20,X224) = X224 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
       => c_List_Oinsert(X5,X20,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def]) ).

fof(i_0_5927,plain,
    ! [X60,X61,X56] :
      ( class_Orderings_Oorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_5928,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20))
          | X20 = X24 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_5929,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_5930,plain,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_5931,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_5932,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_5933,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_5934,plain,
    ! [X61,X60,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),X61))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X61),X60)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_5935,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_5936,plain,
    ! [X166,X122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X122),X166)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).

fof(i_0_5937,plain,
    ! [X31953,X31954] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31954),X31953))
      | hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X31954,X31953)) = X31954 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).

fof(i_0_5938,plain,
    ! [X23,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X23),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).

fof(i_0_5939,plain,
    ! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_emptyE]) ).

fof(i_0_5940,plain,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X92))
       => X86 = hAPP(c_Nat_OSuc,X92) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_5941,plain,
    ! [X31972,X31973] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31973,X31972) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31973,hAPP(c_Nat_OSuc,X31972))),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(i_0_5942,plain,
    ! [X89,X51] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X89),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),X89)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X51),X89))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51),hAPP(c_Nat_OSuc,X89)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(i_0_5943,plain,
    ! [X224,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),hAPP(c_List_Ofilter(X5,X30),X224)) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(i_0_5944,plain,
    ! [X51,X89] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),X51))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X89),hAPP(c_Nat_OSuc,X51)))
      <=> X89 = X51 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_5945,plain,
    ! [X86,X92] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X86))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),hAPP(c_Nat_OSuc,X86)))
       => X86 = X92 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_5946,plain,
    ! [X92,X86] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => X86 = X92 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_5947,plain,
    ! [X26856,X26857] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26857,X26856),c_Divides_Odivmod__nat(X26857,X26856))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(i_0_5948,plain,
    ! [X27096] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X27096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X27096)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).

fof(i_0_5949,plain,
    ! [X31982] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X31982) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31982))),
    inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).

fof(i_0_5950,plain,
    ! [X25933] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25933),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25933)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25933),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25933)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X25933)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5227])]) ).

fof(i_0_5951,plain,
    ! [X25938] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25938),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25938)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25938),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25938)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X25938)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5228])]) ).

fof(i_0_5952,plain,
    ! [X25961,X25962] :
      ( ~ class_Int_Onumber__ring(X25962)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25962),c_Int_Opred(X25961)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25962),hAPP(c_Groups_Ouminus__class_Ouminus(X25962),c_Groups_Oone__class_Oone(X25962))),hAPP(c_Int_Onumber__class_Onumber__of(X25962),X25961)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).

fof(i_0_5953,plain,
    ! [X33235,X33236] :
      ( ~ c_Relation_Otrans(X33236,X33235)
      | c_Transitive__Closure_Otrancl(X33236,X33235) = X33235 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).

fof(i_0_5954,plain,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(i_0_5955,plain,
    ! [X106,X90,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X90,X106)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X90),X106)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(i_0_5956,plain,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(i_0_5957,plain,
    ! [X106,X90,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X90,X106) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X90),X106)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(i_0_5958,plain,
    ! [X26816,X26817] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26817),X26816))
      | c_Divides_Odivmod__nat(X26817,X26816) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26817) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).

fof(i_0_5959,plain,
    ! [X5,X22,X19] :
      ( X19 = X22
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X22))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_5960,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X92)),X92)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_5961,plain,
    ! [X93,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3div(X93,X91) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3div(X93,X91) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91))) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).

fof(i_0_5962,plain,
    ! [X92,X86] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92) ),
    inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).

fof(i_0_5963,plain,
    ! [X92,X86] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = X86 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X92) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92),X92) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__if]) ).

fof(i_0_5964,plain,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => c_List_Oinsert(X5,X20,X224) = hAPP(hAPP(c_List_Olist_OCons(X5),X20),X224) ),
    inference(fof_simplification,[status(thm)],[fact_not__in__set__insert]) ).

fof(i_0_5965,plain,
    ! [X24,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_5966,plain,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(i_0_5967,plain,
    ! [X21,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X21)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(i_0_5968,plain,
    ! [X25934] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25934),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25934)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25934),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25934)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X25934)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5229])]) ).

fof(i_0_5969,plain,
    ! [X37,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X37)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X37,X3),X3))
         => ( c_Predicate_Osymp(X5,X37)
           => ~ c_Predicate_Otransp(X5,X37) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_part__equivpE]) ).

fof(i_0_5970,plain,
    ! [X27080,X27081] :
      ( ( c_Code__Numeral_OSuc__code__numeral(X27081) != c_Code__Numeral_OSuc__code__numeral(X27080)
        | X27081 = X27080 )
      & ( X27081 != X27080
        | c_Code__Numeral_OSuc__code__numeral(X27081) = c_Code__Numeral_OSuc__code__numeral(X27080) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).

fof(i_0_5971,plain,
    ! [X27079] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X27079)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X27079)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).

fof(i_0_5972,plain,
    ! [X26140] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X26140)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26140)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_5973,plain,
    ! [X89,X5,X20,X30] :
      ( ( hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),c_List_Oreplicate(X5,X89,X20)) = c_List_Oreplicate(X5,X89,X20) )
      & ( ~ hBOOL(hAPP(X30,X20))
       => hAPP(c_List_Ofilter(X5,X30),c_List_Oreplicate(X5,X89,X20)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__replicate]) ).

fof(i_0_5974,plain,
    ! [X32311] :
      ( ~ c_List_Onat__list(X32311)
      | c_List_Oembed__list(c_List_Oreturn__list(X32311)) = X32311 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])]) ).

fof(i_0_5975,plain,
    ! [X25985] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25985)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25985)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25985)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25985)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X25985)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5230])]) ).

fof(i_0_5976,plain,
    ! [X19,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
    <=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).

fof(i_0_5977,plain,
    ! [X224,X20,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_List_Oset(X5),X224)))
     => c_List_Oremove1(X5,X20,X224) = X224 ),
    inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).

fof(i_0_5978,plain,
    ! [X31960,X31961] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X31961,X31960)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31960),X31961),
    inference(variable_rename,[status(thm)],[fact_length__upt]) ).

fof(i_0_5979,plain,
    ! [X55,X56] :
      ( class_Groups_Osgn__if(X56)
     => ( ( X55 = c_Groups_Ozero__class_Ozero(X56)
         => c_Groups_Osgn__class_Osgn(X56,X55) = c_Groups_Ozero__class_Ozero(X56) )
        & ( X55 != c_Groups_Ozero__class_Ozero(X56)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
             => c_Groups_Osgn__class_Osgn(X56,X55) = c_Groups_Oone__class_Oone(X56) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Ozero__class_Ozero(X56)),X55))
             => c_Groups_Osgn__class_Osgn(X56,X55) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),c_Groups_Oone__class_Oone(X56)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_5980,plain,
    ! [X31945,X31946] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31946),X31945))
      | c_List_Oupt(X31945,X31946) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).

fof(i_0_5981,plain,
    ! [X31943,X31944] :
      ( ( c_List_Oupt(X31944,X31943) != c_List_Olist_ONil(tc_Nat_Onat)
        | X31943 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31943),X31944)) )
      & ( X31943 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(X31944,X31943) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31943),X31944))
        | c_List_Oupt(X31944,X31943) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv])])]) ).

fof(i_0_5982,plain,
    ! [X93,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3mod(X93,X91) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X91) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
       => c_SMT_Oz3mod(X93,X91) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91)) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).

fof(i_0_5983,plain,
    ! [X60,X56] :
      ( class_Groups_Oabs__if(X56)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = hAPP(c_Groups_Ouminus__class_Ouminus(X56),X60) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X60),c_Groups_Ozero__class_Ozero(X56)))
         => hAPP(c_Groups_Oabs__class_Oabs(X56),X60) = X60 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_5984,plain,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_5985,plain,
    ! [X56] :
      ( class_Rings_Olinordered__semidom(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),c_Groups_Oone__class_Oone(X56)),c_Groups_Ozero__class_Ozero(X56))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_5986,plain,
    ! [X92,X86] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X92))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X92),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X92)) = X86 ),
    inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).

fof(i_0_5987,plain,
    ! [X31974] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X31974) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31974)),
    inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).

fof(i_0_5988,plain,
    ! [X57,X55,X56] :
      ( class_Rings_Olinordered__idom(X56)
     => ( X55 != X57
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_5989,plain,
    ! [X20,X24,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X20))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X24))
        <=> X20 = X24 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_5990,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( X55 != X57
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_5991,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => ( X55 != X57
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X57),X55)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_5992,plain,
    ! [X55,X57,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_5993,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_5994,plain,
    ! [X57,X55,X56] :
      ( class_Orderings_Olinorder(X56)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X56),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_5995,plain,
    ! [X31928,X31929] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31929,X31928)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31929),X31928),
    inference(variable_rename,[status(thm)],[fact_set__upt]) ).

fof(i_0_5996,plain,
    ! [X31930,X31931] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31931),X31930) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31931,X31930)),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(i_0_5997,plain,
    ! [X25924] : c_Int_Osucc(c_Int_Opred(X25924)) = X25924,
    inference(variable_rename,[status(thm)],[fact_succ__pred]) ).

fof(i_0_5998,plain,
    ! [X25959,X25960] :
      ( ~ class_Int_Onumber__ring(X25960)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25960),c_Int_Osucc(X25959)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25960),c_Groups_Oone__class_Oone(X25960)),hAPP(c_Int_Onumber__class_Onumber__of(X25960),X25959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).

fof(i_0_5999,plain,
    ! [X6,X5,X19] :
      ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19)) ),
    inference(fof_simplification,[status(thm)],[fact_equals0D]) ).

fof(i_0_6000,plain,
    ! [X20] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(i_0_6001,plain,
    ! [X20] :
      ~ ! [X38] :
          ( X20 = hAPP(c_Code__Numeral_Oof__nat,X38)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__cases]) ).

fof(i_0_6002,plain,
    ! [X51,X84] :
      ( hAPP(c_Int_Onat,X84) = X51
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X84 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).

fof(i_0_6003,plain,
    ! [X84,X51] :
      ( X51 = hAPP(c_Int_Onat,X84)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X84 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X51) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
         => X51 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).

fof(i_0_6004,plain,
    ! [X58] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = X58 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).

fof(i_0_6005,plain,
    ! [X55,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),X55))
       => c_Nat__Transfer_Otsub(X55,X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X55),X57) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X57),X55))
       => c_Nat__Transfer_Otsub(X55,X57) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).

fof(i_0_6006,plain,
    ! [X122,X56] :
      ( class_Int_Onumber__ring(X56)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(X56) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X56),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(X56),X122) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(i_0_6007,plain,
    ! [X33055,X33056] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X33056),c_List_Olist_ONil(X33056)),X33055)),
    inference(variable_rename,[status(thm)],[i_0_5231]) ).

fof(i_0_6008,plain,
    ! [X26931,X26932] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26932,X26931) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X26932,X26931)),
    inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).

fof(i_0_6009,plain,
    ! [X224,X5,X20,X30] :
      ( ~ hBOOL(hAPP(X30,X20))
     => c_List_Oremove1(X5,X20,hAPP(c_List_Ofilter(X5,X30),X224)) = hAPP(c_List_Ofilter(X5,X30),X224) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).

fof(i_0_6010,plain,
    ! [X27065,X27066] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X27066),X27065) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X27066,X27065)),
    inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).

fof(i_0_6011,plain,
    ! [X122] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).

fof(i_0_6012,plain,
    ! [X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X98) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = X98 ) ),
    inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).

fof(i_0_6013,plain,
    ! [X57,X55] :
      ( X55 != X57
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X55)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_6014,plain,
    ! [X26858,X26859,X26860] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26860,X26859),X26858))
      | c_Divides_Odivmod__nat(X26860,X26859) = X26858 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).

fof(i_0_6015,plain,
    ! [X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_zsgn__def]) ).

fof(i_0_6016,plain,
    ! [X32010,X32011] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X32011,X32010)),
    inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).

fof(i_0_6017,plain,
    ! [X27508,X27509] : c_Wellfounded_Owf(X27509,hAPP(c_Wellfounded_Omeasure(X27509),X27508)),
    inference(variable_rename,[status(thm)],[fact_wf__measure]) ).

fof(i_0_6018,plain,
    ! [X55,X56] :
      ( class_Orderings_Opreorder(X56)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X56),X55),X55)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_6019,plain,
    ! [X91,X93] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Quickcheck_Obeyond(X93,X91) = X91 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X93),X91))
       => c_Quickcheck_Obeyond(X93,X91) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_simplification,[status(thm)],[fact_beyond__def]) ).

fof(i_0_6020,plain,
    ! [X30748] : c_List_Orotate(X30748,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X30748)),
    inference(variable_rename,[status(thm)],[fact_rotate0]) ).

fof(i_0_6021,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_6022,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_6023,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_6024,plain,
    ! [X26815] : c_Divides_Odivmod__nat(X26815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26815),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).

fof(i_0_6025,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X92)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_6026,plain,
    ! [X92] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X92),X92)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_6027,plain,
    ! [X26148,X26149] :
      ( ( c_Int_OBit0(X26149) != c_Int_OBit0(X26148)
        | X26149 = X26148 )
      & ( X26149 != X26148
        | c_Int_OBit0(X26149) = c_Int_OBit0(X26148) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_6028,plain,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X1),X19) = c_Groups_Oone__class_Oone(X17) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(i_0_6029,plain,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__mult(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X17),X2),X19) = c_Groups_Oone__class_Oone(X17) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).

fof(i_0_6030,plain,
    ! [X2,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X2),X19) = c_Groups_Ozero__class_Ozero(X17) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).

fof(i_0_6031,plain,
    ! [X1,X19,X5,X17] :
      ( class_Groups_Ocomm__monoid__add(X17)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X17),X1),X19) = c_Groups_Ozero__class_Ozero(X17) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(i_0_6032,plain,
    ! [X92] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).

fof(i_0_6033,plain,
    ! [X78,X19,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X19,X78)
     => ~ ( c_Relation_Orefl__on(X5,X19,X78)
         => ( c_Relation_Osym(X5,X78)
           => ~ c_Relation_Otrans(X5,X78) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivE]) ).

fof(i_0_6034,plain,
    ! [X27082] : c_Code__Numeral_OSuc__code__numeral(X27082) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(i_0_6035,plain,
    ! [X27083] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X27083),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(i_0_6036,plain,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X30),X29))
      | ~ hBOOL(X30)
      | hBOOL(X29) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).

fof(i_0_6037,plain,
    ! [X19,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).

fof(i_0_6038,plain,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X30),X29))
      | hBOOL(X30)
      | hBOOL(X29) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).

fof(i_0_6039,plain,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X30),X29))
      | hBOOL(X30) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).

fof(i_0_6040,plain,
    ! [X29,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X30),X29))
      | hBOOL(X29) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).

fof(i_0_6041,plain,
    ! [X30,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X30)
    <=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).

fof(i_0_6042,plain,
    ! [X30,X5] :
      ( hAPP(c_Set_OCollect(X5),X30) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(i_0_6043,plain,
    ! [X24,X20] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X20),X24))
      | X20 = X24 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_6044,plain,
    ! [X31337] : hAPP(c_Code__Numeral_Onat__of,X31337) = c_Code__Numeral_Onat__of__aux(X31337,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).

fof(i_0_6045,plain,
    ! [X30,X5] : ~ c_List_Olist__ex1(X5,X30,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(i_0_6046,plain,
    ! [X30,X5] : ~ c_List_Olist__ex(X5,X30,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(i_0_6047,plain,
    ! [X25937] : c_Int_Opred(X25937) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25937),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_pred__def]) ).

fof(i_0_6048,plain,
    ! [X25947] : c_Int_Osucc(X25947) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25947),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_succ__def]) ).

fof(i_0_6049,plain,
    ! [X31947] : c_List_Oupt(X31947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_upt__0]) ).

fof(i_0_6050,plain,
    ! [X29,X30] :
      ( ~ hBOOL(X30)
      | ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fconj,X30),X29)) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).

fof(i_0_6051,plain,
    ! [X26346] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X26346) = c_Int_Opred(X26346),
    inference(variable_rename,[status(thm)],[fact_add__Min]) ).

fof(i_0_6052,plain,
    ! [X56] :
      ( class_Int_Onumber__ring(X56)
     => ~ c_Int_Oiszero(X56,hAPP(c_Int_Onumber__class_Onumber__of(X56),c_Int_OMin)) ),
    inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(i_0_6053,plain,
    ! [X30,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fimplies,X30),X29)) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).

fof(i_0_6054,plain,
    ! [X29,X30] :
      ( ~ hBOOL(X30)
      | hBOOL(hAPP(hAPP(c_fdisj,X30),X29)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).

fof(i_0_6055,plain,
    ! [X30,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fdisj,X30),X29)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).

fof(i_0_6056,plain,
    ! [X26138] :
      ( ( c_Int_OPls != c_Int_OBit0(X26138)
        | c_Int_OPls = X26138 )
      & ( c_Int_OPls != X26138
        | c_Int_OPls = c_Int_OBit0(X26138) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_6057,plain,
    ! [X26139] :
      ( ( c_Int_OBit0(X26139) != c_Int_OPls
        | X26139 = c_Int_OPls )
      & ( X26139 != c_Int_OPls
        | c_Int_OBit0(X26139) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_6058,plain,
    ! [X26334] : c_Int_OBit0(X26334) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(i_0_6059,plain,
    ! [X26335] : c_Int_OMin != c_Int_OBit0(X26335),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(i_0_6060,plain,
    ! [X58] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X58))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X58)) = X58 ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).

fof(i_0_6061,plain,
    ! [X19,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X19))
     => hAPP(c_Finite__Set_Ocard(X5),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_6062,plain,
    ! [X30] :
      ( ~ hBOOL(hAPP(c_fNot,X30))
      | ~ hBOOL(X30) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

fof(i_0_6063,plain,
    ! [X56] :
      ( class_Rings_Osemiring__1(X56)
     => ~ c_Int_Oiszero(X56,c_Groups_Oone__class_Oone(X56)) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).

fof(i_0_6064,plain,
    ! [X37,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X37)
     => ~ ( c_Predicate_Oreflp(X5,X37)
         => ( c_Predicate_Osymp(X5,X37)
           => ~ c_Predicate_Otransp(X5,X37) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivpE]) ).

fof(i_0_6065,plain,
    ! [X30] :
      ( hBOOL(X30)
      | hBOOL(hAPP(c_fNot,X30)) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).

fof(i_0_6066,plain,
    ! [X26004,X26005,X26006,X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26014),esk257_11(X26004,X26005,X26006,X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014)),X26013))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26014,tc_fun(X26008,tc_HOL_Obool)),X26006),hAPP(hAPP(c_COMBB(tc_fun(X26011,tc_fun(X26008,tc_HOL_Obool)),tc_fun(X26008,tc_HOL_Obool),X26014),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26011,tc_fun(X26008,tc_HOL_Obool)),X26005)),X26007))),X26004))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26011,tc_HOL_Obool)),X26005),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26011),X26010),X26009)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26014,tc_HOL_Obool)),X26006),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26014),X26013),X26012)))
        | ~ c_Equiv__Relations_Ocongruent2(X26014,X26011,tc_fun(X26008,tc_HOL_Obool),X26012,X26009,X26007)
        | ~ c_Equiv__Relations_Oequiv(X26011,X26010,X26009)
        | ~ c_Equiv__Relations_Oequiv(X26014,X26013,X26012) )
      & ( hBOOL(hAPP(hAPP(c_member(X26011),esk258_11(X26004,X26005,X26006,X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014)),X26010))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26014,tc_fun(X26008,tc_HOL_Obool)),X26006),hAPP(hAPP(c_COMBB(tc_fun(X26011,tc_fun(X26008,tc_HOL_Obool)),tc_fun(X26008,tc_HOL_Obool),X26014),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26011,tc_fun(X26008,tc_HOL_Obool)),X26005)),X26007))),X26004))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26011,tc_HOL_Obool)),X26005),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26011),X26010),X26009)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26014,tc_HOL_Obool)),X26006),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26014),X26013),X26012)))
        | ~ c_Equiv__Relations_Ocongruent2(X26014,X26011,tc_fun(X26008,tc_HOL_Obool),X26012,X26009,X26007)
        | ~ c_Equiv__Relations_Oequiv(X26011,X26010,X26009)
        | ~ c_Equiv__Relations_Oequiv(X26014,X26013,X26012) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(X26007,esk257_11(X26004,X26005,X26006,X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014)),esk258_11(X26004,X26005,X26006,X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014))),X26004))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26014,tc_fun(X26008,tc_HOL_Obool)),X26006),hAPP(hAPP(c_COMBB(tc_fun(X26011,tc_fun(X26008,tc_HOL_Obool)),tc_fun(X26008,tc_HOL_Obool),X26014),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26011,tc_fun(X26008,tc_HOL_Obool)),X26005)),X26007))),X26004))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26011,tc_HOL_Obool)),X26005),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26011),X26010),X26009)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26014,tc_HOL_Obool)),X26006),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26014),X26013),X26012)))
        | ~ c_Equiv__Relations_Ocongruent2(X26014,X26011,tc_fun(X26008,tc_HOL_Obool),X26012,X26009,X26007)
        | ~ c_Equiv__Relations_Oequiv(X26011,X26010,X26009)
        | ~ c_Equiv__Relations_Oequiv(X26014,X26013,X26012) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2])])])]) ).

fof(i_0_6067,plain,
    ! [X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33894),X33893)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),esk551_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)),esk552_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)))),c_Transitive__Closure_Ortrancl(tc_prod(X33896,X33895),X33890)))
        | hBOOL(hAPP(hAPP(X33889,X33892),X33891))
        | ~ hBOOL(hAPP(hAPP(X33889,X33894),X33893))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33894),X33893)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33892),X33891))),c_Transitive__Closure_Ortrancl(tc_prod(X33896,X33895),X33890))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),esk551_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)),esk552_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896))),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),esk553_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)),esk554_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)))),X33890))
        | hBOOL(hAPP(hAPP(X33889,X33892),X33891))
        | ~ hBOOL(hAPP(hAPP(X33889,X33894),X33893))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33894),X33893)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33892),X33891))),c_Transitive__Closure_Ortrancl(tc_prod(X33896,X33895),X33890))) )
      & ( hBOOL(hAPP(hAPP(X33889,esk551_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)),esk552_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)))
        | hBOOL(hAPP(hAPP(X33889,X33892),X33891))
        | ~ hBOOL(hAPP(hAPP(X33889,X33894),X33893))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33894),X33893)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33892),X33891))),c_Transitive__Closure_Ortrancl(tc_prod(X33896,X33895),X33890))) )
      & ( ~ hBOOL(hAPP(hAPP(X33889,esk553_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)),esk554_8(X33889,X33890,X33891,X33892,X33893,X33894,X33895,X33896)))
        | hBOOL(hAPP(hAPP(X33889,X33892),X33891))
        | ~ hBOOL(hAPP(hAPP(X33889,X33894),X33893))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33896,X33895),tc_prod(X33896,X33895))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33896,X33895),tc_prod(X33896,X33895)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33894),X33893)),hAPP(hAPP(c_Product__Type_OPair(X33896,X33895),X33892),X33891))),c_Transitive__Closure_Ortrancl(tc_prod(X33896,X33895),X33890))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).

fof(i_0_6068,plain,
    ! [X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),esk557_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)),esk558_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917))),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),esk559_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)),esk560_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)))),X33911))
        | hBOOL(hAPP(hAPP(X33910,X33915),X33914))
        | ~ hBOOL(hAPP(hAPP(X33910,X33913),X33912))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33915),X33914)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33913),X33912))),c_Transitive__Closure_Ortrancl(tc_prod(X33917,X33916),X33911))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),esk559_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)),esk560_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917))),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33913),X33912))),c_Transitive__Closure_Ortrancl(tc_prod(X33917,X33916),X33911)))
        | hBOOL(hAPP(hAPP(X33910,X33915),X33914))
        | ~ hBOOL(hAPP(hAPP(X33910,X33913),X33912))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33915),X33914)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33913),X33912))),c_Transitive__Closure_Ortrancl(tc_prod(X33917,X33916),X33911))) )
      & ( hBOOL(hAPP(hAPP(X33910,esk559_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)),esk560_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)))
        | hBOOL(hAPP(hAPP(X33910,X33915),X33914))
        | ~ hBOOL(hAPP(hAPP(X33910,X33913),X33912))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33915),X33914)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33913),X33912))),c_Transitive__Closure_Ortrancl(tc_prod(X33917,X33916),X33911))) )
      & ( ~ hBOOL(hAPP(hAPP(X33910,esk557_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)),esk558_8(X33910,X33911,X33912,X33913,X33914,X33915,X33916,X33917)))
        | hBOOL(hAPP(hAPP(X33910,X33915),X33914))
        | ~ hBOOL(hAPP(hAPP(X33910,X33913),X33912))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33917,X33916),tc_prod(X33917,X33916))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33917,X33916),tc_prod(X33917,X33916)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33915),X33914)),hAPP(hAPP(c_Product__Type_OPair(X33917,X33916),X33913),X33912))),c_Transitive__Closure_Ortrancl(tc_prod(X33917,X33916),X33911))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2])])])]) ).

cnf(i_0_6069,plain,
    c_Divides_Oadjust(X1) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(split_conjunct,[status(thm)],[i_0_5232]) ).

cnf(i_0_6070,plain,
    c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5233]) ).

cnf(i_0_6071,plain,
    c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5234]) ).

cnf(i_0_6072,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Osucc(X1),
    inference(split_conjunct,[status(thm)],[i_0_5235]) ).

fof(i_0_6073,plain,
    ! [X28000,X28001,X28002,X28003,X28004,X28005,X28006] :
      ( ~ class_Rings_Osemiring__0(X28006)
      | ~ c_Fun_Oinj__on(tc_prod(X28005,X28004),X28006,hAPP(c_Product__Type_Oprod_Oprod__case(X28005,X28004,X28006),hAPP(hAPP(c_COMBC(X28005,tc_fun(X28004,X28006),tc_fun(X28004,X28006)),hAPP(hAPP(c_COMBB(tc_fun(X28006,X28006),tc_fun(tc_fun(X28004,X28006),tc_fun(X28004,X28006)),X28005),c_COMBB(X28006,X28006,X28004)),hAPP(hAPP(c_COMBB(X28006,tc_fun(X28006,X28006),X28005),c_Groups_Otimes__class_Otimes(X28006)),X28003))),X28002)),hAPP(hAPP(c_Product__Type_OSigma(X28005,X28004),X28001),hAPP(c_COMBK(tc_fun(X28004,tc_HOL_Obool),X28005),X28000)))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28006),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28005,X28006),X28003),X28001)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28004,X28006),X28002),X28000)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28006,X28006),c_Fun_Oid(X28006)),hAPP(c_Set_OCollect(X28006),hAPP(hAPP(c_COMBB(tc_fun(X28005,tc_HOL_Obool),tc_HOL_Obool,X28006),c_HOL_OEx(X28005)),hAPP(hAPP(c_COMBB(tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool)),tc_fun(X28005,tc_HOL_Obool),X28006),hAPP(c_COMBB(tc_fun(X28004,tc_HOL_Obool),tc_HOL_Obool,X28005),c_HOL_OEx(X28004))),hAPP(hAPP(c_COMBC(X28006,tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool)),tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28005,tc_fun(tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool))),tc_fun(tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool)),tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool))),X28006),c_COMBS(X28005,tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28005,tc_fun(X28004,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X28005,tc_fun(tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool))),X28006),hAPP(c_COMBB(tc_fun(X28004,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool)),X28005),c_COMBS(X28004,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool)),tc_fun(X28005,tc_fun(X28004,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X28006),hAPP(c_COMBB(tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X28005),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28004),c_fconj))),hAPP(hAPP(c_COMBC(X28006,tc_fun(X28005,tc_fun(X28004,X28006)),tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28004,X28006),tc_fun(X28004,tc_HOL_Obool)),tc_fun(tc_fun(X28005,tc_fun(X28004,X28006)),tc_fun(X28005,tc_fun(X28004,tc_HOL_Obool))),X28006),c_COMBB(tc_fun(X28004,X28006),tc_fun(X28004,tc_HOL_Obool),X28005)),hAPP(hAPP(c_COMBB(tc_fun(X28006,tc_HOL_Obool),tc_fun(tc_fun(X28004,X28006),tc_fun(X28004,tc_HOL_Obool)),X28006),c_COMBB(X28006,tc_HOL_Obool,X28004)),c_fequal))),hAPP(hAPP(c_COMBC(X28005,tc_fun(X28004,X28006),tc_fun(X28004,X28006)),hAPP(hAPP(c_COMBB(tc_fun(X28006,X28006),tc_fun(tc_fun(X28004,X28006),tc_fun(X28004,X28006)),X28005),c_COMBB(X28006,X28006,X28004)),hAPP(hAPP(c_COMBB(X28006,tc_fun(X28006,X28006),X28005),c_Groups_Otimes__class_Otimes(X28006)),X28003))),X28002)))))),hAPP(hAPP(c_COMBC(X28005,tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28004,tc_HOL_Obool),tc_fun(X28004,tc_HOL_Obool)),X28005),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28004)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28005),c_fconj),hAPP(hAPP(c_COMBC(X28005,tc_fun(X28005,tc_HOL_Obool),tc_HOL_Obool),c_member(X28005)),X28001)))),hAPP(hAPP(c_COMBC(X28004,tc_fun(X28004,tc_HOL_Obool),tc_HOL_Obool),c_member(X28004)),X28000))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).

fof(i_0_6074,plain,
    ! [X27337,X27338,X27339,X27340,X27341] : hAPP(hAPP(c_Relation_Orel__comp(X27341,X27340,X27339),X27338),X27337) = hAPP(c_Set_OCollect(tc_prod(X27341,X27339)),hAPP(c_Product__Type_Oprod_Oprod__case(X27341,X27339,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27339,tc_fun(X27340,tc_HOL_Obool)),tc_fun(X27339,tc_HOL_Obool),X27341),hAPP(c_COMBB(tc_fun(X27340,tc_HOL_Obool),tc_HOL_Obool,X27339),c_HOL_OEx(X27340))),hAPP(hAPP(c_COMBC(X27341,tc_fun(X27339,tc_fun(X27340,tc_HOL_Obool)),tc_fun(X27339,tc_fun(X27340,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27340,tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),tc_fun(tc_fun(X27339,tc_fun(X27340,tc_HOL_Obool)),tc_fun(X27339,tc_fun(X27340,tc_HOL_Obool))),X27341),c_COMBB(tc_fun(X27340,tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool),X27339)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27340,tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),X27341),c_COMBS(X27340,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_HOL_Obool),tc_fun(X27340,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27341),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27340),c_fconj)),hAPP(hAPP(c_COMBC(X27341,tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_fun(tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),X27341),c_COMBC(X27340,tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_prod(X27341,X27340)),tc_fun(X27340,tc_fun(tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_HOL_Obool)),X27341),hAPP(c_COMBB(tc_prod(X27341,X27340),tc_fun(tc_fun(tc_prod(X27341,X27340),tc_HOL_Obool),tc_HOL_Obool),X27340),c_member(tc_prod(X27341,X27340)))),c_Product__Type_OPair(X27341,X27340)))),X27338))))),hAPP(hAPP(c_COMBC(X27339,tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_fun(tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_fun(X27340,tc_HOL_Obool)),X27339),c_COMBC(X27340,tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27340,tc_prod(X27340,X27339)),tc_fun(X27340,tc_fun(tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_HOL_Obool)),X27339),hAPP(c_COMBB(tc_prod(X27340,X27339),tc_fun(tc_fun(tc_prod(X27340,X27339),tc_HOL_Obool),tc_HOL_Obool),X27340),c_member(tc_prod(X27340,X27339)))),hAPP(c_COMBC(X27340,X27339,tc_prod(X27340,X27339)),c_Product__Type_OPair(X27340,X27339))))),X27337))))),
    inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).

fof(i_0_6075,plain,
    ! [X25412,X25413,X25414] :
      ( ~ class_Orderings_Olinorder(X25414)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25413))
      | X25413 = c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25412))
      | X25412 = c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25414),c_Big__Operators_Olattice_OInf__fin(X25414,c_Orderings_Oord__class_Omin(X25414),X25413)),c_Big__Operators_Olattice_OInf__fin(X25414,c_Orderings_Oord__class_Omin(X25414),X25412)) = c_Big__Operators_Olattice_OInf__fin(X25414,c_Orderings_Oord__class_Omin(X25414),hAPP(c_Set_OCollect(X25414),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_HOL_Obool),tc_HOL_Obool,X25414),c_HOL_OEx(X25414)),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool)),tc_fun(X25414,tc_HOL_Obool),X25414),hAPP(c_COMBB(tc_fun(X25414,tc_HOL_Obool),tc_HOL_Obool,X25414),c_HOL_OEx(X25414))),hAPP(hAPP(c_COMBC(X25414,tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool)),tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_fun(tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool))),tc_fun(tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool)),tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool))),X25414),c_COMBS(X25414,tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_fun(X25414,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25414,tc_fun(tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool))),X25414),hAPP(c_COMBB(tc_fun(X25414,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool)),X25414),c_COMBS(X25414,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool)),tc_fun(X25414,tc_fun(X25414,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25414),hAPP(c_COMBB(tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25414),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25414),c_fconj))),hAPP(hAPP(c_COMBC(X25414,tc_fun(X25414,tc_fun(X25414,X25414)),tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25414,X25414),tc_fun(X25414,tc_HOL_Obool)),tc_fun(tc_fun(X25414,tc_fun(X25414,X25414)),tc_fun(X25414,tc_fun(X25414,tc_HOL_Obool))),X25414),c_COMBB(tc_fun(X25414,X25414),tc_fun(X25414,tc_HOL_Obool),X25414)),hAPP(hAPP(c_COMBB(tc_fun(X25414,tc_HOL_Obool),tc_fun(tc_fun(X25414,X25414),tc_fun(X25414,tc_HOL_Obool)),X25414),c_COMBB(X25414,tc_HOL_Obool,X25414)),c_fequal))),c_Orderings_Oord__class_Omax(X25414)))))),hAPP(hAPP(c_COMBC(X25414,tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25414,tc_HOL_Obool),tc_fun(X25414,tc_HOL_Obool)),X25414),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25414)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25414),c_fconj),hAPP(hAPP(c_COMBC(X25414,tc_fun(X25414,tc_HOL_Obool),tc_HOL_Obool),c_member(X25414)),X25413)))),hAPP(hAPP(c_COMBC(X25414,tc_fun(X25414,tc_HOL_Obool),tc_HOL_Obool),c_member(X25414)),X25412))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).

fof(i_0_6076,plain,
    ! [X25452,X25453,X25454] :
      ( ~ class_Orderings_Olinorder(X25454)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25454),X25453))
      | X25453 = c_Orderings_Obot__class_Obot(tc_fun(X25454,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25454),X25452))
      | X25452 = c_Orderings_Obot__class_Obot(tc_fun(X25454,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25454),c_Big__Operators_Olattice_OSup__fin(X25454,c_Orderings_Oord__class_Omax(X25454),X25453)),c_Big__Operators_Olattice_OSup__fin(X25454,c_Orderings_Oord__class_Omax(X25454),X25452)) = c_Big__Operators_Olattice_OSup__fin(X25454,c_Orderings_Oord__class_Omax(X25454),hAPP(c_Set_OCollect(X25454),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_HOL_Obool),tc_HOL_Obool,X25454),c_HOL_OEx(X25454)),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool)),tc_fun(X25454,tc_HOL_Obool),X25454),hAPP(c_COMBB(tc_fun(X25454,tc_HOL_Obool),tc_HOL_Obool,X25454),c_HOL_OEx(X25454))),hAPP(hAPP(c_COMBC(X25454,tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool)),tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_fun(tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool))),tc_fun(tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool)),tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool))),X25454),c_COMBS(X25454,tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_fun(X25454,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25454,tc_fun(tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool))),X25454),hAPP(c_COMBB(tc_fun(X25454,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool)),X25454),c_COMBS(X25454,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool)),tc_fun(X25454,tc_fun(X25454,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25454),hAPP(c_COMBB(tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25454),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25454),c_fconj))),hAPP(hAPP(c_COMBC(X25454,tc_fun(X25454,tc_fun(X25454,X25454)),tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25454,X25454),tc_fun(X25454,tc_HOL_Obool)),tc_fun(tc_fun(X25454,tc_fun(X25454,X25454)),tc_fun(X25454,tc_fun(X25454,tc_HOL_Obool))),X25454),c_COMBB(tc_fun(X25454,X25454),tc_fun(X25454,tc_HOL_Obool),X25454)),hAPP(hAPP(c_COMBB(tc_fun(X25454,tc_HOL_Obool),tc_fun(tc_fun(X25454,X25454),tc_fun(X25454,tc_HOL_Obool)),X25454),c_COMBB(X25454,tc_HOL_Obool,X25454)),c_fequal))),c_Orderings_Oord__class_Omin(X25454)))))),hAPP(hAPP(c_COMBC(X25454,tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25454,tc_HOL_Obool),tc_fun(X25454,tc_HOL_Obool)),X25454),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25454)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25454),c_fconj),hAPP(hAPP(c_COMBC(X25454,tc_fun(X25454,tc_HOL_Obool),tc_HOL_Obool),c_member(X25454)),X25453)))),hAPP(hAPP(c_COMBC(X25454,tc_fun(X25454,tc_HOL_Obool),tc_HOL_Obool),c_member(X25454)),X25452))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).

fof(i_0_6077,plain,
    ! [X25446,X25447,X25448] :
      ( ~ class_Lattices_Odistrib__lattice(X25448)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25448),X25447))
      | X25447 = c_Orderings_Obot__class_Obot(tc_fun(X25448,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25448),X25446))
      | X25446 = c_Orderings_Obot__class_Obot(tc_fun(X25448,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25448),c_Big__Operators_Olattice__class_OSup__fin(X25448,X25447)),c_Big__Operators_Olattice__class_OSup__fin(X25448,X25446)) = c_Big__Operators_Olattice__class_OSup__fin(X25448,hAPP(c_Set_OCollect(X25448),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_HOL_Obool),tc_HOL_Obool,X25448),c_HOL_OEx(X25448)),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool)),tc_fun(X25448,tc_HOL_Obool),X25448),hAPP(c_COMBB(tc_fun(X25448,tc_HOL_Obool),tc_HOL_Obool,X25448),c_HOL_OEx(X25448))),hAPP(hAPP(c_COMBC(X25448,tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool)),tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_fun(tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool))),tc_fun(tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool)),tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool))),X25448),c_COMBS(X25448,tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_fun(X25448,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25448,tc_fun(tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool))),X25448),hAPP(c_COMBB(tc_fun(X25448,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool)),X25448),c_COMBS(X25448,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool)),tc_fun(X25448,tc_fun(X25448,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25448),hAPP(c_COMBB(tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25448),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25448),c_fconj))),hAPP(hAPP(c_COMBC(X25448,tc_fun(X25448,tc_fun(X25448,X25448)),tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25448,X25448),tc_fun(X25448,tc_HOL_Obool)),tc_fun(tc_fun(X25448,tc_fun(X25448,X25448)),tc_fun(X25448,tc_fun(X25448,tc_HOL_Obool))),X25448),c_COMBB(tc_fun(X25448,X25448),tc_fun(X25448,tc_HOL_Obool),X25448)),hAPP(hAPP(c_COMBB(tc_fun(X25448,tc_HOL_Obool),tc_fun(tc_fun(X25448,X25448),tc_fun(X25448,tc_HOL_Obool)),X25448),c_COMBB(X25448,tc_HOL_Obool,X25448)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X25448)))))),hAPP(hAPP(c_COMBC(X25448,tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25448,tc_HOL_Obool),tc_fun(X25448,tc_HOL_Obool)),X25448),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25448)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25448),c_fconj),hAPP(hAPP(c_COMBC(X25448,tc_fun(X25448,tc_HOL_Obool),tc_HOL_Obool),c_member(X25448)),X25447)))),hAPP(hAPP(c_COMBC(X25448,tc_fun(X25448,tc_HOL_Obool),tc_HOL_Obool),c_member(X25448)),X25446))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).

fof(i_0_6078,plain,
    ! [X25440,X25441,X25442] :
      ( ~ class_Lattices_Odistrib__lattice(X25442)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25442),X25441))
      | X25441 = c_Orderings_Obot__class_Obot(tc_fun(X25442,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25442),X25440))
      | X25440 = c_Orderings_Obot__class_Obot(tc_fun(X25442,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25442),c_Big__Operators_Olattice__class_OInf__fin(X25442,X25441)),c_Big__Operators_Olattice__class_OInf__fin(X25442,X25440)) = c_Big__Operators_Olattice__class_OInf__fin(X25442,hAPP(c_Set_OCollect(X25442),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_HOL_Obool),tc_HOL_Obool,X25442),c_HOL_OEx(X25442)),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool)),tc_fun(X25442,tc_HOL_Obool),X25442),hAPP(c_COMBB(tc_fun(X25442,tc_HOL_Obool),tc_HOL_Obool,X25442),c_HOL_OEx(X25442))),hAPP(hAPP(c_COMBC(X25442,tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool)),tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_fun(tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool))),tc_fun(tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool)),tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool))),X25442),c_COMBS(X25442,tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_fun(X25442,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25442,tc_fun(tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool))),X25442),hAPP(c_COMBB(tc_fun(X25442,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool)),X25442),c_COMBS(X25442,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool)),tc_fun(X25442,tc_fun(X25442,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25442),hAPP(c_COMBB(tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25442),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25442),c_fconj))),hAPP(hAPP(c_COMBC(X25442,tc_fun(X25442,tc_fun(X25442,X25442)),tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25442,X25442),tc_fun(X25442,tc_HOL_Obool)),tc_fun(tc_fun(X25442,tc_fun(X25442,X25442)),tc_fun(X25442,tc_fun(X25442,tc_HOL_Obool))),X25442),c_COMBB(tc_fun(X25442,X25442),tc_fun(X25442,tc_HOL_Obool),X25442)),hAPP(hAPP(c_COMBB(tc_fun(X25442,tc_HOL_Obool),tc_fun(tc_fun(X25442,X25442),tc_fun(X25442,tc_HOL_Obool)),X25442),c_COMBB(X25442,tc_HOL_Obool,X25442)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X25442)))))),hAPP(hAPP(c_COMBC(X25442,tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25442,tc_HOL_Obool),tc_fun(X25442,tc_HOL_Obool)),X25442),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25442)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25442),c_fconj),hAPP(hAPP(c_COMBC(X25442,tc_fun(X25442,tc_HOL_Obool),tc_HOL_Obool),c_member(X25442)),X25441)))),hAPP(hAPP(c_COMBC(X25442,tc_fun(X25442,tc_HOL_Obool),tc_HOL_Obool),c_member(X25442)),X25440))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).

fof(i_0_6079,plain,
    ! [X29578,X29579,X29580] : c_List_Oset__Cons(X29580,X29579,X29578) = hAPP(c_Set_OCollect(tc_List_Olist(X29580)),hAPP(hAPP(c_COMBB(tc_fun(X29580,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X29580)),c_HOL_OEx(X29580)),hAPP(hAPP(c_COMBB(tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_fun(X29580,tc_HOL_Obool),tc_List_Olist(X29580)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_HOL_Obool,X29580),c_HOL_OEx(tc_List_Olist(X29580)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29580),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29580,tc_fun(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),tc_fun(tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),tc_List_Olist(X29580)),c_COMBS(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29580,tc_fun(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),tc_List_Olist(X29580)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29580),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),X29580),c_COMBS(tc_List_Olist(X29580),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X29580)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29580),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29580)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29580),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_List_Olist(X29580))),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X29580),tc_List_Olist(X29580)),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_fun(tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_List_Olist(X29580))),tc_fun(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool))),tc_List_Olist(X29580)),c_COMBB(tc_fun(tc_List_Olist(X29580),tc_List_Olist(X29580)),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),X29580)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29580),tc_List_Olist(X29580)),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),tc_List_Olist(X29580)),c_COMBB(tc_List_Olist(X29580),tc_HOL_Obool,tc_List_Olist(X29580))),c_fequal))),c_List_Olist_OCons(X29580)))))),hAPP(hAPP(c_COMBC(X29580,tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool)),X29580),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X29580))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29580),c_fconj),hAPP(hAPP(c_COMBC(X29580,tc_fun(X29580,tc_HOL_Obool),tc_HOL_Obool),c_member(X29580)),X29579)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29580),tc_fun(tc_List_Olist(X29580),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X29580))),X29578)))))),
    inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).

fof(i_0_6080,plain,
    ! [X28155,X28156,X28157,X28158,X28159,X28160,X28161,X28162] :
      ( ( X28160 = hAPP(hAPP(c_Product__Type_OPair(X28162,X28161),hAPP(X28157,esk308_8(X28155,X28156,X28157,X28158,X28159,X28160,X28161,X28162))),hAPP(X28156,esk309_8(X28155,X28156,X28157,X28158,X28159,X28160,X28161,X28162)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28162,X28161)),X28160),hAPP(c_Set_Oimage(tc_prod(X28159,X28158),tc_prod(X28162,X28161),c_Product__Type_Omap__pair(X28159,X28162,X28158,X28161,X28157,X28156)),X28155))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28159,X28158)),hAPP(hAPP(c_Product__Type_OPair(X28159,X28158),esk308_8(X28155,X28156,X28157,X28158,X28159,X28160,X28161,X28162)),esk309_8(X28155,X28156,X28157,X28158,X28159,X28160,X28161,X28162))),X28155))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28162,X28161)),X28160),hAPP(c_Set_Oimage(tc_prod(X28159,X28158),tc_prod(X28162,X28161),c_Product__Type_Omap__pair(X28159,X28162,X28158,X28161,X28157,X28156)),X28155))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5236])])])]) ).

fof(i_0_6081,plain,
    ! [X33901,X33902,X33903,X33904,X33905,X33906,X33907] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33907,X33906),tc_prod(X33907,X33906))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33907,X33906),tc_prod(X33907,X33906)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33905),X33904)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),esk555_7(X33901,X33902,X33903,X33904,X33905,X33906,X33907)),esk556_7(X33901,X33902,X33903,X33904,X33905,X33906,X33907)))),X33901))
        | hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33905),X33904) = hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33903),X33902)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33907,X33906),tc_prod(X33907,X33906))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33907,X33906),tc_prod(X33907,X33906)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33905),X33904)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33903),X33902))),c_Transitive__Closure_Ortrancl(tc_prod(X33907,X33906),X33901))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33907,X33906),tc_prod(X33907,X33906))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33907,X33906),tc_prod(X33907,X33906)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),esk555_7(X33901,X33902,X33903,X33904,X33905,X33906,X33907)),esk556_7(X33901,X33902,X33903,X33904,X33905,X33906,X33907))),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33903),X33902))),c_Transitive__Closure_Ortrancl(tc_prod(X33907,X33906),X33901)))
        | hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33905),X33904) = hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33903),X33902)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33907,X33906),tc_prod(X33907,X33906))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33907,X33906),tc_prod(X33907,X33906)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33905),X33904)),hAPP(hAPP(c_Product__Type_OPair(X33907,X33906),X33903),X33902))),c_Transitive__Closure_Ortrancl(tc_prod(X33907,X33906),X33901))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5237])])])]) ).

cnf(i_0_6082,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5238]) ).

cnf(i_0_6083,plain,
    c_Product__Type_Oapsnd(X1,X2,X3,X4) = c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_5239]) ).

cnf(i_0_6084,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5240]) ).

fof(i_0_6085,plain,
    ! [X23279,X23280,X23281,X23282,X23283,X23284,X23285,X23286] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23282),esk153_8(X23279,X23280,X23281,X23282,X23283,X23284,X23285,X23286)),X23281))
        | ~ hBOOL(hAPP(hAPP(c_member(X23282),X23279),X23281))
        | hAPP(c_Set_Oimage(X23286,X23285,X23284),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X23282,tc_fun(X23286,tc_HOL_Obool)),X23281),X23280)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X23282,tc_fun(X23285,tc_HOL_Obool)),X23281),hAPP(hAPP(c_COMBB(tc_fun(X23286,tc_HOL_Obool),tc_fun(X23285,tc_HOL_Obool),X23282),c_Set_Oimage(X23286,X23285,X23284)),X23280))
        | ~ c_Fun_Oinj__on(X23286,X23285,X23284,X23283) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23286,tc_HOL_Obool)),hAPP(X23280,esk153_8(X23279,X23280,X23281,X23282,X23283,X23284,X23285,X23286))),X23283))
        | ~ hBOOL(hAPP(hAPP(c_member(X23282),X23279),X23281))
        | hAPP(c_Set_Oimage(X23286,X23285,X23284),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X23282,tc_fun(X23286,tc_HOL_Obool)),X23281),X23280)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X23282,tc_fun(X23285,tc_HOL_Obool)),X23281),hAPP(hAPP(c_COMBB(tc_fun(X23286,tc_HOL_Obool),tc_fun(X23285,tc_HOL_Obool),X23282),c_Set_Oimage(X23286,X23285,X23284)),X23280))
        | ~ c_Fun_Oinj__on(X23286,X23285,X23284,X23283) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__INT])])])]) ).

fof(i_0_6086,plain,
    ! [X26419,X26420,X26421,X26422,X26423,X26424] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26424,tc_fun(X26423,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26424,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),X26424),c_COMBC(X26423,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_prod(X26424,X26423)),tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),X26424),hAPP(c_COMBB(tc_prod(X26424,X26423),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool),X26423),c_member(tc_prod(X26424,X26423)))),c_Product__Type_OPair(X26424,X26423)))),X26422)),hAPP(hAPP(c_COMBC(X26424,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),X26424),c_COMBC(X26423,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_prod(X26424,X26423)),tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),X26424),hAPP(c_COMBB(tc_prod(X26424,X26423),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool),X26423),c_member(tc_prod(X26424,X26423)))),c_Product__Type_OPair(X26424,X26423)))),X26421)),X26420),X26419))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26424,X26423)),hAPP(hAPP(c_Product__Type_OPair(X26424,X26423),X26420),X26419)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool)),X26422),X26421))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26424,X26423)),hAPP(hAPP(c_Product__Type_OPair(X26424,X26423),X26420),X26419)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool)),X26422),X26421)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26424,tc_fun(X26423,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26424,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),X26424),c_COMBC(X26423,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_prod(X26424,X26423)),tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),X26424),hAPP(c_COMBB(tc_prod(X26424,X26423),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool),X26423),c_member(tc_prod(X26424,X26423)))),c_Product__Type_OPair(X26424,X26423)))),X26422)),hAPP(hAPP(c_COMBC(X26424,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_fun(X26423,tc_HOL_Obool)),X26424),c_COMBC(X26423,tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26423,tc_prod(X26424,X26423)),tc_fun(X26423,tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool)),X26424),hAPP(c_COMBB(tc_prod(X26424,X26423),tc_fun(tc_fun(tc_prod(X26424,X26423),tc_HOL_Obool),tc_HOL_Obool),X26423),c_member(tc_prod(X26424,X26423)))),c_Product__Type_OPair(X26424,X26423)))),X26421)),X26420),X26419)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).

fof(i_0_6087,plain,
    ! [X26401,X26402,X26403,X26404,X26405,X26406] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26406,tc_fun(X26405,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26406,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),X26406),c_COMBC(X26405,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_prod(X26406,X26405)),tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),X26406),hAPP(c_COMBB(tc_prod(X26406,X26405),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool),X26405),c_member(tc_prod(X26406,X26405)))),c_Product__Type_OPair(X26406,X26405)))),X26404)),hAPP(hAPP(c_COMBC(X26406,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),X26406),c_COMBC(X26405,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_prod(X26406,X26405)),tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),X26406),hAPP(c_COMBB(tc_prod(X26406,X26405),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool),X26405),c_member(tc_prod(X26406,X26405)))),c_Product__Type_OPair(X26406,X26405)))),X26403)),X26402),X26401))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26406,X26405)),hAPP(hAPP(c_Product__Type_OPair(X26406,X26405),X26402),X26401)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool)),X26404),X26403))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26406,X26405)),hAPP(hAPP(c_Product__Type_OPair(X26406,X26405),X26402),X26401)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool)),X26404),X26403)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26406,tc_fun(X26405,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26406,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),X26406),c_COMBC(X26405,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_prod(X26406,X26405)),tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),X26406),hAPP(c_COMBB(tc_prod(X26406,X26405),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool),X26405),c_member(tc_prod(X26406,X26405)))),c_Product__Type_OPair(X26406,X26405)))),X26404)),hAPP(hAPP(c_COMBC(X26406,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_fun(X26405,tc_HOL_Obool)),X26406),c_COMBC(X26405,tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26405,tc_prod(X26406,X26405)),tc_fun(X26405,tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool)),X26406),hAPP(c_COMBB(tc_prod(X26406,X26405),tc_fun(tc_fun(tc_prod(X26406,X26405),tc_HOL_Obool),tc_HOL_Obool),X26405),c_member(tc_prod(X26406,X26405)))),c_Product__Type_OPair(X26406,X26405)))),X26403)),X26402),X26401)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).

fof(i_0_6088,plain,
    ! [X29546,X29547] : c_List_Olenlex(X29547,X29546) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X29547),tc_List_Olist(X29547),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X29547),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),tc_List_Olist(X29547)),c_COMBS(tc_List_Olist(X29547),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X29547)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29547)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29547),tc_fun(tc_List_Olist(X29547),tc_Nat_Onat),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29547),tc_Nat_Onat),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),tc_List_Olist(X29547)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X29547))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29547)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X29547))))),c_Nat_Osize__class_Osize(tc_List_Olist(X29547)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X29547),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),tc_List_Olist(X29547)),c_COMBS(tc_List_Olist(X29547),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X29547)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29547)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29547),tc_fun(tc_List_Olist(X29547),tc_Nat_Onat),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29547),tc_Nat_Onat),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),tc_List_Olist(X29547)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X29547))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29547)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29547))))),c_Nat_Osize__class_Osize(tc_List_Olist(X29547)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29547),tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_fun(tc_List_Olist(X29547),tc_HOL_Obool)),tc_List_Olist(X29547)),c_COMBC(tc_List_Olist(X29547),tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29547),tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547))),tc_fun(tc_List_Olist(X29547),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X29547)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29547)),c_member(tc_prod(tc_List_Olist(X29547),tc_List_Olist(X29547))))),c_Product__Type_OPair(tc_List_Olist(X29547),tc_List_Olist(X29547))))),c_List_Olex(X29547,X29546)))))),
    inference(variable_rename,[status(thm)],[fact_lenlex__conv]) ).

fof(i_0_6089,plain,
    ! [X32467,X32468,X32469,X32470,X32471,X32472,X32473,X32474] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32474),esk455_8(X32467,X32468,X32469,X32470,X32471,X32472,X32473,X32474)),hAPP(c_List_Oset(X32474),X32473)))
        | hAPP(c_List_Ofoldl(X32472,X32474,hAPP(c_COMBC(X32474,X32472,X32472),X32470),hAPP(X32469,X32467)),X32473) = hAPP(X32469,hAPP(c_List_Ofoldl(X32471,X32474,hAPP(c_COMBC(X32474,X32471,X32471),X32468),X32467),X32473)) )
      & ( hAPP(c_Fun_Ocomp(X32472,X32472,X32471,hAPP(X32470,esk455_8(X32467,X32468,X32469,X32470,X32471,X32472,X32473,X32474))),X32469) != hAPP(c_Fun_Ocomp(X32471,X32472,X32471,X32469),hAPP(X32468,esk455_8(X32467,X32468,X32469,X32470,X32471,X32472,X32473,X32474)))
        | hAPP(c_List_Ofoldl(X32472,X32474,hAPP(c_COMBC(X32474,X32472,X32472),X32470),hAPP(X32469,X32467)),X32473) = hAPP(X32469,hAPP(c_List_Ofoldl(X32471,X32474,hAPP(c_COMBC(X32474,X32471,X32471),X32468),X32467),X32473)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__apply])])])]) ).

cnf(i_0_6090,plain,
    c_Nitpick_Oplus__frac(X1,X2,X3) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X1),X2),hAPP(c_Nitpick_Odenom(X1),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X3)))))),c_COMBI(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_5241]) ).

cnf(i_0_6091,plain,
    c_Nitpick_Odenom(X1) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5242]) ).

cnf(i_0_6092,plain,
    c_Nitpick_Onum(X1) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5243]) ).

fof(i_0_6093,plain,
    ! [X26475,X26476,X26477,X26478,X26479,X26480] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26480,tc_fun(X26479,tc_fun(X26478,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26480,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26479,tc_fun(X26478,tc_HOL_Obool)),X26480),hAPP(c_COMBC(X26479,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26478,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26478,tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26478,tc_HOL_Obool)),X26479),c_COMBC(X26478,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26478,tc_prod(X26479,X26478)),tc_fun(X26478,tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),X26479),hAPP(c_COMBB(tc_prod(X26479,X26478),tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool),X26478),c_member(tc_prod(X26479,X26478)))),c_Product__Type_OPair(X26479,X26478))))),X26477)),X26476),X26475))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26479,X26478)),hAPP(hAPP(c_Product__Type_OPair(X26479,X26478),X26476),X26475)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26480,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26480,tc_HOL_Obool))),X26477))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26479,X26478)),hAPP(hAPP(c_Product__Type_OPair(X26479,X26478),X26476),X26475)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26480,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26480,tc_HOL_Obool))),X26477)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26480,tc_fun(X26479,tc_fun(X26478,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26480,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26479,tc_fun(X26478,tc_HOL_Obool)),X26480),hAPP(c_COMBC(X26479,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26478,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26478,tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_fun(X26478,tc_HOL_Obool)),X26479),c_COMBC(X26478,tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26478,tc_prod(X26479,X26478)),tc_fun(X26478,tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool)),X26479),hAPP(c_COMBB(tc_prod(X26479,X26478),tc_fun(tc_fun(tc_prod(X26479,X26478),tc_HOL_Obool),tc_HOL_Obool),X26478),c_member(tc_prod(X26479,X26478)))),c_Product__Type_OPair(X26479,X26478))))),X26477)),X26476),X26475)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).

fof(i_0_6094,plain,
    ! [X26481,X26482,X26483,X26484,X26485,X26486] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26486,tc_fun(X26485,tc_fun(X26484,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26486,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26485,tc_fun(X26484,tc_HOL_Obool)),X26486),hAPP(c_COMBC(X26485,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26484,tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26484,tc_HOL_Obool)),X26485),c_COMBC(X26484,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26484,tc_prod(X26485,X26484)),tc_fun(X26484,tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),X26485),hAPP(c_COMBB(tc_prod(X26485,X26484),tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool),X26484),c_member(tc_prod(X26485,X26484)))),c_Product__Type_OPair(X26485,X26484))))),X26483)),X26482),X26481))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26485,X26484)),hAPP(hAPP(c_Product__Type_OPair(X26485,X26484),X26482),X26481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26486,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26486,tc_HOL_Obool))),X26483))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26485,X26484)),hAPP(hAPP(c_Product__Type_OPair(X26485,X26484),X26482),X26481)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26486,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26486,tc_HOL_Obool))),X26483)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26486,tc_fun(X26485,tc_fun(X26484,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26486,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26485,tc_fun(X26484,tc_HOL_Obool)),X26486),hAPP(c_COMBC(X26485,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26484,tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_fun(X26484,tc_HOL_Obool)),X26485),c_COMBC(X26484,tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26484,tc_prod(X26485,X26484)),tc_fun(X26484,tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool)),X26485),hAPP(c_COMBB(tc_prod(X26485,X26484),tc_fun(tc_fun(tc_prod(X26485,X26484),tc_HOL_Obool),tc_HOL_Obool),X26484),c_member(tc_prod(X26485,X26484)))),c_Product__Type_OPair(X26485,X26484))))),X26483)),X26482),X26481)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])]) ).

fof(i_0_6095,plain,
    ! [X27469,X27470,X27471,X27472,X27473,X27474,X27475] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27475,X27474,X27473,hAPP(hAPP(c_COMBC(X27475,tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_fun(X27474,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_fun(X27474,tc_HOL_Obool)),X27475),c_COMBC(X27474,tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_prod(X27475,X27474)),tc_fun(X27474,tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),X27475),hAPP(c_COMBB(tc_prod(X27475,X27474),tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool),X27474),c_member(tc_prod(X27475,X27474)))),c_Product__Type_OPair(X27475,X27474)))),X27472),hAPP(hAPP(c_COMBC(X27474,tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_fun(X27473,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27473,tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_fun(X27473,tc_HOL_Obool)),X27474),c_COMBC(X27473,tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27473,tc_prod(X27474,X27473)),tc_fun(X27473,tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),X27474),hAPP(c_COMBB(tc_prod(X27474,X27473),tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool),X27473),c_member(tc_prod(X27474,X27473)))),c_Product__Type_OPair(X27474,X27473)))),X27471)),X27470),X27469))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27475,X27473)),hAPP(hAPP(c_Product__Type_OPair(X27475,X27473),X27470),X27469)),hAPP(hAPP(c_Relation_Orel__comp(X27475,X27474,X27473),X27472),X27471))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27475,X27473)),hAPP(hAPP(c_Product__Type_OPair(X27475,X27473),X27470),X27469)),hAPP(hAPP(c_Relation_Orel__comp(X27475,X27474,X27473),X27472),X27471)))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27475,X27474,X27473,hAPP(hAPP(c_COMBC(X27475,tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_fun(X27474,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_fun(X27474,tc_HOL_Obool)),X27475),c_COMBC(X27474,tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_prod(X27475,X27474)),tc_fun(X27474,tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool)),X27475),hAPP(c_COMBB(tc_prod(X27475,X27474),tc_fun(tc_fun(tc_prod(X27475,X27474),tc_HOL_Obool),tc_HOL_Obool),X27474),c_member(tc_prod(X27475,X27474)))),c_Product__Type_OPair(X27475,X27474)))),X27472),hAPP(hAPP(c_COMBC(X27474,tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_fun(X27473,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27473,tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_fun(X27473,tc_HOL_Obool)),X27474),c_COMBC(X27473,tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27473,tc_prod(X27474,X27473)),tc_fun(X27473,tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool)),X27474),hAPP(c_COMBB(tc_prod(X27474,X27473),tc_fun(tc_fun(tc_prod(X27474,X27473),tc_HOL_Obool),tc_HOL_Obool),X27473),c_member(tc_prod(X27474,X27473)))),c_Product__Type_OPair(X27474,X27473)))),X27471)),X27470),X27469)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).

cnf(i_0_6096,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5244]) ).

cnf(i_0_6097,plain,
    c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5245]) ).

fof(i_0_6098,plain,
    ! [X26833,X26834,X26835,X26836,X26837,X26838,X26839] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26839),esk265_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839)),X26838))
        | X26834 = X26833
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26833),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26834),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26834),X26835) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26833),X26835)
        | ~ c_Equiv__Relations_Ocongruent(X26839,tc_fun(X26836,tc_HOL_Obool),X26837,X26835)
        | ~ c_Equiv__Relations_Oequiv(X26839,X26838,X26837) )
      & ( hBOOL(hAPP(hAPP(c_member(X26839),esk266_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839)),X26838))
        | X26834 = X26833
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26833),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26834),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26834),X26835) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26833),X26835)
        | ~ c_Equiv__Relations_Ocongruent(X26839,tc_fun(X26836,tc_HOL_Obool),X26837,X26835)
        | ~ c_Equiv__Relations_Oequiv(X26839,X26838,X26837) )
      & ( hAPP(X26835,esk265_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839)) = hAPP(X26835,esk266_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839))
        | X26834 = X26833
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26833),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26834),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26834),X26835) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26833),X26835)
        | ~ c_Equiv__Relations_Ocongruent(X26839,tc_fun(X26836,tc_HOL_Obool),X26837,X26835)
        | ~ c_Equiv__Relations_Oequiv(X26839,X26838,X26837) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26839,X26839)),hAPP(hAPP(c_Product__Type_OPair(X26839,X26839),esk265_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839)),esk266_7(X26833,X26834,X26835,X26836,X26837,X26838,X26839))),X26837))
        | X26834 = X26833
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26833),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26839,tc_HOL_Obool)),X26834),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26839),X26838),X26837)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26834),X26835) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26839,tc_fun(X26836,tc_HOL_Obool)),X26833),X26835)
        | ~ c_Equiv__Relations_Ocongruent(X26839,tc_fun(X26836,tc_HOL_Obool),X26837,X26835)
        | ~ c_Equiv__Relations_Oequiv(X26839,X26838,X26837) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject])])])]) ).

cnf(i_0_6099,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Relation_OId(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5244]) ).

cnf(i_0_6100,plain,
    hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_5246]) ).

fof(i_0_6101,plain,
    ! [X25421,X25422,X25423,X25424] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25424),hAPP(c_Set_OCollect(X25424),X25423)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X25422),hAPP(c_Set_OCollect(X25422),hAPP(hAPP(c_COMBB(tc_fun(X25424,tc_HOL_Obool),tc_HOL_Obool,X25422),c_HOL_OEx(X25424)),hAPP(hAPP(c_COMBC(X25422,tc_fun(X25424,tc_HOL_Obool),tc_fun(X25424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25424,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25424,tc_HOL_Obool),tc_fun(X25424,tc_HOL_Obool)),X25422),c_COMBS(X25424,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25424,tc_HOL_Obool),tc_fun(X25424,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25422),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25424),c_fconj)),hAPP(hAPP(c_COMBC(X25422,tc_fun(X25424,X25422),tc_fun(X25424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25422,tc_HOL_Obool),tc_fun(tc_fun(X25424,X25422),tc_fun(X25424,tc_HOL_Obool)),X25422),c_COMBB(X25422,tc_HOL_Obool,X25424)),c_fequal)),X25421)))),X25423))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).

fof(i_0_6102,plain,
    ! [X18221,X18222,X18223,X18224,X18225,X18226,X18227,X18228] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18227),esk35_8(X18221,X18222,X18223,X18224,X18225,X18226,X18227,X18228)),X18224))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18226,X18228),X18221),X18223) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18227,X18228),X18222),X18224)
        | X18223 != hAPP(c_Set_Oimage(X18227,X18226,X18225),X18224)
        | ~ c_Fun_Oinj__on(X18227,X18226,X18225,X18224)
        | ~ class_Groups_Ocomm__monoid__add(X18228) )
      & ( hAPP(X18222,esk35_8(X18221,X18222,X18223,X18224,X18225,X18226,X18227,X18228)) != hAPP(X18221,hAPP(X18225,esk35_8(X18221,X18222,X18223,X18224,X18225,X18226,X18227,X18228)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18226,X18228),X18221),X18223) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18227,X18228),X18222),X18224)
        | X18223 != hAPP(c_Set_Oimage(X18227,X18226,X18225),X18224)
        | ~ c_Fun_Oinj__on(X18227,X18226,X18225,X18224)
        | ~ class_Groups_Ocomm__monoid__add(X18228) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong])])])]) ).

cnf(i_0_6103,plain,
    c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X4)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X2))),c_Transitive__Closure_Ortrancl(X1,X4))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X3))),c_Transitive__Closure_Ortrancl(X1,X4)))))),
    inference(split_conjunct,[status(thm)],[i_0_5247]) ).

cnf(i_0_6104,plain,
    c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5248]) ).

cnf(i_0_6105,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5249]) ).

fof(i_0_6106,plain,
    ! [X32850,X32851,X32852,X32853,X32854] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32854,X32853,hAPP(hAPP(c_COMBC(X32854,tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_fun(X32853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32853,tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_fun(X32853,tc_HOL_Obool)),X32854),c_COMBC(X32853,tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32853,tc_prod(X32854,X32853)),tc_fun(X32853,tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),X32854),hAPP(c_COMBB(tc_prod(X32854,X32853),tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool),X32853),c_member(tc_prod(X32854,X32853)))),c_Product__Type_OPair(X32854,X32853)))),X32852)),X32851),X32850))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32853,X32854)),hAPP(hAPP(c_Product__Type_OPair(X32853,X32854),X32851),X32850)),hAPP(c_Relation_Oconverse(X32854,X32853),X32852))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32853,X32854)),hAPP(hAPP(c_Product__Type_OPair(X32853,X32854),X32851),X32850)),hAPP(c_Relation_Oconverse(X32854,X32853),X32852)))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32854,X32853,hAPP(hAPP(c_COMBC(X32854,tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_fun(X32853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32853,tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_fun(X32853,tc_HOL_Obool)),X32854),c_COMBC(X32853,tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32853,tc_prod(X32854,X32853)),tc_fun(X32853,tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool)),X32854),hAPP(c_COMBB(tc_prod(X32854,X32853),tc_fun(tc_fun(tc_prod(X32854,X32853),tc_HOL_Obool),tc_HOL_Obool),X32853),c_member(tc_prod(X32854,X32853)))),c_Product__Type_OPair(X32854,X32853)))),X32852)),X32851),X32850)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])]) ).

fof(i_0_6107,plain,
    ! [X28788,X28789,X28790,X28791,X28792,X28793,X28794,X28795] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28794),esk332_8(X28788,X28789,X28790,X28791,X28792,X28793,X28794,X28795)),X28791))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28793,X28795),X28788),X28790) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28794,X28795),X28789),X28791)
        | X28790 != hAPP(c_Set_Oimage(X28794,X28793,X28792),X28791)
        | ~ c_Fun_Oinj__on(X28794,X28793,X28792,X28791)
        | ~ class_Groups_Ocomm__monoid__mult(X28795) )
      & ( hAPP(X28789,esk332_8(X28788,X28789,X28790,X28791,X28792,X28793,X28794,X28795)) != hAPP(hAPP(c_Fun_Ocomp(X28793,X28795,X28794,X28788),X28792),esk332_8(X28788,X28789,X28790,X28791,X28792,X28793,X28794,X28795))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28793,X28795),X28788),X28790) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28794,X28795),X28789),X28791)
        | X28790 != hAPP(c_Set_Oimage(X28794,X28793,X28792),X28791)
        | ~ c_Fun_Oinj__on(X28794,X28793,X28792,X28791)
        | ~ class_Groups_Ocomm__monoid__mult(X28795) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong])])])]) ).

fof(i_0_6108,plain,
    ! [X28835,X28836,X28837,X28838,X28839,X28840,X28841,X28842] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28841),X28839),esk339_8(X28835,X28836,X28837,X28838,X28839,X28840,X28841,X28842)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28836),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28840),X28838)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28835),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28839),X28837))
        | X28838 != X28837
        | X28840 != X28839
        | ~ class_Groups_Ocomm__monoid__add(X28842)
        | ~ class_Orderings_Oord(X28841) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),esk339_8(X28835,X28836,X28837,X28838,X28839,X28840,X28841,X28842)),X28837))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28836),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28840),X28838)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28835),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28839),X28837))
        | X28838 != X28837
        | X28840 != X28839
        | ~ class_Groups_Ocomm__monoid__add(X28842)
        | ~ class_Orderings_Oord(X28841) )
      & ( hAPP(X28836,esk339_8(X28835,X28836,X28837,X28838,X28839,X28840,X28841,X28842)) != hAPP(X28835,esk339_8(X28835,X28836,X28837,X28838,X28839,X28840,X28841,X28842))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28836),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28840),X28838)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28841,X28842),X28835),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28841,X28839),X28837))
        | X28838 != X28837
        | X28840 != X28839
        | ~ class_Groups_Ocomm__monoid__add(X28842)
        | ~ class_Orderings_Oord(X28841) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong])])])]) ).

fof(i_0_6109,plain,
    ! [X27314] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27314) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X27314)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(variable_rename,[status(thm)],[fact_minus__int__def]) ).

fof(i_0_6110,plain,
    ! [X33187,X33188,X33189,X33190,X33191,X33192,X33193] :
      ( ( hBOOL(hAPP(hAPP(X33193,esk506_7(X33187,X33188,X33189,X33190,X33191,X33192,X33193)),esk505_7(X33187,X33188,X33189,X33190,X33191,X33192,X33193)))
        | hBOOL(hAPP(X33189,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33192,X33191,X33187),X33188),X33190)))
        | ~ hBOOL(hAPP(hAPP(X33193,hAPP(c_Product__Type_Osnd(X33192,X33191),X33190)),hAPP(c_Product__Type_Ofst(X33192,X33191),X33190))) )
      & ( ~ hBOOL(hAPP(X33189,hAPP(hAPP(X33188,esk505_7(X33187,X33188,X33189,X33190,X33191,X33192,X33193)),esk506_7(X33187,X33188,X33189,X33190,X33191,X33192,X33193))))
        | hBOOL(hAPP(X33189,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33192,X33191,X33187),X33188),X33190)))
        | ~ hBOOL(hAPP(hAPP(X33193,hAPP(c_Product__Type_Osnd(X33192,X33191),X33190)),hAPP(c_Product__Type_Ofst(X33192,X33191),X33190))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__realizer])])])]) ).

fof(i_0_6111,plain,
    ! [X27097,X27098] : c_FunDef_Orp__inv__image(X27098,X27097) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))))),tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))),tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27097,X27098),tc_fun(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)),tc_fun(tc_fun(X27097,X27098),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool)),c_COMBS(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27097,X27098),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)),tc_fun(tc_fun(X27097,X27098),tc_fun(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),tc_fun(tc_prod(X27098,X27098),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool))),tc_fun(X27097,X27098)),c_Product__Type_OPair(tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool),tc_fun(tc_prod(X27097,X27097),tc_HOL_Obool)))),c_Relation_Oinv__image(X27098,X27097))))),c_Relation_Oinv__image(X27098,X27097))),
    inference(variable_rename,[status(thm)],[fact_rp__inv__image__def]) ).

fof(i_0_6112,plain,
    ! [X27070,X27071,X27072,X27073] : hAPP(hAPP(c_Relation_Oinv__image(X27073,X27072),X27071),X27070) = hAPP(c_Set_OCollect(tc_prod(X27072,X27072)),hAPP(c_Product__Type_Oprod_Oprod__case(X27072,X27072,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27072,tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_fun(X27072,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27072,tc_fun(tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_fun(X27072,tc_HOL_Obool)),X27072),c_COMBC(X27072,tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27072,tc_prod(X27073,X27073)),tc_fun(X27072,tc_fun(tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_HOL_Obool)),X27072),hAPP(c_COMBB(tc_prod(X27073,X27073),tc_fun(tc_fun(tc_prod(X27073,X27073),tc_HOL_Obool),tc_HOL_Obool),X27072),c_member(tc_prod(X27073,X27073)))),hAPP(hAPP(c_COMBC(X27072,tc_fun(X27072,X27073),tc_fun(X27072,tc_prod(X27073,X27073))),hAPP(hAPP(c_COMBB(tc_fun(X27073,tc_prod(X27073,X27073)),tc_fun(tc_fun(X27072,X27073),tc_fun(X27072,tc_prod(X27073,X27073))),X27072),c_COMBB(X27073,tc_prod(X27073,X27073),X27072)),hAPP(hAPP(c_COMBB(X27073,tc_fun(X27073,tc_prod(X27073,X27073)),X27072),c_Product__Type_OPair(X27073,X27073)),X27070))),X27070)))),X27071))),
    inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).

fof(i_0_6113,plain,
    ! [X29925,X29926,X29927,X29928] : hAPP(c_List_Oset(tc_prod(X29928,X29927)),hAPP(hAPP(c_List_Ozip(X29928,X29927),X29926),X29925)) = hAPP(c_Set_OCollect(tc_prod(X29928,X29927)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X29928,X29927)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X29928,X29927),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X29928,X29927)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X29928,X29927)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X29928,X29927),tc_fun(tc_Nat_Onat,tc_prod(X29928,X29927)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29928,X29927),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X29928,X29927)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X29928,X29927)),c_COMBB(tc_prod(X29928,X29927),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X29927,tc_prod(X29928,X29927)),hAPP(hAPP(c_COMBB(X29928,tc_fun(X29927,tc_prod(X29928,X29927)),tc_Nat_Onat),c_Product__Type_OPair(X29928,X29927)),hAPP(c_List_Onth(X29928),X29926))),hAPP(c_List_Onth(X29927),X29925)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29928)),X29926)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29927)),X29925)))))),
    inference(variable_rename,[status(thm)],[fact_set__zip]) ).

fof(i_0_6114,plain,
    ! [X17247,X17248,X17249,X17250,X17251] : c_Hoare__Mirabelle_Ohoare__derivs(X17251,X17250,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17251)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17251),hAPP(hAPP(c_COMBC(X17251,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X17251),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X17251),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X17249))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X17248))),c_Com_Ocom_OWhile(X17248,X17247)),X17249)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17251),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_LoopF]) ).

fof(i_0_6115,plain,
    ! [X26407,X26408,X26409,X26410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26410,tc_fun(X26409,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26410,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),X26410),c_COMBC(X26409,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_prod(X26410,X26409)),tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),X26410),hAPP(c_COMBB(tc_prod(X26410,X26409),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool),X26409),c_member(tc_prod(X26410,X26409)))),c_Product__Type_OPair(X26410,X26409)))),X26408)),hAPP(hAPP(c_COMBC(X26410,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),X26410),c_COMBC(X26409,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_prod(X26410,X26409)),tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),X26410),hAPP(c_COMBB(tc_prod(X26410,X26409),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool),X26409),c_member(tc_prod(X26410,X26409)))),c_Product__Type_OPair(X26410,X26409)))),X26407)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool)),X26408),X26407)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool)),X26408),X26407))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26410,tc_fun(X26409,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26410,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),X26410),c_COMBC(X26409,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_prod(X26410,X26409)),tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),X26410),hAPP(c_COMBB(tc_prod(X26410,X26409),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool),X26409),c_member(tc_prod(X26410,X26409)))),c_Product__Type_OPair(X26410,X26409)))),X26408)),hAPP(hAPP(c_COMBC(X26410,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_fun(X26409,tc_HOL_Obool)),X26410),c_COMBC(X26409,tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26409,tc_prod(X26410,X26409)),tc_fun(X26409,tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool)),X26410),hAPP(c_COMBB(tc_prod(X26410,X26409),tc_fun(tc_fun(tc_prod(X26410,X26409),tc_HOL_Obool),tc_HOL_Obool),X26409),c_member(tc_prod(X26410,X26409)))),c_Product__Type_OPair(X26410,X26409)))),X26407))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_6116,plain,
    ! [X25417,X25418] : hAPP(c_Set_OPow(X25418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25418,tc_HOL_Obool)),X25417)) = hAPP(c_Set_OCollect(tc_fun(X25418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X25418,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X25418,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X25418,tc_HOL_Obool),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X25418,tc_HOL_Obool)),c_COMBS(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X25418,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X25418,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X25418,tc_HOL_Obool),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_fun(X25418,tc_HOL_Obool)),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_fun(X25418,tc_HOL_Obool)),tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X25418,tc_HOL_Obool)),c_COMBB(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X25418,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X25418,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25418,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X25418,tc_HOL_Obool)),hAPP(c_member(tc_fun(X25418,tc_HOL_Obool)),X25417)),c_Set_OPow(X25418))))),
    inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).

fof(i_0_6117,plain,
    ! [X26017,X26018,X26019,X26020,X26021,X26022,X26023] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26023),esk259_7(X26017,X26018,X26019,X26020,X26021,X26022,X26023)),X26022))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X26020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26023,tc_fun(X26020,tc_HOL_Obool)),X26018),X26019)),X26017))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26023,tc_HOL_Obool)),X26018),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26023),X26022),X26021)))
        | ~ c_Equiv__Relations_Ocongruent(X26023,tc_fun(X26020,tc_HOL_Obool),X26021,X26019)
        | ~ c_Equiv__Relations_Oequiv(X26023,X26022,X26021) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26020,tc_HOL_Obool)),hAPP(X26019,esk259_7(X26017,X26018,X26019,X26020,X26021,X26022,X26023))),X26017))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X26020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26023,tc_fun(X26020,tc_HOL_Obool)),X26018),X26019)),X26017))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26023,tc_HOL_Obool)),X26018),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26023),X26022),X26021)))
        | ~ c_Equiv__Relations_Ocongruent(X26023,tc_fun(X26020,tc_HOL_Obool),X26021,X26019)
        | ~ c_Equiv__Relations_Oequiv(X26023,X26022,X26021) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type])])])]) ).

fof(i_0_6118,plain,
    ! [X33116,X33117,X33118,X33119,X33120,X33121,X33122] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33122),esk501_7(X33116,X33117,X33118,X33119,X33120,X33121,X33122)),X33121))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33122,tc_fun(X33117,tc_fun(X33116,tc_HOL_Obool))),X33121),X33120),X33119),X33118)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X33120,esk501_7(X33116,X33117,X33118,X33119,X33120,X33121,X33122)),X33119),X33118))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33122,tc_fun(X33117,tc_fun(X33116,tc_HOL_Obool))),X33121),X33120),X33119),X33118)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__I])])])]) ).

fof(i_0_6119,plain,
    ! [X22043,X22044,X22045,X22046,X22047,X22048,X22049,X22050,X22051,X22052,X22053,X22054,X22055,X22056,X22057] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22049,tc_fun(X22048,tc_fun(X22047,tc_HOL_Obool))),X22046),X22045),X22044),X22043))
        | ~ hBOOL(hAPP(hAPP(c_member(X22049),X22050),X22046))
        | hBOOL(hAPP(hAPP(hAPP(X22045,X22050),X22044),X22043)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22057),esk119_7(X22051,X22052,X22053,X22054,X22055,X22056,X22057)),X22054))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22057,tc_fun(X22056,tc_fun(X22055,tc_HOL_Obool))),X22054),X22053),X22052),X22051)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X22053,esk119_7(X22051,X22052,X22053,X22054,X22055,X22056,X22057)),X22052),X22051))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22057,tc_fun(X22056,tc_fun(X22055,tc_HOL_Obool))),X22054),X22053),X22052),X22051)) ) ),
    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_INF2__iff])])])])])]) ).

fof(i_0_6120,plain,
    ! [X25406,X25407,X25408] :
      ( ~ class_Orderings_Olinorder(X25408)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25408),X25407))
      | X25407 = c_Orderings_Obot__class_Obot(tc_fun(X25408,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25408),X25406),c_Big__Operators_Olattice_OInf__fin(X25408,c_Orderings_Oord__class_Omin(X25408),X25407)) = c_Big__Operators_Olattice_OInf__fin(X25408,c_Orderings_Oord__class_Omin(X25408),hAPP(c_Set_OCollect(X25408),hAPP(hAPP(c_COMBB(tc_fun(X25408,tc_HOL_Obool),tc_HOL_Obool,X25408),c_HOL_OEx(X25408)),hAPP(hAPP(c_COMBC(X25408,tc_fun(X25408,tc_HOL_Obool),tc_fun(X25408,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25408,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25408,tc_HOL_Obool),tc_fun(X25408,tc_HOL_Obool)),X25408),c_COMBS(X25408,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25408,tc_HOL_Obool),tc_fun(X25408,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25408),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25408),c_fconj)),hAPP(hAPP(c_COMBC(X25408,tc_fun(X25408,X25408),tc_fun(X25408,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25408,tc_HOL_Obool),tc_fun(tc_fun(X25408,X25408),tc_fun(X25408,tc_HOL_Obool)),X25408),c_COMBB(X25408,tc_HOL_Obool,X25408)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X25408),X25406))))),hAPP(hAPP(c_COMBC(X25408,tc_fun(X25408,tc_HOL_Obool),tc_HOL_Obool),c_member(X25408)),X25407))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).

fof(i_0_6121,plain,
    ! [X25409,X25410,X25411] :
      ( ~ class_Orderings_Olinorder(X25411)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25411),X25410))
      | X25410 = c_Orderings_Obot__class_Obot(tc_fun(X25411,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25411),X25409),c_Big__Operators_Olattice_OSup__fin(X25411,c_Orderings_Oord__class_Omax(X25411),X25410)) = c_Big__Operators_Olattice_OSup__fin(X25411,c_Orderings_Oord__class_Omax(X25411),hAPP(c_Set_OCollect(X25411),hAPP(hAPP(c_COMBB(tc_fun(X25411,tc_HOL_Obool),tc_HOL_Obool,X25411),c_HOL_OEx(X25411)),hAPP(hAPP(c_COMBC(X25411,tc_fun(X25411,tc_HOL_Obool),tc_fun(X25411,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25411,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25411,tc_HOL_Obool),tc_fun(X25411,tc_HOL_Obool)),X25411),c_COMBS(X25411,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25411,tc_HOL_Obool),tc_fun(X25411,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25411),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25411),c_fconj)),hAPP(hAPP(c_COMBC(X25411,tc_fun(X25411,X25411),tc_fun(X25411,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25411,tc_HOL_Obool),tc_fun(tc_fun(X25411,X25411),tc_fun(X25411,tc_HOL_Obool)),X25411),c_COMBB(X25411,tc_HOL_Obool,X25411)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X25411),X25409))))),hAPP(hAPP(c_COMBC(X25411,tc_fun(X25411,tc_HOL_Obool),tc_HOL_Obool),c_member(X25411)),X25410))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).

fof(i_0_6122,plain,
    ! [X25449,X25450,X25451] :
      ( ~ class_Lattices_Odistrib__lattice(X25451)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25451),X25450))
      | X25450 = c_Orderings_Obot__class_Obot(tc_fun(X25451,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25451),X25449),c_Big__Operators_Olattice__class_OSup__fin(X25451,X25450)) = c_Big__Operators_Olattice__class_OSup__fin(X25451,hAPP(c_Set_OCollect(X25451),hAPP(hAPP(c_COMBB(tc_fun(X25451,tc_HOL_Obool),tc_HOL_Obool,X25451),c_HOL_OEx(X25451)),hAPP(hAPP(c_COMBC(X25451,tc_fun(X25451,tc_HOL_Obool),tc_fun(X25451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25451,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25451,tc_HOL_Obool),tc_fun(X25451,tc_HOL_Obool)),X25451),c_COMBS(X25451,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25451,tc_HOL_Obool),tc_fun(X25451,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25451),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25451),c_fconj)),hAPP(hAPP(c_COMBC(X25451,tc_fun(X25451,X25451),tc_fun(X25451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25451,tc_HOL_Obool),tc_fun(tc_fun(X25451,X25451),tc_fun(X25451,tc_HOL_Obool)),X25451),c_COMBB(X25451,tc_HOL_Obool,X25451)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25451),X25449))))),hAPP(hAPP(c_COMBC(X25451,tc_fun(X25451,tc_HOL_Obool),tc_HOL_Obool),c_member(X25451)),X25450))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).

fof(i_0_6123,plain,
    ! [X25443,X25444,X25445] :
      ( ~ class_Lattices_Odistrib__lattice(X25445)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25445),X25444))
      | X25444 = c_Orderings_Obot__class_Obot(tc_fun(X25445,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25445),X25443),c_Big__Operators_Olattice__class_OInf__fin(X25445,X25444)) = c_Big__Operators_Olattice__class_OInf__fin(X25445,hAPP(c_Set_OCollect(X25445),hAPP(hAPP(c_COMBB(tc_fun(X25445,tc_HOL_Obool),tc_HOL_Obool,X25445),c_HOL_OEx(X25445)),hAPP(hAPP(c_COMBC(X25445,tc_fun(X25445,tc_HOL_Obool),tc_fun(X25445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25445,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25445,tc_HOL_Obool),tc_fun(X25445,tc_HOL_Obool)),X25445),c_COMBS(X25445,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25445,tc_HOL_Obool),tc_fun(X25445,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25445),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25445),c_fconj)),hAPP(hAPP(c_COMBC(X25445,tc_fun(X25445,X25445),tc_fun(X25445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25445,tc_HOL_Obool),tc_fun(tc_fun(X25445,X25445),tc_fun(X25445,tc_HOL_Obool)),X25445),c_COMBB(X25445,tc_HOL_Obool,X25445)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25445),X25443))))),hAPP(hAPP(c_COMBC(X25445,tc_fun(X25445,tc_HOL_Obool),tc_HOL_Obool),c_member(X25445)),X25444))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).

fof(i_0_6124,plain,
    ! [X25434,X25435,X25436] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X25436)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25436),X25435))
      | X25435 = c_Orderings_Obot__class_Obot(tc_fun(X25436,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25436),X25434),c_Big__Operators_Olinorder__class_OMin(X25436,X25435)) = c_Big__Operators_Olinorder__class_OMin(X25436,hAPP(c_Set_OCollect(X25436),hAPP(hAPP(c_COMBB(tc_fun(X25436,tc_HOL_Obool),tc_HOL_Obool,X25436),c_HOL_OEx(X25436)),hAPP(hAPP(c_COMBC(X25436,tc_fun(X25436,tc_HOL_Obool),tc_fun(X25436,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25436,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25436,tc_HOL_Obool),tc_fun(X25436,tc_HOL_Obool)),X25436),c_COMBS(X25436,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25436,tc_HOL_Obool),tc_fun(X25436,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25436),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25436),c_fconj)),hAPP(hAPP(c_COMBC(X25436,tc_fun(X25436,X25436),tc_fun(X25436,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25436,tc_HOL_Obool),tc_fun(tc_fun(X25436,X25436),tc_fun(X25436,tc_HOL_Obool)),X25436),c_COMBB(X25436,tc_HOL_Obool,X25436)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X25436),X25434))))),hAPP(hAPP(c_COMBC(X25436,tc_fun(X25436,tc_HOL_Obool),tc_HOL_Obool),c_member(X25436)),X25435))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).

fof(i_0_6125,plain,
    ! [X25437,X25438,X25439] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X25439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25439),X25438))
      | X25438 = c_Orderings_Obot__class_Obot(tc_fun(X25439,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25439),X25437),c_Big__Operators_Olinorder__class_OMax(X25439,X25438)) = c_Big__Operators_Olinorder__class_OMax(X25439,hAPP(c_Set_OCollect(X25439),hAPP(hAPP(c_COMBB(tc_fun(X25439,tc_HOL_Obool),tc_HOL_Obool,X25439),c_HOL_OEx(X25439)),hAPP(hAPP(c_COMBC(X25439,tc_fun(X25439,tc_HOL_Obool),tc_fun(X25439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25439,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25439,tc_HOL_Obool),tc_fun(X25439,tc_HOL_Obool)),X25439),c_COMBS(X25439,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25439,tc_HOL_Obool),tc_fun(X25439,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25439),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25439),c_fconj)),hAPP(hAPP(c_COMBC(X25439,tc_fun(X25439,X25439),tc_fun(X25439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25439,tc_HOL_Obool),tc_fun(tc_fun(X25439,X25439),tc_fun(X25439,tc_HOL_Obool)),X25439),c_COMBB(X25439,tc_HOL_Obool,X25439)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X25439),X25437))))),hAPP(hAPP(c_COMBC(X25439,tc_fun(X25439,tc_HOL_Obool),tc_HOL_Obool),c_member(X25439)),X25438))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).

fof(i_0_6126,hypothesis,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
    | c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(i_0_6127,plain,
    ! [X17179,X17180,X17181,X17182,X17183] :
      ( ( hBOOL(hAPP(hAPP(X17183,esk5_5(X17179,X17180,X17181,X17182,X17183)),esk6_5(X17179,X17180,X17181,X17182,X17183)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17182,X17181,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17182)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17182),X17183),X17180),X17179)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17182),tc_HOL_Obool)))) )
      & ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17182,X17181,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17182)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17182),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X17182),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk6_5(X17179,X17180,X17181,X17182,X17183)))),X17180),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X17182),hAPP(X17179,esk5_5(X17179,X17180,X17181,X17182,X17183))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17182),tc_HOL_Obool))))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17182,X17181,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17182)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17182),X17183),X17180),X17179)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17182),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_escape])])])]) ).

fof(i_0_6128,plain,
    ! [X29915,X29916,X29917,X29918,X29919,X29920,X29921,X29922,X29923] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29918)),X29917) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29918)),X29916)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29918),tc_List_Olist(X29918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29918),tc_List_Olist(X29918)),X29917),X29916)),c_List_Olistrel(X29918,X29915))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29918,X29918)),X29919),hAPP(c_List_Oset(tc_prod(X29918,X29918)),hAPP(hAPP(c_List_Ozip(X29918,X29918),X29917),X29916))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29918,X29918,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29918,tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_fun(X29918,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29918,tc_fun(tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_fun(X29918,tc_HOL_Obool)),X29918),c_COMBC(X29918,tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29918,tc_prod(X29918,X29918)),tc_fun(X29918,tc_fun(tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_HOL_Obool)),X29918),hAPP(c_COMBB(tc_prod(X29918,X29918),tc_fun(tc_fun(tc_prod(X29918,X29918),tc_HOL_Obool),tc_HOL_Obool),X29918),c_member(tc_prod(X29918,X29918)))),c_Product__Type_OPair(X29918,X29918)))),X29915)),X29919))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29918),tc_List_Olist(X29918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29918),tc_List_Olist(X29918)),X29917),X29916)),c_List_Olistrel(X29918,X29915))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29923,X29923)),esk395_4(X29920,X29921,X29922,X29923)),hAPP(c_List_Oset(tc_prod(X29923,X29923)),hAPP(hAPP(c_List_Ozip(X29923,X29923),X29922),X29921))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29923)),X29922) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29923)),X29921)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29923),tc_List_Olist(X29923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29923),tc_List_Olist(X29923)),X29922),X29921)),c_List_Olistrel(X29923,X29920))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29923,X29923,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29923,tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_fun(X29923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29923,tc_fun(tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_fun(X29923,tc_HOL_Obool)),X29923),c_COMBC(X29923,tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29923,tc_prod(X29923,X29923)),tc_fun(X29923,tc_fun(tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_HOL_Obool)),X29923),hAPP(c_COMBB(tc_prod(X29923,X29923),tc_fun(tc_fun(tc_prod(X29923,X29923),tc_HOL_Obool),tc_HOL_Obool),X29923),c_member(tc_prod(X29923,X29923)))),c_Product__Type_OPair(X29923,X29923)))),X29920)),esk395_4(X29920,X29921,X29922,X29923)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29923)),X29922) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29923)),X29921)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29923),tc_List_Olist(X29923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29923),tc_List_Olist(X29923)),X29922),X29921)),c_List_Olistrel(X29923,X29920))) ) ),
    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_listrel__iff__zip])])])])])]) ).

fof(i_0_6129,plain,
    ! [X27765,X27766,X27767,X27768] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X27768,X27767,hAPP(hAPP(c_COMBC(X27768,tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_fun(X27767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27767,tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_fun(X27767,tc_HOL_Obool)),X27768),c_COMBC(X27767,tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27767,tc_prod(X27768,X27767)),tc_fun(X27767,tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),X27768),hAPP(c_COMBB(tc_prod(X27768,X27767),tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool),X27767),c_member(tc_prod(X27768,X27767)))),c_Product__Type_OPair(X27768,X27767)))),X27766)),X27765))
        | hBOOL(hAPP(hAPP(c_member(X27768),X27765),hAPP(c_Relation_ODomain(X27768,X27767),X27766))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27768),X27765),hAPP(c_Relation_ODomain(X27768,X27767),X27766)))
        | hBOOL(hAPP(c_Predicate_ODomainP(X27768,X27767,hAPP(hAPP(c_COMBC(X27768,tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_fun(X27767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27767,tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_fun(X27767,tc_HOL_Obool)),X27768),c_COMBC(X27767,tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27767,tc_prod(X27768,X27767)),tc_fun(X27767,tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool)),X27768),hAPP(c_COMBB(tc_prod(X27768,X27767),tc_fun(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool),tc_HOL_Obool),X27767),c_member(tc_prod(X27768,X27767)))),c_Product__Type_OPair(X27768,X27767)))),X27766)),X27765)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).

fof(i_0_6130,plain,
    ! [X27678,X27679,X27680,X27681] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X27681,X27680,hAPP(hAPP(c_COMBC(X27681,tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27680,tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_fun(X27680,tc_HOL_Obool)),X27681),c_COMBC(X27680,tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27680,tc_prod(X27681,X27680)),tc_fun(X27680,tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),X27681),hAPP(c_COMBB(tc_prod(X27681,X27680),tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool),X27680),c_member(tc_prod(X27681,X27680)))),c_Product__Type_OPair(X27681,X27680)))),X27679)),X27678))
        | hBOOL(hAPP(hAPP(c_member(X27680),X27678),hAPP(c_Relation_ORange(X27681,X27680),X27679))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27680),X27678),hAPP(c_Relation_ORange(X27681,X27680),X27679)))
        | hBOOL(hAPP(c_Predicate_ORangeP(X27681,X27680,hAPP(hAPP(c_COMBC(X27681,tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27680,tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_fun(X27680,tc_HOL_Obool)),X27681),c_COMBC(X27680,tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27680,tc_prod(X27681,X27680)),tc_fun(X27680,tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool)),X27681),hAPP(c_COMBB(tc_prod(X27681,X27680),tc_fun(tc_fun(tc_prod(X27681,X27680),tc_HOL_Obool),tc_HOL_Obool),X27680),c_member(tc_prod(X27681,X27680)))),c_Product__Type_OPair(X27681,X27680)))),X27679)),X27678)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).

fof(i_0_6131,plain,
    ! [X27334,X27335,X27336] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X27336,hAPP(hAPP(c_COMBC(X27336,tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_fun(X27336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27336,tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_fun(X27336,tc_HOL_Obool)),X27336),c_COMBC(X27336,tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27336,tc_prod(X27336,X27336)),tc_fun(X27336,tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),X27336),hAPP(c_COMBB(tc_prod(X27336,X27336),tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool),X27336),c_member(tc_prod(X27336,X27336)))),c_Product__Type_OPair(X27336,X27336)))),X27335)),X27334))
        | hBOOL(hAPP(hAPP(c_member(X27336),X27334),c_Wellfounded_Oacc(X27336,X27335))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27336),X27334),c_Wellfounded_Oacc(X27336,X27335)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X27336,hAPP(hAPP(c_COMBC(X27336,tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_fun(X27336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27336,tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_fun(X27336,tc_HOL_Obool)),X27336),c_COMBC(X27336,tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27336,tc_prod(X27336,X27336)),tc_fun(X27336,tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool)),X27336),hAPP(c_COMBB(tc_prod(X27336,X27336),tc_fun(tc_fun(tc_prod(X27336,X27336),tc_HOL_Obool),tc_HOL_Obool),X27336),c_member(tc_prod(X27336,X27336)))),c_Product__Type_OPair(X27336,X27336)))),X27335)),X27334)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).

fof(i_0_6132,plain,
    ! [X33026,X33027,X33028] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33028,X33027),X33026) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33028,tc_Lazy__Sequence_Olazy__sequence(X33028)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33028,tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X33028,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat)),X33028),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X33028),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X33028)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X33028,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33028),tc_Nat_Onat)),X33028),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X33028))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X33028),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33027))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33028,X33027))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X33028),X33026)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(i_0_6133,plain,
    ! [X17993,X17994,X17995,X17996,X17997,X17998,X17999,X18002,X18003,X18004,X18005,X18006,X18007,X18008,X18009,X18010] :
      ( ( hAPP(hAPP(X17997,X17994),X17993) = hAPP(hAPP(X17997,esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),esk26_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999))
        | X17995 = c_Orderings_Obot__class_Obot(tc_fun(X17999,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17999),esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),X17995))
        | X17995 = c_Orderings_Obot__class_Obot(tc_fun(X17999,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17999,tc_HOL_Obool)),X17995),hAPP(hAPP(c_Set_Oinsert(X17999),esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),c_Orderings_Obot__class_Obot(tc_fun(X17999,tc_HOL_Obool)))),esk26_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999))
        | X17995 = c_Orderings_Obot__class_Obot(tc_fun(X17999,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( hAPP(hAPP(X17997,X17994),X17993) = hAPP(hAPP(X17997,esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),esk26_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999))
        | hAPP(hAPP(X17997,X17994),X17993) = X17996
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17999),esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),X17995))
        | hAPP(hAPP(X17997,X17994),X17993) = X17996
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17999,tc_HOL_Obool)),X17995),hAPP(hAPP(c_Set_Oinsert(X17999),esk25_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999)),c_Orderings_Obot__class_Obot(tc_fun(X17999,tc_HOL_Obool)))),esk26_7(X17993,X17994,X17995,X17996,X17997,X17998,X17999))
        | hAPP(hAPP(X17997,X17994),X17993) = X17996
        | ~ c_Nitpick_Ofold__graph_H(X17999,X17998,X17997,X17996,X17995,hAPP(hAPP(X17997,X17994),X17993)) )
      & ( X18004 != c_Orderings_Obot__class_Obot(tc_fun(X18008,tc_HOL_Obool))
        | hAPP(hAPP(X18006,X18003),X18002) != X18005
        | c_Nitpick_Ofold__graph_H(X18008,X18007,X18006,X18005,X18004,hAPP(hAPP(X18006,X18003),X18002)) )
      & ( hAPP(hAPP(X18006,X18003),X18002) != hAPP(hAPP(X18006,X18009),X18010)
        | ~ hBOOL(hAPP(hAPP(c_member(X18008),X18009),X18004))
        | ~ c_Nitpick_Ofold__graph_H(X18008,X18007,X18006,X18005,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18008,tc_HOL_Obool)),X18004),hAPP(hAPP(c_Set_Oinsert(X18008),X18009),c_Orderings_Obot__class_Obot(tc_fun(X18008,tc_HOL_Obool)))),X18010)
        | c_Nitpick_Ofold__graph_H(X18008,X18007,X18006,X18005,X18004,hAPP(hAPP(X18006,X18003),X18002)) ) ),
    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_fold__graph_H_Oequations_I2_J])])])])])]) ).

fof(i_0_6134,plain,
    ! [X33124,X33125,X33126,X33127,X33128,X33129,X33130] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33130),esk502_7(X33124,X33125,X33126,X33127,X33128,X33129,X33130)),X33127))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33130,tc_fun(X33129,tc_fun(X33128,tc_HOL_Obool))),X33127),X33126),X33125),X33124)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X33126,esk502_7(X33124,X33125,X33126,X33127,X33128,X33129,X33130)),X33125),X33124))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33130,tc_fun(X33129,tc_fun(X33128,tc_HOL_Obool))),X33127),X33126),X33125),X33124)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5250])])])]) ).

fof(i_0_6135,plain,
    ! [X21219,X21220,X21221,X21222,X21223,X21224,X21225,X21227,X21228,X21229,X21230,X21231,X21232,X21233,X21234] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21225),esk96_7(X21219,X21220,X21221,X21222,X21223,X21224,X21225)),X21222))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21225,tc_fun(X21224,tc_fun(X21223,tc_HOL_Obool))),X21222),X21221),X21220),X21219)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X21221,esk96_7(X21219,X21220,X21221,X21222,X21223,X21224,X21225)),X21220),X21219))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21225,tc_fun(X21224,tc_fun(X21223,tc_HOL_Obool))),X21222),X21221),X21220),X21219)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21233),X21234),X21230))
        | ~ hBOOL(hAPP(hAPP(hAPP(X21229,X21234),X21228),X21227))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21233,tc_fun(X21232,tc_fun(X21231,tc_HOL_Obool))),X21230),X21229),X21228),X21227)) ) ),
    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_SUP2__iff])])])])])]) ).

fof(i_0_6136,plain,
    ! [X31416,X31417,X31418,X31419] : c_List_Opartition(X31419,X31418,hAPP(hAPP(c_List_Olist_OCons(X31419),X31417),X31416)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31419),tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),hAPP(hAPP(c_COMBS(tc_List_Olist(X31419),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31419),tc_fun(tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),tc_fun(tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),tc_List_Olist(X31419)),c_COMBS(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_fun(tc_List_Olist(X31419),tc_fun(tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),tc_List_Olist(X31419)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_fun(tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_List_Olist(X31419)),hAPP(c_If(tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),hAPP(X31418,X31417)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X31419),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_List_Olist(X31419)),c_Product__Type_OPair(tc_List_Olist(X31419),tc_List_Olist(X31419))),hAPP(c_List_Olist_OCons(X31419),X31417))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31419),tc_fun(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419))),tc_fun(tc_fun(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_fun(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)))),tc_List_Olist(X31419)),c_COMBB(tc_List_Olist(X31419),tc_prod(tc_List_Olist(X31419),tc_List_Olist(X31419)),tc_List_Olist(X31419))),c_Product__Type_OPair(tc_List_Olist(X31419),tc_List_Olist(X31419)))),hAPP(c_List_Olist_OCons(X31419),X31417)))),c_List_Opartition(X31419,X31418,X31416)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(i_0_6137,plain,
    ! [X29551,X29552,X29553] : hAPP(c_List_Olexn(X29553,X29552),hAPP(c_Nat_OSuc,X29551)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X29553),tc_List_Olist(X29553)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X29553,tc_List_Olist(X29553)),tc_prod(X29553,tc_List_Olist(X29553))),tc_prod(tc_List_Olist(X29553),tc_List_Olist(X29553)),c_Product__Type_Omap__pair(tc_prod(X29553,tc_List_Olist(X29553)),tc_List_Olist(X29553),tc_prod(X29553,tc_List_Olist(X29553)),tc_List_Olist(X29553),hAPP(c_Product__Type_Oprod_Oprod__case(X29553,tc_List_Olist(X29553),tc_List_Olist(X29553)),c_List_Olist_OCons(X29553)),hAPP(c_Product__Type_Oprod_Oprod__case(X29553,tc_List_Olist(X29553),tc_List_Olist(X29553)),c_List_Olist_OCons(X29553)))),c_Wellfounded_Olex__prod(X29553,tc_List_Olist(X29553),X29552,hAPP(c_List_Olexn(X29553,X29552),X29551)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X29553),tc_List_Olist(X29553))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X29553),tc_List_Olist(X29553),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X29553),tc_fun(tc_List_Olist(X29553),tc_HOL_Obool),tc_fun(tc_List_Olist(X29553),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29553),tc_HOL_Obool),tc_fun(tc_List_Olist(X29553),tc_HOL_Obool)),tc_List_Olist(X29553)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X29553))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29553)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29553),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29553)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29553)))),hAPP(c_Nat_OSuc,X29551))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29553),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29553)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29553)))),hAPP(c_Nat_OSuc,X29551)))))),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

cnf(i_0_6138,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5251]) ).

cnf(i_0_6139,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5251]) ).

cnf(i_0_6140,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5252]) ).

fof(i_0_6141,plain,
    ! [X29803,X29804,X29805] : hAPP(c_List_Oset(X29805),c_List_Osublist(X29805,X29804,X29803)) = hAPP(c_Set_OCollect(X29805),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X29805),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X29805,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29805),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29805),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X29805,tc_fun(tc_Nat_Onat,X29805),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29805,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X29805),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29805),c_COMBB(X29805,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X29805),X29804))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29805)),X29804)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29803))))),
    inference(variable_rename,[status(thm)],[fact_set__sublist]) ).

cnf(i_0_6142,plain,
    ( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5253]) ).

cnf(i_0_6143,plain,
    c_List_Oconcat(X1,X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_5254]) ).

cnf(i_0_6144,plain,
    c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4))))),
    inference(split_conjunct,[status(thm)],[i_0_5255]) ).

fof(i_0_6145,plain,
    ! [X25455,X25456,X25457,X25458,X25459,X25460] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25458),esk241_6(X25455,X25456,X25457,X25458,X25459,X25460)),X25457))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25460,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_Nat_Onat,X25460),c_Finite__Set_Ocard(X25458)),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_fun(X25458,tc_HOL_Obool),X25460),c_Set_OCollect(X25458)),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_fun(X25458,tc_HOL_Obool),X25460),hAPP(c_COMBS(X25458,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25458),c_fconj),hAPP(hAPP(c_COMBC(X25458,tc_fun(X25458,tc_HOL_Obool),tc_HOL_Obool),c_member(X25458)),X25457)))),X25456)))),X25459) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25458,tc_Nat_Onat),X25455),X25457)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25458),X25457))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25460),X25459)) )
      & ( hAPP(c_Finite__Set_Ocard(X25460),hAPP(c_Set_OCollect(X25460),hAPP(hAPP(c_COMBS(X25460,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25460),c_fconj),hAPP(hAPP(c_COMBC(X25460,tc_fun(X25460,tc_HOL_Obool),tc_HOL_Obool),c_member(X25460)),X25459))),hAPP(hAPP(c_COMBC(X25460,X25458,tc_HOL_Obool),X25456),esk241_6(X25455,X25456,X25457,X25458,X25459,X25460))))) != hAPP(X25455,esk241_6(X25455,X25456,X25457,X25458,X25459,X25460))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25460,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_Nat_Onat,X25460),c_Finite__Set_Ocard(X25458)),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_fun(X25458,tc_HOL_Obool),X25460),c_Set_OCollect(X25458)),hAPP(hAPP(c_COMBB(tc_fun(X25458,tc_HOL_Obool),tc_fun(X25458,tc_HOL_Obool),X25460),hAPP(c_COMBS(X25458,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25458),c_fconj),hAPP(hAPP(c_COMBC(X25458,tc_fun(X25458,tc_HOL_Obool),tc_HOL_Obool),c_member(X25458)),X25457)))),X25456)))),X25459) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25458,tc_Nat_Onat),X25455),X25457)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25458),X25457))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25460),X25459)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen])])])]) ).

fof(i_0_6146,plain,
    ! [X29907,X29908] : hAPP(c_List_Oset(X29908),X29907) = hAPP(c_Set_OCollect(X29908),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X29908),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X29908,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29908),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29908),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X29908,tc_fun(tc_Nat_Onat,X29908),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29908,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X29908),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29908),c_COMBB(X29908,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X29908),X29907))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29908)),X29907))))),
    inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).

fof(i_0_6147,plain,
    ! [X27993,X27994,X27995,X27996] : hAPP(hAPP(c_Product__Type_OSigma(X27996,X27995),X27994),X27993) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27996,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),X27994),hAPP(hAPP(c_COMBS(X27996,tc_fun(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_HOL_Obool),tc_fun(tc_fun(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),X27996),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),X27993)),hAPP(hAPP(c_COMBC(X27996,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),X27996),c_COMBC(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_prod(X27996,X27995)),tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))),X27996),hAPP(c_COMBB(tc_prod(X27996,X27995),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool)),X27995),c_Set_Oinsert(tc_prod(X27996,X27995)))),c_Product__Type_OPair(X27996,X27995)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Sigma__def]) ).

cnf(i_0_6148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5256]) ).

fof(i_0_6149,plain,
    ! [X25399,X25400,X25401,X25402,X25403,X25404] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25402),esk239_6(X25399,X25400,X25401,X25402,X25403,X25404)),X25401))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25404,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_Nat_Onat,X25404),c_Finite__Set_Ocard(X25402)),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_fun(X25402,tc_HOL_Obool),X25404),c_Set_OCollect(X25402)),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_fun(X25402,tc_HOL_Obool),X25404),hAPP(c_COMBS(X25402,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25402),c_fconj),hAPP(hAPP(c_COMBC(X25402,tc_fun(X25402,tc_HOL_Obool),tc_HOL_Obool),c_member(X25402)),X25401)))),X25400)))),X25403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25399),hAPP(c_Finite__Set_Ocard(X25402),X25401))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25402),X25401))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25404),X25403)) )
      & ( hAPP(c_Finite__Set_Ocard(X25404),hAPP(c_Set_OCollect(X25404),hAPP(hAPP(c_COMBS(X25404,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25404),c_fconj),hAPP(hAPP(c_COMBC(X25404,tc_fun(X25404,tc_HOL_Obool),tc_HOL_Obool),c_member(X25404)),X25403))),hAPP(hAPP(c_COMBC(X25404,X25402,tc_HOL_Obool),X25400),esk239_6(X25399,X25400,X25401,X25402,X25403,X25404))))) != X25399
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25404,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_Nat_Onat,X25404),c_Finite__Set_Ocard(X25402)),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_fun(X25402,tc_HOL_Obool),X25404),c_Set_OCollect(X25402)),hAPP(hAPP(c_COMBB(tc_fun(X25402,tc_HOL_Obool),tc_fun(X25402,tc_HOL_Obool),X25404),hAPP(c_COMBS(X25402,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25402),c_fconj),hAPP(hAPP(c_COMBC(X25402,tc_fun(X25402,tc_HOL_Obool),tc_HOL_Obool),c_member(X25402)),X25401)))),X25400)))),X25403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25399),hAPP(c_Finite__Set_Ocard(X25402),X25401))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25402),X25401))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25404),X25403)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount])])])]) ).

fof(i_0_6150,plain,
    ! [X25365,X25366,X25367,X25368,X25369,X25370,X25371] :
      ( ~ class_Groups_Ocomm__monoid__add(X25371)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25370),X25369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25368),X25367))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25370,X25371),hAPP(hAPP(c_COMBS(X25370,tc_fun(X25368,tc_HOL_Obool),X25371),hAPP(hAPP(c_COMBB(tc_fun(X25368,X25371),tc_fun(tc_fun(X25368,tc_HOL_Obool),X25371),X25370),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25368,X25371)),X25366)),hAPP(hAPP(c_COMBB(tc_fun(X25368,tc_HOL_Obool),tc_fun(X25368,tc_HOL_Obool),X25370),c_Set_OCollect(X25368)),hAPP(hAPP(c_COMBB(tc_fun(X25368,tc_HOL_Obool),tc_fun(X25368,tc_HOL_Obool),X25370),hAPP(c_COMBS(X25368,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25368),c_fconj),hAPP(hAPP(c_COMBC(X25368,tc_fun(X25368,tc_HOL_Obool),tc_HOL_Obool),c_member(X25368)),X25367)))),X25365)))),X25369) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25368,X25371),hAPP(hAPP(c_COMBS(X25368,tc_fun(X25370,tc_HOL_Obool),X25371),hAPP(hAPP(c_COMBB(tc_fun(X25370,X25371),tc_fun(tc_fun(X25370,tc_HOL_Obool),X25371),X25368),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25370,X25371)),hAPP(c_COMBC(X25370,X25368,X25371),X25366))),hAPP(hAPP(c_COMBB(tc_fun(X25370,tc_HOL_Obool),tc_fun(X25370,tc_HOL_Obool),X25368),c_Set_OCollect(X25370)),hAPP(hAPP(c_COMBB(tc_fun(X25370,tc_HOL_Obool),tc_fun(X25370,tc_HOL_Obool),X25368),hAPP(c_COMBS(X25370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25370),c_fconj),hAPP(hAPP(c_COMBC(X25370,tc_fun(X25370,tc_HOL_Obool),tc_HOL_Obool),c_member(X25370)),X25369)))),hAPP(c_COMBC(X25370,X25368,tc_HOL_Obool),X25365))))),X25367) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).

fof(i_0_6151,plain,
    ! [X30348,X30349,X30350,X30351,X30352] :
      ( ( X30352 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X30351,X30350,X30349),X30352),X30348) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30350),X30351),c_List_Olist_ONil(X30350)),X30348) )
      & ( X30352 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X30351,X30350,X30349),X30352),X30348) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X30350),X30351),tc_prod(X30350,X30351),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30350),X30351),c_List_Olist_ONil(X30350)),X30348),hAPP(c_Product__Type_Oprod_Oprod__case(X30350,X30351,tc_prod(tc_List_Olist(X30350),X30351)),hAPP(hAPP(c_COMBC(X30350,tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351)),tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X30350),X30351),tc_prod(tc_List_Olist(X30350),X30351)),tc_fun(tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351)),tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351))),X30350),c_COMBB(tc_prod(tc_List_Olist(X30350),X30351),tc_prod(tc_List_Olist(X30350),X30351),X30351)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30350),tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351))),tc_fun(tc_prod(tc_List_Olist(X30350),X30351),tc_prod(tc_List_Olist(X30350),X30351)),X30350),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X30350),X30351,tc_prod(tc_List_Olist(X30350),X30351))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30350),tc_List_Olist(X30350)),tc_fun(tc_List_Olist(X30350),tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351))),X30350),hAPP(c_COMBB(tc_List_Olist(X30350),tc_fun(X30351,tc_prod(tc_List_Olist(X30350),X30351)),tc_List_Olist(X30350)),c_Product__Type_OPair(tc_List_Olist(X30350),X30351))),c_List_Olist_OCons(X30350))))),hAPP(c_Lazy__Sequence_Oanamorph(X30351,X30350,X30349),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30352),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X30349,X30348)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).

fof(i_0_6152,plain,
    ! [X29077,X29078,X29079,X29080,X29081] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29081,X29081)),hAPP(hAPP(c_Product__Type_OPair(X29081,X29081),hAPP(X29080,hAPP(c_Nat_OSuc,esk341_5(X29077,X29078,X29079,X29080,X29081)))),hAPP(X29080,esk341_5(X29077,X29078,X29079,X29080,X29081)))),c_Transitive__Closure_Ortrancl(X29081,X29079)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29081,X29081)),hAPP(hAPP(c_Product__Type_OPair(X29081,X29081),hAPP(X29080,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29078),X29077))),hAPP(X29080,X29078))),c_Transitive__Closure_Ortrancl(X29081,X29079))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).

fof(i_0_6153,plain,
    ! [X33373,X33374,X33375,X33376,X33377,X33378] : c_Partial__Function_Ofun__lub(X33378,X33377,X33376,X33375,X33374,X33373) = hAPP(X33375,hAPP(c_Set_OCollect(X33378),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool),tc_HOL_Obool,X33378),c_HOL_OEx(tc_fun(X33376,X33378))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool),tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool),X33378),hAPP(c_COMBS(tc_fun(X33376,X33378),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33376,X33378)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33376,X33378),tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33376,X33378))),X33374)))),hAPP(hAPP(c_COMBC(X33378,tc_fun(tc_fun(X33376,X33378),X33378),tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33378,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33376,X33378),X33378),tc_fun(tc_fun(X33376,X33378),tc_HOL_Obool)),X33378),c_COMBB(X33378,tc_HOL_Obool,tc_fun(X33376,X33378))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33376,X33378),X33376,X33378),c_COMBI(tc_fun(X33376,X33378))),X33373)))))),
    inference(variable_rename,[status(thm)],[fact_fun__lub__def]) ).

fof(i_0_6154,plain,
    ! [X33299,X33300,X33301,X33302] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33302)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X33301,X33302),X33300),X33299) = c_Complete__Lattice_OSup__class_OSup(X33302,hAPP(c_Set_OCollect(X33302),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool),tc_HOL_Obool,X33302),c_HOL_OEx(tc_fun(X33301,X33302))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool),tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool),X33302),hAPP(c_COMBS(tc_fun(X33301,X33302),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33301,X33302)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33301,X33302),tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33301,X33302))),X33300)))),hAPP(hAPP(c_COMBC(X33302,tc_fun(tc_fun(X33301,X33302),X33302),tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33302,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33301,X33302),X33302),tc_fun(tc_fun(X33301,X33302),tc_HOL_Obool)),X33302),c_COMBB(X33302,tc_HOL_Obool,tc_fun(X33301,X33302))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33301,X33302),X33301,X33302),c_COMBI(tc_fun(X33301,X33302))),X33299)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__apply])]) ).

fof(i_0_6155,plain,
    ! [X33295,X33296,X33297,X33298] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33298)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X33297,X33298),X33296),X33295) = c_Complete__Lattice_OSup__class_OSup(X33298,hAPP(c_Set_OCollect(X33298),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool),tc_HOL_Obool,X33298),c_HOL_OEx(tc_fun(X33297,X33298))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool),tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool),X33298),hAPP(c_COMBS(tc_fun(X33297,X33298),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33297,X33298)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33297,X33298),tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33297,X33298))),X33296)))),hAPP(hAPP(c_COMBC(X33298,tc_fun(tc_fun(X33297,X33298),X33298),tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33298,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33297,X33298),X33298),tc_fun(tc_fun(X33297,X33298),tc_HOL_Obool)),X33298),c_COMBB(X33298,tc_HOL_Obool,tc_fun(X33297,X33298))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33297,X33298),X33297,X33298),c_COMBI(tc_fun(X33297,X33298))),X33295)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fun__def])]) ).

fof(i_0_6156,plain,
    ! [X33307,X33308,X33309,X33310] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33310)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X33309,X33310),X33308),X33307) = c_Complete__Lattice_OInf__class_OInf(X33310,hAPP(c_Set_OCollect(X33310),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool),tc_HOL_Obool,X33310),c_HOL_OEx(tc_fun(X33309,X33310))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool),tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool),X33310),hAPP(c_COMBS(tc_fun(X33309,X33310),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33309,X33310)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33309,X33310),tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33309,X33310))),X33308)))),hAPP(hAPP(c_COMBC(X33310,tc_fun(tc_fun(X33309,X33310),X33310),tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33310,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33309,X33310),X33310),tc_fun(tc_fun(X33309,X33310),tc_HOL_Obool)),X33310),c_COMBB(X33310,tc_HOL_Obool,tc_fun(X33309,X33310))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33309,X33310),X33309,X33310),c_COMBI(tc_fun(X33309,X33310))),X33307)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fun__def])]) ).

fof(i_0_6157,plain,
    ! [X33303,X33304,X33305,X33306] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33306)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X33305,X33306),X33304),X33303) = c_Complete__Lattice_OInf__class_OInf(X33306,hAPP(c_Set_OCollect(X33306),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool),tc_HOL_Obool,X33306),c_HOL_OEx(tc_fun(X33305,X33306))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool),tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool),X33306),hAPP(c_COMBS(tc_fun(X33305,X33306),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33305,X33306)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33305,X33306),tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33305,X33306))),X33304)))),hAPP(hAPP(c_COMBC(X33306,tc_fun(tc_fun(X33305,X33306),X33306),tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33306,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33305,X33306),X33306),tc_fun(tc_fun(X33305,X33306),tc_HOL_Obool)),X33306),c_COMBB(X33306,tc_HOL_Obool,tc_fun(X33305,X33306))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33305,X33306),X33305,X33306),c_COMBI(tc_fun(X33305,X33306))),X33303)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__apply])]) ).

fof(i_0_6158,plain,
    ! [X33922,X33923,X33924,X33925,X33926,X33927] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33927,X33927)),hAPP(hAPP(c_Product__Type_OPair(X33927,X33927),esk561_6(X33922,X33923,X33924,X33925,X33926,X33927)),esk562_6(X33922,X33923,X33924,X33925,X33926,X33927))),X33926))
        | c_Equiv__Relations_Ocongruent2(X33927,X33925,X33922,X33926,X33924,X33923) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33925,X33925)),hAPP(hAPP(c_Product__Type_OPair(X33925,X33925),esk563_6(X33922,X33923,X33924,X33925,X33926,X33927)),esk564_6(X33922,X33923,X33924,X33925,X33926,X33927))),X33924))
        | c_Equiv__Relations_Ocongruent2(X33927,X33925,X33922,X33926,X33924,X33923) )
      & ( hAPP(hAPP(X33923,esk561_6(X33922,X33923,X33924,X33925,X33926,X33927)),esk563_6(X33922,X33923,X33924,X33925,X33926,X33927)) != hAPP(hAPP(X33923,esk562_6(X33922,X33923,X33924,X33925,X33926,X33927)),esk564_6(X33922,X33923,X33924,X33925,X33926,X33927))
        | c_Equiv__Relations_Ocongruent2(X33927,X33925,X33922,X33926,X33924,X33923) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2I_H])])])]) ).

fof(i_0_6159,plain,
    ! [X29478,X29479,X29480,X29481,X29482,X29483] :
      ( ( X29481 = hAPP(hAPP(c_Product__Type_OPair(X29483,X29482),esk373_6(X29478,X29479,X29480,X29481,X29482,X29483)),esk375_6(X29478,X29479,X29480,X29481,X29482,X29483))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29483,X29482)),X29481),hAPP(hAPP(c_Relation_Orel__comp(X29483,X29480,X29482),X29479),X29478))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29483,X29480)),hAPP(hAPP(c_Product__Type_OPair(X29483,X29480),esk373_6(X29478,X29479,X29480,X29481,X29482,X29483)),esk374_6(X29478,X29479,X29480,X29481,X29482,X29483))),X29479))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29483,X29482)),X29481),hAPP(hAPP(c_Relation_Orel__comp(X29483,X29480,X29482),X29479),X29478))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29480,X29482)),hAPP(hAPP(c_Product__Type_OPair(X29480,X29482),esk374_6(X29478,X29479,X29480,X29481,X29482,X29483)),esk375_6(X29478,X29479,X29480,X29481,X29482,X29483))),X29478))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29483,X29482)),X29481),hAPP(hAPP(c_Relation_Orel__comp(X29483,X29480,X29482),X29479),X29478))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5257])])])]) ).

fof(i_0_6160,plain,
    ! [X26390,X26391] : c_Divides_Odivmod__int__rel(X26391,X26390) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X26391))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26390)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26390))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X26390))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26390)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26390))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(variable_rename,[status(thm)],[fact_divmod__int__rel__def]) ).

fof(i_0_6161,plain,
    ! [X18474,X18475,X18476,X18477,X18478,X18479,X18480] :
      ( ~ class_Rings_Osemiring__0(X18480)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18480),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18479,X18480),X18478),X18477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18476,X18480),X18475),X18474)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18479,X18480),hAPP(hAPP(c_COMBC(X18479,tc_fun(X18476,tc_HOL_Obool),X18480),hAPP(hAPP(c_COMBB(tc_fun(X18476,X18480),tc_fun(tc_fun(X18476,tc_HOL_Obool),X18480),X18479),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18476,X18480)),hAPP(hAPP(c_COMBC(X18479,tc_fun(X18476,X18480),tc_fun(X18476,X18480)),hAPP(hAPP(c_COMBB(tc_fun(X18480,X18480),tc_fun(tc_fun(X18476,X18480),tc_fun(X18476,X18480)),X18479),c_COMBB(X18480,X18480,X18476)),hAPP(hAPP(c_COMBB(X18480,tc_fun(X18480,X18480),X18479),c_Groups_Otimes__class_Otimes(X18480)),X18478))),X18475))),X18474)),X18477) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).

fof(i_0_6162,plain,
    ! [X28012,X28013,X28014,X28015,X28016,X28017] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28016),esk301_6(X28012,X28013,X28014,X28015,X28016,X28017)),X28015))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28017,X28016,c_Groups_Otimes__class_Otimes(X28017)),hAPP(hAPP(c_COMBS(X28016,tc_fun(X28014,tc_HOL_Obool),X28017),hAPP(hAPP(c_COMBC(X28016,X28017,tc_fun(tc_fun(X28014,tc_HOL_Obool),X28017)),hAPP(hAPP(c_COMBB(tc_fun(X28014,X28017),tc_fun(X28017,tc_fun(tc_fun(X28014,tc_HOL_Obool),X28017)),X28016),c_Finite__Set_Ofold__image(X28017,X28014,c_Groups_Otimes__class_Otimes(X28017))),X28012)),c_Groups_Oone__class_Oone(X28017))),X28013)),c_Groups_Oone__class_Oone(X28017)),X28015) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28017,tc_prod(X28016,X28014),c_Groups_Otimes__class_Otimes(X28017)),hAPP(c_Product__Type_Oprod_Oprod__case(X28016,X28014,X28017),X28012)),c_Groups_Oone__class_Oone(X28017)),hAPP(hAPP(c_Product__Type_OSigma(X28016,X28014),X28015),X28013))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28016),X28015))
        | ~ class_Groups_Ocomm__monoid__mult(X28017) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28014),hAPP(X28013,esk301_6(X28012,X28013,X28014,X28015,X28016,X28017))))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28017,X28016,c_Groups_Otimes__class_Otimes(X28017)),hAPP(hAPP(c_COMBS(X28016,tc_fun(X28014,tc_HOL_Obool),X28017),hAPP(hAPP(c_COMBC(X28016,X28017,tc_fun(tc_fun(X28014,tc_HOL_Obool),X28017)),hAPP(hAPP(c_COMBB(tc_fun(X28014,X28017),tc_fun(X28017,tc_fun(tc_fun(X28014,tc_HOL_Obool),X28017)),X28016),c_Finite__Set_Ofold__image(X28017,X28014,c_Groups_Otimes__class_Otimes(X28017))),X28012)),c_Groups_Oone__class_Oone(X28017))),X28013)),c_Groups_Oone__class_Oone(X28017)),X28015) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28017,tc_prod(X28016,X28014),c_Groups_Otimes__class_Otimes(X28017)),hAPP(c_Product__Type_Oprod_Oprod__case(X28016,X28014,X28017),X28012)),c_Groups_Oone__class_Oone(X28017)),hAPP(hAPP(c_Product__Type_OSigma(X28016,X28014),X28015),X28013))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28016),X28015))
        | ~ class_Groups_Ocomm__monoid__mult(X28017) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma])])])]) ).

cnf(i_0_6163,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5258]) ).

fof(i_0_6164,plain,
    ! [X29912,X29913,X29914] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29914),X29913))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29914)),hAPP(c_Set_OCollect(tc_List_Olist(X29914)),hAPP(hAPP(c_COMBS(tc_List_Olist(X29914),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29914)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29914),tc_fun(X29914,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29914,tc_HOL_Obool),tc_fun(tc_fun(X29914,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29914)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29914,tc_HOL_Obool))),c_List_Oset(X29914))),X29913))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29914),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29914)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X29914)))),X29912))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).

fof(i_0_6165,plain,
    ! [X29909,X29910,X29911] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29911),X29910))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29911)),hAPP(c_Set_OCollect(tc_List_Olist(X29911)),hAPP(hAPP(c_COMBS(tc_List_Olist(X29911),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29911)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29911),tc_fun(X29911,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29911,tc_HOL_Obool),tc_fun(tc_fun(X29911,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29911)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29911,tc_HOL_Obool))),c_List_Oset(X29911))),X29910))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29911),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29911)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29911)))),X29909))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])]) ).

cnf(i_0_6166,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5251]) ).

fof(i_0_6167,plain,
    ! [X25252,X25253,X25254,X25255,X25256,X25257,X25258,X25259] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25258),esk236_7(X25252,X25253,X25254,X25255,X25256,X25257,X25258)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25258,tc_HOL_Obool)),X25253),X25252)))
        | hAPP(X25254,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25258,tc_HOL_Obool)),X25253),X25252)) = hAPP(hAPP(X25257,hAPP(X25254,X25253)),hAPP(X25254,X25252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25258),X25252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25258),X25253))
        | ~ c_Finite__Set_Ofolding__image__simple(X25259,X25258,X25257,X25256,X25255,X25254) )
      & ( hAPP(X25255,esk236_7(X25252,X25253,X25254,X25255,X25256,X25257,X25258)) != X25256
        | hAPP(X25254,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25258,tc_HOL_Obool)),X25253),X25252)) = hAPP(hAPP(X25257,hAPP(X25254,X25253)),hAPP(X25254,X25252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25258),X25252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25258),X25253))
        | ~ c_Finite__Set_Ofolding__image__simple(X25259,X25258,X25257,X25256,X25255,X25254) ) ),
    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_folding__image__simple_Ounion__inter__neutral])])])])])]) ).

fof(i_0_6168,plain,
    ! [X26975] : hAPP(c_Int_Onat,X26975) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26975)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(variable_rename,[status(thm)],[fact_nat__def]) ).

fof(i_0_6169,plain,
    ! [X33960,X33961,X33962,X33963,X33964,X33965,X33966,X33967] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33966),esk568_7(X33960,X33961,X33962,X33963,X33964,X33965,X33966)),X33962))
        | hAPP(hAPP(X33963,X33961),X33962) = hAPP(hAPP(X33963,X33960),X33962)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33966),X33962))
        | ~ c_Finite__Set_Ofolding__image(X33967,X33966,X33965,X33964,X33963) )
      & ( hAPP(X33961,esk568_7(X33960,X33961,X33962,X33963,X33964,X33965,X33966)) != hAPP(X33960,esk568_7(X33960,X33961,X33962,X33963,X33964,X33965,X33966))
        | hAPP(hAPP(X33963,X33961),X33962) = hAPP(hAPP(X33963,X33960),X33962)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33966),X33962))
        | ~ c_Finite__Set_Ofolding__image(X33967,X33966,X33965,X33964,X33963) ) ),
    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_folding__image_Ocong])])])])])]) ).

fof(i_0_6170,plain,
    ! [X32526,X32527,X32528,X32529,X32530,X32533,X32534,X32535,X32536,X32537,X32538,X32539,X32540] :
      ( ( X32526 = hAPP(hAPP(c_List_Oappend(X32530),esk463_5(X32526,X32527,X32528,X32529,X32530)),hAPP(hAPP(c_List_Olist_OCons(X32530),X32529),esk464_5(X32526,X32527,X32528,X32529,X32530)))
        | hAPP(hAPP(c_List_Olist_OCons(X32530),X32529),X32528) != hAPP(c_List_Ofilter(X32530,X32527),X32526) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32530),X32533),hAPP(c_List_Oset(X32530),esk463_5(X32526,X32527,X32528,X32529,X32530))))
        | ~ hBOOL(hAPP(X32527,X32533))
        | hAPP(hAPP(c_List_Olist_OCons(X32530),X32529),X32528) != hAPP(c_List_Ofilter(X32530,X32527),X32526) )
      & ( hBOOL(hAPP(X32527,X32529))
        | hAPP(hAPP(c_List_Olist_OCons(X32530),X32529),X32528) != hAPP(c_List_Ofilter(X32530,X32527),X32526) )
      & ( X32528 = hAPP(c_List_Ofilter(X32530,X32527),esk464_5(X32526,X32527,X32528,X32529,X32530))
        | hAPP(hAPP(c_List_Olist_OCons(X32530),X32529),X32528) != hAPP(c_List_Ofilter(X32530,X32527),X32526) )
      & ( hBOOL(hAPP(hAPP(c_member(X32538),esk465_7(X32534,X32535,X32536,X32537,X32538,X32539,X32540)),hAPP(c_List_Oset(X32538),X32539)))
        | X32534 != hAPP(hAPP(c_List_Oappend(X32538),X32539),hAPP(hAPP(c_List_Olist_OCons(X32538),X32537),X32540))
        | ~ hBOOL(hAPP(X32535,X32537))
        | X32536 != hAPP(c_List_Ofilter(X32538,X32535),X32540)
        | hAPP(hAPP(c_List_Olist_OCons(X32538),X32537),X32536) = hAPP(c_List_Ofilter(X32538,X32535),X32534) )
      & ( hBOOL(hAPP(X32535,esk465_7(X32534,X32535,X32536,X32537,X32538,X32539,X32540)))
        | X32534 != hAPP(hAPP(c_List_Oappend(X32538),X32539),hAPP(hAPP(c_List_Olist_OCons(X32538),X32537),X32540))
        | ~ hBOOL(hAPP(X32535,X32537))
        | X32536 != hAPP(c_List_Ofilter(X32538,X32535),X32540)
        | hAPP(hAPP(c_List_Olist_OCons(X32538),X32537),X32536) = hAPP(c_List_Ofilter(X32538,X32535),X32534) ) ),
    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)],[i_0_5259])])])])])]) ).

fof(i_0_6171,plain,
    ! [X32542,X32543,X32544,X32545,X32546,X32549,X32550,X32551,X32552,X32553,X32554,X32555,X32556] :
      ( ( X32544 = hAPP(hAPP(c_List_Oappend(X32546),esk466_5(X32542,X32543,X32544,X32545,X32546)),hAPP(hAPP(c_List_Olist_OCons(X32546),X32543),esk467_5(X32542,X32543,X32544,X32545,X32546)))
        | hAPP(c_List_Ofilter(X32546,X32545),X32544) != hAPP(hAPP(c_List_Olist_OCons(X32546),X32543),X32542) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32546),X32549),hAPP(c_List_Oset(X32546),esk466_5(X32542,X32543,X32544,X32545,X32546))))
        | ~ hBOOL(hAPP(X32545,X32549))
        | hAPP(c_List_Ofilter(X32546,X32545),X32544) != hAPP(hAPP(c_List_Olist_OCons(X32546),X32543),X32542) )
      & ( hBOOL(hAPP(X32545,X32543))
        | hAPP(c_List_Ofilter(X32546,X32545),X32544) != hAPP(hAPP(c_List_Olist_OCons(X32546),X32543),X32542) )
      & ( X32542 = hAPP(c_List_Ofilter(X32546,X32545),esk467_5(X32542,X32543,X32544,X32545,X32546))
        | hAPP(c_List_Ofilter(X32546,X32545),X32544) != hAPP(hAPP(c_List_Olist_OCons(X32546),X32543),X32542) )
      & ( hBOOL(hAPP(hAPP(c_member(X32554),esk468_7(X32550,X32551,X32552,X32553,X32554,X32555,X32556)),hAPP(c_List_Oset(X32554),X32555)))
        | X32552 != hAPP(hAPP(c_List_Oappend(X32554),X32555),hAPP(hAPP(c_List_Olist_OCons(X32554),X32551),X32556))
        | ~ hBOOL(hAPP(X32553,X32551))
        | X32550 != hAPP(c_List_Ofilter(X32554,X32553),X32556)
        | hAPP(c_List_Ofilter(X32554,X32553),X32552) = hAPP(hAPP(c_List_Olist_OCons(X32554),X32551),X32550) )
      & ( hBOOL(hAPP(X32553,esk468_7(X32550,X32551,X32552,X32553,X32554,X32555,X32556)))
        | X32552 != hAPP(hAPP(c_List_Oappend(X32554),X32555),hAPP(hAPP(c_List_Olist_OCons(X32554),X32551),X32556))
        | ~ hBOOL(hAPP(X32553,X32551))
        | X32550 != hAPP(c_List_Ofilter(X32554,X32553),X32556)
        | hAPP(c_List_Ofilter(X32554,X32553),X32552) = hAPP(hAPP(c_List_Olist_OCons(X32554),X32551),X32550) ) ),
    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)],[i_0_5260])])])])])]) ).

fof(i_0_6172,plain,
    ! [X29444,X29445,X29446,X29447] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk365_4(X29444,X29445,X29446,X29447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk364_4(X29444,X29445,X29446,X29447))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X29444,X29445,X29446,X29447)),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk364_4(X29444,X29445,X29446,X29447))) )
      & ( hAPP(X29445,esk365_4(X29444,X29445,X29446,X29447)) = X29444
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk364_4(X29444,X29445,X29446,X29447))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk365_4(X29444,X29445,X29446,X29447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),X29446)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X29444,X29445,X29446,X29447)),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),X29446)) )
      & ( hAPP(X29445,esk365_4(X29444,X29445,X29446,X29447)) = X29444
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),X29446)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29447),esk365_4(X29444,X29445,X29446,X29447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X29445,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29445,esk364_4(X29444,X29445,X29446,X29447))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X29444,X29445,X29446,X29447)),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X29445,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29445,esk364_4(X29444,X29445,X29446,X29447))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X29445,esk365_4(X29444,X29445,X29446,X29447)) = X29444
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29444),hAPP(X29445,X29446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29445,X29447)),X29444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29447),X29446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X29445,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X29444,X29445,X29446,X29447)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29445,esk364_4(X29444,X29445,X29446,X29447))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val])])])]) ).

fof(i_0_6173,plain,
    ! [X33250,X33251,X33252,X33253,X33254] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33251),hAPP(c_Set_OCollect(X33251),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool,X33251),c_HOL_OEx(X33253)),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_fun(X33253,tc_HOL_Obool),X33251),hAPP(c_COMBS(X33253,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33253),c_fconj),hAPP(hAPP(c_COMBC(X33253,tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool),c_member(X33253)),X33252)))),X33250)))))
        | ~ hBOOL(hAPP(hAPP(c_member(X33253),X33254),X33252))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33251),hAPP(c_Set_OCollect(X33251),hAPP(hAPP(c_COMBC(X33251,X33253,tc_HOL_Obool),X33250),X33254))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33253),X33252)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33253),esk510_4(X33250,X33251,X33252,X33253)),X33252))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33251),hAPP(c_Set_OCollect(X33251),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool,X33251),c_HOL_OEx(X33253)),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_fun(X33253,tc_HOL_Obool),X33251),hAPP(c_COMBS(X33253,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33253),c_fconj),hAPP(hAPP(c_COMBC(X33253,tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool),c_member(X33253)),X33252)))),X33250)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33253),X33252)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33251),hAPP(c_Set_OCollect(X33251),hAPP(hAPP(c_COMBC(X33251,X33253,tc_HOL_Obool),X33250),esk510_4(X33250,X33251,X33252,X33253)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33251),hAPP(c_Set_OCollect(X33251),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool,X33251),c_HOL_OEx(X33253)),hAPP(hAPP(c_COMBB(tc_fun(X33253,tc_HOL_Obool),tc_fun(X33253,tc_HOL_Obool),X33251),hAPP(c_COMBS(X33253,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33253),c_fconj),hAPP(hAPP(c_COMBC(X33253,tc_fun(X33253,tc_HOL_Obool),tc_HOL_Obool),c_member(X33253)),X33252)))),X33250)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33253),X33252)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__bex])])])])]) ).

fof(i_0_6174,plain,
    ! [X33882,X33883,X33884,X33885,X33886,X33887] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33887),esk550_6(X33882,X33883,X33884,X33885,X33886,X33887)),X33885))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33884,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33887,tc_fun(X33884,tc_HOL_Obool)),X33885),X33883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33887,tc_fun(X33884,tc_HOL_Obool)),X33885),X33882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33887,tc_HOL_Obool)),X33886),X33885)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33884,tc_HOL_Obool)),hAPP(X33883,esk550_6(X33882,X33883,X33884,X33885,X33886,X33887))),hAPP(X33882,esk550_6(X33882,X33883,X33884,X33885,X33886,X33887))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33884,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33887,tc_fun(X33884,tc_HOL_Obool)),X33885),X33883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33887,tc_fun(X33884,tc_HOL_Obool)),X33885),X33882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33887,tc_HOL_Obool)),X33886),X33885)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__anti__mono])])])]) ).

fof(i_0_6175,plain,
    ! [X28797,X28798,X28799,X28800,X28801,X28802] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28802),esk333_6(X28797,X28798,X28799,X28800,X28801,X28802)),X28801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28802,X28799),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28802,X28799),X28801),X28798)),hAPP(hAPP(c_Product__Type_OSigma(X28802,X28799),X28800),X28797)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28802,tc_HOL_Obool)),X28801),X28800)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28799,tc_HOL_Obool)),hAPP(X28798,esk333_6(X28797,X28798,X28799,X28800,X28801,X28802))),hAPP(X28797,esk333_6(X28797,X28798,X28799,X28800,X28801,X28802))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28802,X28799),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28802,X28799),X28801),X28798)),hAPP(hAPP(c_Product__Type_OSigma(X28802,X28799),X28800),X28797)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28802,tc_HOL_Obool)),X28801),X28800)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).

fof(i_0_6176,plain,
    ! [X28301,X28302,X28303,X28304,X28305,X28306] :
      ( ( X28306 = hAPP(hAPP(c_Product__Type_OPair(X28305,X28304),esk324_6(X28301,X28302,X28303,X28304,X28305,X28306)),esk325_6(X28301,X28302,X28303,X28304,X28305,X28306))
        | hBOOL(hAPP(hAPP(c_member(X28303),X28302),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28305,X28304,tc_fun(X28303,tc_HOL_Obool)),X28301),X28306))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28303),X28302),hAPP(hAPP(X28301,esk324_6(X28301,X28302,X28303,X28304,X28305,X28306)),esk325_6(X28301,X28302,X28303,X28304,X28305,X28306))))
        | hBOOL(hAPP(hAPP(c_member(X28303),X28302),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28305,X28304,tc_fun(X28303,tc_HOL_Obool)),X28301),X28306))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).

cnf(i_0_6177,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5261]) ).

cnf(i_0_6178,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5262]) ).

fof(i_0_6179,plain,
    ! [X29187,X29188,X29189] : hAPP(c_Relation_Oconverse(X29189,X29188),X29187) = hAPP(c_Set_OCollect(tc_prod(X29188,X29189)),hAPP(c_Product__Type_Oprod_Oprod__case(X29188,X29189,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29188,tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_fun(X29189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29189,tc_fun(tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_fun(X29189,tc_HOL_Obool)),X29188),c_COMBC(X29189,tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29189,tc_prod(X29189,X29188)),tc_fun(X29189,tc_fun(tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_HOL_Obool)),X29188),hAPP(c_COMBB(tc_prod(X29189,X29188),tc_fun(tc_fun(tc_prod(X29189,X29188),tc_HOL_Obool),tc_HOL_Obool),X29189),c_member(tc_prod(X29189,X29188)))),hAPP(c_COMBC(X29189,X29188,tc_prod(X29189,X29188)),c_Product__Type_OPair(X29189,X29188))))),X29187))),
    inference(variable_rename,[status(thm)],[fact_converse__def]) ).

fof(i_0_6180,plain,
    ! [X31263,X31264,X31265,X31266] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31265),X31264))
        | c_Nitpick_Osetsum_H(X31265,X31266,X31263,X31264) = hAPP(c_List_Omonoid__add__class_Olistsum(X31266),hAPP(hAPP(c_List_Omap(X31265,X31266),X31263),c_Hilbert__Choice_OEps(tc_List_Olist(X31265),hAPP(hAPP(c_COMBS(tc_List_Olist(X31265),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X31265)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X31265),tc_fun(X31265,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X31265,tc_HOL_Obool),tc_fun(tc_fun(X31265,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X31265)),c_fequal),c_List_Oset(X31265))),X31264))),c_List_Odistinct(X31265)))))
        | ~ class_Groups_Ocomm__monoid__add(X31266) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X31265),X31264))
        | c_Nitpick_Osetsum_H(X31265,X31266,X31263,X31264) = c_Groups_Ozero__class_Ozero(X31266)
        | ~ class_Groups_Ocomm__monoid__add(X31266) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5263])])]) ).

fof(i_0_6181,plain,
    ! [X33588,X33589,X33590,X33591,X33592,X33593] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33592),esk531_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | hBOOL(hAPP(hAPP(c_member(X33592),esk530_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( hBOOL(hAPP(hAPP(c_member(X33592),esk532_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | hBOOL(hAPP(hAPP(c_member(X33592),esk530_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( esk531_6(X33588,X33589,X33590,X33591,X33592,X33593) != esk532_6(X33588,X33589,X33590,X33591,X33592,X33593)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | hBOOL(hAPP(hAPP(c_member(X33592),esk530_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33590,tc_HOL_Obool)),hAPP(X33589,esk531_6(X33588,X33589,X33590,X33591,X33592,X33593))),hAPP(X33589,esk532_6(X33588,X33589,X33590,X33591,X33592,X33593))) != c_Orderings_Obot__class_Obot(tc_fun(X33590,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | hBOOL(hAPP(hAPP(c_member(X33592),esk530_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( hBOOL(hAPP(hAPP(c_member(X33592),esk531_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33590),hAPP(X33589,esk530_6(X33588,X33589,X33590,X33591,X33592,X33593))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( hBOOL(hAPP(hAPP(c_member(X33592),esk532_6(X33588,X33589,X33590,X33591,X33592,X33593)),X33591))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33590),hAPP(X33589,esk530_6(X33588,X33589,X33590,X33591,X33592,X33593))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( esk531_6(X33588,X33589,X33590,X33591,X33592,X33593) != esk532_6(X33588,X33589,X33590,X33591,X33592,X33593)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33590),hAPP(X33589,esk530_6(X33588,X33589,X33590,X33591,X33592,X33593))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33590,tc_HOL_Obool)),hAPP(X33589,esk531_6(X33588,X33589,X33590,X33591,X33592,X33593))),hAPP(X33589,esk532_6(X33588,X33589,X33590,X33591,X33592,X33593))) != c_Orderings_Obot__class_Obot(tc_fun(X33590,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33592,tc_fun(X33590,tc_HOL_Obool)),X33591),X33589)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33592,c_Groups_Otimes__class_Otimes(X33593)),hAPP(hAPP(c_COMBB(tc_fun(X33590,tc_HOL_Obool),X33593,X33592),hAPP(hAPP(c_Finite__Set_Ofold__image(X33593,X33590,c_Groups_Otimes__class_Otimes(X33593)),X33588),c_Groups_Oone__class_Oone(X33593))),X33589)),c_Groups_Oone__class_Oone(X33593)),X33591)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33590),hAPP(X33589,esk530_6(X33588,X33589,X33590,X33591,X33592,X33593))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33592),X33591))
        | ~ class_Groups_Ocomm__monoid__mult(X33593) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__UN__disjoint])])])]) ).

fof(i_0_6182,plain,
    ! [X33291,X33292,X33293,X33294] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33294,tc_fun(X33293,tc_HOL_Obool)),X33292),X33291) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X33293,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X33293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33294,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33293,tc_HOL_Obool)),c_HOL_OEx(X33294)),hAPP(hAPP(c_COMBB(tc_fun(X33294,tc_HOL_Obool),tc_fun(X33294,tc_HOL_Obool),tc_fun(X33293,tc_HOL_Obool)),hAPP(c_COMBS(X33294,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33294),c_fconj),hAPP(hAPP(c_COMBC(X33294,tc_fun(X33294,tc_HOL_Obool),tc_HOL_Obool),c_member(X33294)),X33292)))),hAPP(hAPP(c_COMBC(tc_fun(X33293,tc_HOL_Obool),tc_fun(X33294,tc_fun(X33293,tc_HOL_Obool)),tc_fun(X33294,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33293,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33294,tc_fun(X33293,tc_HOL_Obool)),tc_fun(X33294,tc_HOL_Obool)),tc_fun(X33293,tc_HOL_Obool)),c_COMBB(tc_fun(X33293,tc_HOL_Obool),tc_HOL_Obool,X33294)),c_fequal)),X33291))))),
    inference(variable_rename,[status(thm)],[fact_INT__eq]) ).

fof(i_0_6183,plain,
    ! [X33287,X33288,X33289,X33290] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33290,tc_fun(X33289,tc_HOL_Obool)),X33288),X33287) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X33289,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X33289,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33290,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33289,tc_HOL_Obool)),c_HOL_OEx(X33290)),hAPP(hAPP(c_COMBB(tc_fun(X33290,tc_HOL_Obool),tc_fun(X33290,tc_HOL_Obool),tc_fun(X33289,tc_HOL_Obool)),hAPP(c_COMBS(X33290,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33290),c_fconj),hAPP(hAPP(c_COMBC(X33290,tc_fun(X33290,tc_HOL_Obool),tc_HOL_Obool),c_member(X33290)),X33288)))),hAPP(hAPP(c_COMBC(tc_fun(X33289,tc_HOL_Obool),tc_fun(X33290,tc_fun(X33289,tc_HOL_Obool)),tc_fun(X33290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33289,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33290,tc_fun(X33289,tc_HOL_Obool)),tc_fun(X33290,tc_HOL_Obool)),tc_fun(X33289,tc_HOL_Obool)),c_COMBB(tc_fun(X33289,tc_HOL_Obool),tc_HOL_Obool,X33290)),c_fequal)),X33287))))),
    inference(variable_rename,[status(thm)],[fact_UN__eq]) ).

cnf(i_0_6184,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5264]) ).

cnf(i_0_6185,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3))),X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(split_conjunct,[status(thm)],[i_0_5265]) ).

cnf(i_0_6186,plain,
    c_List_Ofoldr(X1,X2,X3,X4,X5) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X5),hAPP(c_List_Orev(X1),X4)),
    inference(split_conjunct,[status(thm)],[i_0_5266]) ).

fof(i_0_6187,plain,
    ! [X33466,X33467] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33467,X33466)
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X33467,tc_HOL_Obool)),esk527_2(X33466,X33467)),hAPP(hAPP(c_COMBB(tc_fun(X33467,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33467,tc_HOL_Obool)),c_HOL_OEx(X33467)),hAPP(hAPP(c_COMBB(tc_fun(X33467,tc_HOL_Obool),tc_fun(X33467,tc_HOL_Obool),tc_fun(X33467,tc_HOL_Obool)),hAPP(c_COMBS(X33467,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33467),c_fconj),hAPP(hAPP(c_COMBS(X33467,X33467,tc_HOL_Obool),X33466),c_COMBI(X33467))))),hAPP(hAPP(c_COMBC(tc_fun(X33467,tc_HOL_Obool),tc_fun(X33467,tc_fun(X33467,tc_HOL_Obool)),tc_fun(X33467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33467,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33467,tc_fun(X33467,tc_HOL_Obool)),tc_fun(X33467,tc_HOL_Obool)),tc_fun(X33467,tc_HOL_Obool)),c_COMBB(tc_fun(X33467,tc_HOL_Obool),tc_HOL_Obool,X33467)),c_fequal)),X33466))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__typedef])])]) ).

cnf(i_0_6188,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))),
    inference(split_conjunct,[status(thm)],[i_0_5267]) ).

cnf(i_0_6189,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_List_Oupt(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5268]) ).

fof(i_0_6190,plain,
    ! [X25265,X25266] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25266))
      | hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X25266))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25265))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X25266))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X25265))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).

fof(i_0_6191,plain,
    ! [X25387,X25388,X25389,X25390,X25391,X25392] :
      ( ~ class_Groups_Ocomm__monoid__add(X25392)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25391),X25390))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25391,X25392),X25389),X25390) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25388,X25392),hAPP(hAPP(c_COMBB(tc_fun(X25391,tc_HOL_Obool),X25392,X25388),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25391,X25392),X25389)),hAPP(hAPP(c_COMBB(tc_fun(X25391,tc_HOL_Obool),tc_fun(X25391,tc_HOL_Obool),X25388),c_Set_OCollect(X25391)),hAPP(hAPP(c_COMBB(tc_fun(X25391,tc_HOL_Obool),tc_fun(X25391,tc_HOL_Obool),X25388),hAPP(c_COMBS(X25391,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25391),c_fconj),hAPP(hAPP(c_COMBC(X25391,tc_fun(X25391,tc_HOL_Obool),tc_HOL_Obool),c_member(X25391)),X25390)))),hAPP(c_COMBC(X25391,X25388,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X25388,tc_fun(X25388,tc_HOL_Obool),X25391),c_fequal),X25387)))))),hAPP(c_Set_Oimage(X25391,X25388,X25387),X25390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).

fof(i_0_6192,plain,
    ! [X28246,X28247,X28248,X28249,X28250,X28251,X28252,X28253] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28248,X28248)),X28249),X28246))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28248,X28248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28248,tc_fun(X28248,tc_HOL_Obool),tc_fun(X28248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28248,tc_HOL_Obool),tc_fun(X28248,tc_HOL_Obool)),X28248),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28248)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28248),c_fconj),hAPP(hAPP(c_COMBC(X28248,tc_fun(X28248,tc_HOL_Obool),tc_HOL_Obool),c_member(X28248)),X28247)))),hAPP(hAPP(c_COMBC(X28248,tc_fun(X28248,tc_HOL_Obool),tc_HOL_Obool),c_member(X28248)),X28247))),X28249))
        | ~ c_Relation_Orefl__on(X28248,X28247,X28246) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28248),X28250),X28247))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28248,X28248)),hAPP(hAPP(c_Product__Type_OPair(X28248,X28248),X28250),X28250)),X28246))
        | ~ c_Relation_Orefl__on(X28248,X28247,X28246) )
      & ( hBOOL(hAPP(hAPP(c_member(X28253),esk316_3(X28251,X28252,X28253)),X28252))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28253,X28253)),esk315_3(X28251,X28252,X28253)),X28251))
        | c_Relation_Orefl__on(X28253,X28252,X28251) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28253,X28253)),hAPP(hAPP(c_Product__Type_OPair(X28253,X28253),esk316_3(X28251,X28252,X28253)),esk316_3(X28251,X28252,X28253))),X28251))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28253,X28253)),esk315_3(X28251,X28252,X28253)),X28251))
        | c_Relation_Orefl__on(X28253,X28252,X28251) )
      & ( hBOOL(hAPP(hAPP(c_member(X28253),esk316_3(X28251,X28252,X28253)),X28252))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28253,X28253,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_fun(X28253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28253,tc_HOL_Obool),tc_fun(X28253,tc_HOL_Obool)),X28253),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28253)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28253),c_fconj),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_HOL_Obool),c_member(X28253)),X28252)))),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_HOL_Obool),c_member(X28253)),X28252))),esk315_3(X28251,X28252,X28253)))
        | c_Relation_Orefl__on(X28253,X28252,X28251) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28253,X28253)),hAPP(hAPP(c_Product__Type_OPair(X28253,X28253),esk316_3(X28251,X28252,X28253)),esk316_3(X28251,X28252,X28253))),X28251))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28253,X28253,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_fun(X28253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28253,tc_HOL_Obool),tc_fun(X28253,tc_HOL_Obool)),X28253),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28253)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28253),c_fconj),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_HOL_Obool),c_member(X28253)),X28252)))),hAPP(hAPP(c_COMBC(X28253,tc_fun(X28253,tc_HOL_Obool),tc_HOL_Obool),c_member(X28253)),X28252))),esk315_3(X28251,X28252,X28253)))
        | c_Relation_Orefl__on(X28253,X28252,X28251) ) ),
    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_refl__on__def_H])])])])])]) ).

fof(i_0_6193,plain,
    ! [X33169,X33170,X33171,X33172] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X33172),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X33171,X33170,X33172,X33169) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X33171)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X33172),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X33171,X33170,X33172,X33169) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X33170,X33169)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X33171,X33170,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33172),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X33169))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171))))),tc_prod(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X33171)),hAPP(hAPP(c_COMBB(X33171,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33171)))),tc_prod(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X33171)),c_Product__Type_Ofst(X33171,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5269])]) ).

cnf(i_0_6194,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5270]) ).

cnf(i_0_6195,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_5271]) ).

cnf(i_0_6196,plain,
    hAPP(c_New__DSequence_Opos__not__seq(X1),X2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2))),
    inference(split_conjunct,[status(thm)],[i_0_5272]) ).

fof(i_0_6197,plain,
    ! [X30316,X30317,X30318,X30319,X30320] : hAPP(hAPP(c_List_Ozip(X30320,X30319),X30318),hAPP(hAPP(c_List_Olist_OCons(X30319),X30317),X30316)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X30320,X30319)),X30320,c_List_Olist_ONil(tc_prod(X30320,X30319)),hAPP(hAPP(c_COMBC(X30320,tc_fun(tc_List_Olist(X30320),tc_List_Olist(tc_prod(X30320,X30319))),tc_fun(tc_List_Olist(X30320),tc_List_Olist(tc_prod(X30320,X30319)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X30320,X30319)),tc_List_Olist(tc_prod(X30320,X30319))),tc_fun(tc_fun(tc_List_Olist(X30320),tc_List_Olist(tc_prod(X30320,X30319))),tc_fun(tc_List_Olist(X30320),tc_List_Olist(tc_prod(X30320,X30319)))),X30320),c_COMBB(tc_List_Olist(tc_prod(X30320,X30319)),tc_List_Olist(tc_prod(X30320,X30319)),tc_List_Olist(X30320))),hAPP(hAPP(c_COMBB(tc_prod(X30320,X30319),tc_fun(tc_List_Olist(tc_prod(X30320,X30319)),tc_List_Olist(tc_prod(X30320,X30319))),X30320),c_List_Olist_OCons(tc_prod(X30320,X30319))),hAPP(hAPP(c_COMBC(X30320,X30319,tc_prod(X30320,X30319)),c_Product__Type_OPair(X30320,X30319)),X30317)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30320),tc_List_Olist(X30319),tc_List_Olist(tc_prod(X30320,X30319))),c_List_Ozip(X30320,X30319)),X30316))),X30318),
    inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).

fof(i_0_6198,plain,
    ! [X27279,X27280,X27281,X27282] :
      ( ( ~ c_Wellfounded_Omax__extp(X27282,hAPP(hAPP(c_COMBC(X27282,tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27282,tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),X27282),c_COMBC(X27282,tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27282,tc_prod(X27282,X27282)),tc_fun(X27282,tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),X27282),hAPP(c_COMBB(tc_prod(X27282,X27282),tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool),X27282),c_member(tc_prod(X27282,X27282)))),c_Product__Type_OPair(X27282,X27282)))),X27281),X27280,X27279)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27282,tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27282,tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),X27280),X27279)),c_Wellfounded_Omax__ext(X27282,X27281))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27282,tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27282,tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),X27280),X27279)),c_Wellfounded_Omax__ext(X27282,X27281)))
        | c_Wellfounded_Omax__extp(X27282,hAPP(hAPP(c_COMBC(X27282,tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27282,tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_fun(X27282,tc_HOL_Obool)),X27282),c_COMBC(X27282,tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27282,tc_prod(X27282,X27282)),tc_fun(X27282,tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool)),X27282),hAPP(c_COMBB(tc_prod(X27282,X27282),tc_fun(tc_fun(tc_prod(X27282,X27282),tc_HOL_Obool),tc_HOL_Obool),X27282),c_member(tc_prod(X27282,X27282)))),c_Product__Type_OPair(X27282,X27282)))),X27281),X27280,X27279) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).

fof(i_0_6199,plain,
    ! [X29696,X29697,X29698,X29699] :
      ( ( ~ c_List_Olistrelp(X29699,hAPP(hAPP(c_COMBC(X29699,tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_fun(X29699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29699,tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_fun(X29699,tc_HOL_Obool)),X29699),c_COMBC(X29699,tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29699,tc_prod(X29699,X29699)),tc_fun(X29699,tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),X29699),hAPP(c_COMBB(tc_prod(X29699,X29699),tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool),X29699),c_member(tc_prod(X29699,X29699)))),c_Product__Type_OPair(X29699,X29699)))),X29698),X29697,X29696)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29699),tc_List_Olist(X29699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29699),tc_List_Olist(X29699)),X29697),X29696)),c_List_Olistrel(X29699,X29698))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29699),tc_List_Olist(X29699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29699),tc_List_Olist(X29699)),X29697),X29696)),c_List_Olistrel(X29699,X29698)))
        | c_List_Olistrelp(X29699,hAPP(hAPP(c_COMBC(X29699,tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_fun(X29699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29699,tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_fun(X29699,tc_HOL_Obool)),X29699),c_COMBC(X29699,tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29699,tc_prod(X29699,X29699)),tc_fun(X29699,tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool)),X29699),hAPP(c_COMBB(tc_prod(X29699,X29699),tc_fun(tc_fun(tc_prod(X29699,X29699),tc_HOL_Obool),tc_HOL_Obool),X29699),c_member(tc_prod(X29699,X29699)))),c_Product__Type_OPair(X29699,X29699)))),X29698),X29697,X29696) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).

fof(i_0_6200,plain,
    ! [X27985,X27986,X27987,X27988,X27989,X27990,X27991,X27992] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X27992,X27991),tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27992,X27991),X27988),hAPP(c_COMBK(tc_fun(X27991,tc_HOL_Obool),X27992),X27987))),hAPP(c_Product__Type_Oprod_Oprod__case(X27992,X27991,tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27992,tc_fun(X27991,tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool))),tc_fun(X27991,tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool)),tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool)),tc_fun(tc_fun(X27991,tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool))),tc_fun(X27991,tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool))),X27992),c_COMBB(tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool)),tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool),X27991)),hAPP(hAPP(c_COMBB(tc_fun(X27990,tc_HOL_Obool),tc_fun(tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool)),tc_fun(tc_prod(X27990,X27989),tc_HOL_Obool)),X27992),c_Product__Type_OSigma(X27990,X27989)),X27986))),hAPP(hAPP(c_COMBB(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27990,tc_fun(X27989,tc_HOL_Obool)),X27991),c_COMBK(tc_fun(X27989,tc_HOL_Obool),X27990)),X27985)))) = hAPP(hAPP(c_Product__Type_OSigma(X27990,X27989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27992,tc_fun(X27990,tc_HOL_Obool)),X27988),X27986)),hAPP(c_COMBK(tc_fun(X27989,tc_HOL_Obool),X27990),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27991,tc_fun(X27989,tc_HOL_Obool)),X27987),X27985))),
    inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).

fof(i_0_6201,plain,
    ! [X27126,X27127] :
      ( ( ~ c_Equiv__Relations_Oequiv(X27127,c_Orderings_Otop__class_Otop(tc_fun(X27127,tc_HOL_Obool)),X27126)
        | c_Equiv__Relations_Oequivp(X27127,hAPP(hAPP(c_COMBC(X27127,tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_fun(X27127,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27127,tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_fun(X27127,tc_HOL_Obool)),X27127),c_COMBC(X27127,tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27127,tc_prod(X27127,X27127)),tc_fun(X27127,tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),X27127),hAPP(c_COMBB(tc_prod(X27127,X27127),tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool),X27127),c_member(tc_prod(X27127,X27127)))),c_Product__Type_OPair(X27127,X27127)))),X27126)) )
      & ( ~ c_Equiv__Relations_Oequivp(X27127,hAPP(hAPP(c_COMBC(X27127,tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_fun(X27127,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27127,tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_fun(X27127,tc_HOL_Obool)),X27127),c_COMBC(X27127,tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27127,tc_prod(X27127,X27127)),tc_fun(X27127,tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool)),X27127),hAPP(c_COMBB(tc_prod(X27127,X27127),tc_fun(tc_fun(tc_prod(X27127,X27127),tc_HOL_Obool),tc_HOL_Obool),X27127),c_member(tc_prod(X27127,X27127)))),c_Product__Type_OPair(X27127,X27127)))),X27126))
        | c_Equiv__Relations_Oequiv(X27127,c_Orderings_Otop__class_Otop(tc_fun(X27127,tc_HOL_Obool)),X27126) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).

fof(i_0_6202,plain,
    ! [X28217,X28218] :
      ( ( ~ c_Wellfounded_OwfP(X28218,hAPP(hAPP(c_COMBC(X28218,tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28218,tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),X28218),c_COMBC(X28218,tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28218,tc_prod(X28218,X28218)),tc_fun(X28218,tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),X28218),hAPP(c_COMBB(tc_prod(X28218,X28218),tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool),X28218),c_member(tc_prod(X28218,X28218)))),c_Product__Type_OPair(X28218,X28218)))),X28217))
        | c_Wellfounded_Owf(X28218,X28217) )
      & ( ~ c_Wellfounded_Owf(X28218,X28217)
        | c_Wellfounded_OwfP(X28218,hAPP(hAPP(c_COMBC(X28218,tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28218,tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),X28218),c_COMBC(X28218,tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28218,tc_prod(X28218,X28218)),tc_fun(X28218,tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool)),X28218),hAPP(c_COMBB(tc_prod(X28218,X28218),tc_fun(tc_fun(tc_prod(X28218,X28218),tc_HOL_Obool),tc_HOL_Obool),X28218),c_member(tc_prod(X28218,X28218)))),c_Product__Type_OPair(X28218,X28218)))),X28217)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).

fof(i_0_6203,plain,
    ! [X26415,X26416,X26417,X26418] :
      ( ( hAPP(hAPP(c_COMBC(X26418,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),X26418),c_COMBC(X26417,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_prod(X26418,X26417)),tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),X26418),hAPP(c_COMBB(tc_prod(X26418,X26417),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool),X26417),c_member(tc_prod(X26418,X26417)))),c_Product__Type_OPair(X26418,X26417)))),X26416) != hAPP(hAPP(c_COMBC(X26418,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),X26418),c_COMBC(X26417,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_prod(X26418,X26417)),tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),X26418),hAPP(c_COMBB(tc_prod(X26418,X26417),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool),X26417),c_member(tc_prod(X26418,X26417)))),c_Product__Type_OPair(X26418,X26417)))),X26415)
        | X26416 = X26415 )
      & ( X26416 != X26415
        | hAPP(hAPP(c_COMBC(X26418,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),X26418),c_COMBC(X26417,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_prod(X26418,X26417)),tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),X26418),hAPP(c_COMBB(tc_prod(X26418,X26417),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool),X26417),c_member(tc_prod(X26418,X26417)))),c_Product__Type_OPair(X26418,X26417)))),X26416) = hAPP(hAPP(c_COMBC(X26418,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_fun(X26417,tc_HOL_Obool)),X26418),c_COMBC(X26417,tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26417,tc_prod(X26418,X26417)),tc_fun(X26417,tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool)),X26418),hAPP(c_COMBB(tc_prod(X26418,X26417),tc_fun(tc_fun(tc_prod(X26418,X26417),tc_HOL_Obool),tc_HOL_Obool),X26417),c_member(tc_prod(X26418,X26417)))),c_Product__Type_OPair(X26418,X26417)))),X26415) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_6204,plain,
    ! [X28309,X28310,X28311,X28312,X28313,X28314] :
      ( ( X28309 = hAPP(hAPP(c_Product__Type_OPair(X28312,X28311),esk326_6(X28309,X28310,X28311,X28312,X28313,X28314)),esk327_6(X28309,X28310,X28311,X28312,X28313,X28314))
        | ~ hBOOL(hAPP(hAPP(c_member(X28314),X28313),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28312,X28311,tc_fun(X28314,tc_HOL_Obool)),X28310),X28309))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28314),X28313),hAPP(hAPP(X28310,esk326_6(X28309,X28310,X28311,X28312,X28313,X28314)),esk327_6(X28309,X28310,X28311,X28312,X28313,X28314))))
        | ~ hBOOL(hAPP(hAPP(c_member(X28314),X28313),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28312,X28311,tc_fun(X28314,tc_HOL_Obool)),X28310),X28309))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5273])])])]) ).

fof(i_0_6205,plain,
    ! [X31041,X31042,X31043,X31044,X31045,X31046,X31047,X31048] : hAPP(hAPP(c_List_Omap(tc_prod(X31048,X31047),X31046),X31045),hAPP(hAPP(c_List_Ozip(X31048,X31047),X31044),hAPP(hAPP(c_List_Omap(X31043,X31047),X31042),X31041))) = hAPP(hAPP(c_List_Omap(tc_prod(X31048,X31043),X31046),hAPP(c_Product__Type_Oprod_Oprod__case(X31048,X31043,X31046),hAPP(hAPP(c_COMBB(tc_fun(X31043,tc_prod(X31048,X31047)),tc_fun(X31043,X31046),X31048),hAPP(c_COMBB(tc_prod(X31048,X31047),X31046,X31043),X31045)),hAPP(hAPP(c_COMBC(X31048,tc_fun(X31043,X31047),tc_fun(X31043,tc_prod(X31048,X31047))),hAPP(hAPP(c_COMBB(tc_fun(X31047,tc_prod(X31048,X31047)),tc_fun(tc_fun(X31043,X31047),tc_fun(X31043,tc_prod(X31048,X31047))),X31048),c_COMBB(X31047,tc_prod(X31048,X31047),X31043)),c_Product__Type_OPair(X31048,X31047))),X31042)))),hAPP(hAPP(c_List_Ozip(X31048,X31043),X31044),X31041)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).

fof(i_0_6206,plain,
    ! [X18179,X18180,X18181,X18182,X18183,X18184,X18185] :
      ( ( X18180 = hAPP(hAPP(X18183,X18179),esk29_7(X18179,X18180,X18181,X18182,X18183,X18184,X18185))
        | ~ hBOOL(hAPP(hAPP(c_member(X18185),X18179),X18181))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18185,X18184,X18183,X18182,X18181),X18180))
        | ~ c_Finite__Set_Ofun__left__comm(X18185,X18184,X18183) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18185,X18184,X18183,X18182,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18185,tc_HOL_Obool)),X18181),hAPP(hAPP(c_Set_Oinsert(X18185),X18179),c_Orderings_Obot__class_Obot(tc_fun(X18185,tc_HOL_Obool))))),esk29_7(X18179,X18180,X18181,X18182,X18183,X18184,X18185)))
        | ~ hBOOL(hAPP(hAPP(c_member(X18185),X18179),X18181))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18185,X18184,X18183,X18182,X18181),X18180))
        | ~ c_Finite__Set_Ofun__left__comm(X18185,X18184,X18183) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux])])])]) ).

fof(i_0_6207,plain,
    ! [X18208,X18209,X18210,X18211,X18212,X18213,X18214] :
      ( ( X18208 = hAPP(hAPP(X18212,X18210),esk34_7(X18208,X18209,X18210,X18211,X18212,X18213,X18214))
        | hBOOL(hAPP(hAPP(c_member(X18214),X18210),X18209))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18214,X18213,X18212,X18211,hAPP(hAPP(c_Set_Oinsert(X18214),X18210),X18209)),X18208))
        | ~ c_Finite__Set_Ofun__left__comm(X18214,X18213,X18212) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18214,X18213,X18212,X18211,X18209),esk34_7(X18208,X18209,X18210,X18211,X18212,X18213,X18214)))
        | hBOOL(hAPP(hAPP(c_member(X18214),X18210),X18209))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18214,X18213,X18212,X18211,hAPP(hAPP(c_Set_Oinsert(X18214),X18210),X18209)),X18208))
        | ~ c_Finite__Set_Ofun__left__comm(X18214,X18213,X18212) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5274])])])]) ).

fof(i_0_6208,plain,
    ! [X30334,X30335,X30336,X30337,X30338] : hAPP(hAPP(c_List_Ozip(X30338,X30337),hAPP(hAPP(c_List_Olist_OCons(X30338),X30336),X30335)),X30334) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X30338,X30337)),X30337,c_List_Olist_ONil(tc_prod(X30338,X30337)),hAPP(hAPP(c_COMBC(X30337,tc_fun(tc_List_Olist(X30337),tc_List_Olist(tc_prod(X30338,X30337))),tc_fun(tc_List_Olist(X30337),tc_List_Olist(tc_prod(X30338,X30337)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X30338,X30337)),tc_List_Olist(tc_prod(X30338,X30337))),tc_fun(tc_fun(tc_List_Olist(X30337),tc_List_Olist(tc_prod(X30338,X30337))),tc_fun(tc_List_Olist(X30337),tc_List_Olist(tc_prod(X30338,X30337)))),X30337),c_COMBB(tc_List_Olist(tc_prod(X30338,X30337)),tc_List_Olist(tc_prod(X30338,X30337)),tc_List_Olist(X30337))),hAPP(hAPP(c_COMBB(tc_prod(X30338,X30337),tc_fun(tc_List_Olist(tc_prod(X30338,X30337)),tc_List_Olist(tc_prod(X30338,X30337))),X30337),c_List_Olist_OCons(tc_prod(X30338,X30337))),hAPP(c_Product__Type_OPair(X30338,X30337),X30336)))),hAPP(c_List_Ozip(X30338,X30337),X30335))),X30334),
    inference(variable_rename,[status(thm)],[fact_zip__Cons1]) ).

cnf(i_0_6209,plain,
    ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_5275]) ).

cnf(i_0_6210,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5264]) ).

cnf(i_0_6211,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5264]) ).

cnf(i_0_6212,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5276]) ).

fof(i_0_6213,plain,
    ! [X25470,X25471,X25472,X25473] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25473),esk244_4(X25470,X25471,X25472,X25473)),X25472))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25471),hAPP(c_Set_Oimage(X25473,X25471,X25470),X25472)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25473),X25472)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25473),hAPP(c_Set_OCollect(X25473),hAPP(hAPP(c_COMBS(X25473,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25473),c_fconj),hAPP(hAPP(c_COMBC(X25473,tc_fun(X25473,tc_HOL_Obool),tc_HOL_Obool),c_member(X25473)),X25472))),hAPP(hAPP(c_COMBC(X25473,X25471,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X25471,tc_fun(X25471,tc_HOL_Obool),X25473),c_fequal),X25470)),hAPP(X25470,esk244_4(X25470,X25471,X25472,X25473)))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25471),hAPP(c_Set_Oimage(X25473,X25471,X25470),X25472)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25473),X25472)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5277])])])]) ).

fof(i_0_6214,plain,
    ! [X27598,X27599,X27600,X27601] :
      ( ( hBOOL(hAPP(X27601,esk291_4(X27598,X27599,X27600,X27601)))
        | c_Wellfounded_Owf(X27598,hAPP(c_Set_OCollect(tc_prod(X27598,X27598)),hAPP(c_Product__Type_Oprod_Oprod__case(X27598,X27598,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27598,tc_HOL_Obool),tc_fun(X27598,tc_HOL_Obool),X27598),hAPP(c_COMBS(X27598,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27598),c_fconj),X27601))),hAPP(hAPP(c_COMBC(X27598,tc_fun(X27598,X27598),tc_fun(X27598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27598,tc_HOL_Obool),tc_fun(tc_fun(X27598,X27598),tc_fun(X27598,tc_HOL_Obool)),X27598),c_COMBB(X27598,tc_HOL_Obool,X27598)),c_fequal)),X27599))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27600,hAPP(X27599,esk291_4(X27598,X27599,X27600,X27601)))),hAPP(X27600,esk291_4(X27598,X27599,X27600,X27601))))
        | c_Wellfounded_Owf(X27598,hAPP(c_Set_OCollect(tc_prod(X27598,X27598)),hAPP(c_Product__Type_Oprod_Oprod__case(X27598,X27598,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27598,tc_HOL_Obool),tc_fun(X27598,tc_HOL_Obool),X27598),hAPP(c_COMBS(X27598,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27598),c_fconj),X27601))),hAPP(hAPP(c_COMBC(X27598,tc_fun(X27598,X27598),tc_fun(X27598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27598,tc_HOL_Obool),tc_fun(tc_fun(X27598,X27598),tc_fun(X27598,tc_HOL_Obool)),X27598),c_COMBB(X27598,tc_HOL_Obool,X27598)),c_fequal)),X27599))))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__if__measure])])])]) ).

fof(i_0_6215,plain,
    ! [X27421,X27422,X27423] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27423,X27423),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27423,X27423,X27423),X27422),X27421)),X27422))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27423,X27422)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27423,X27421)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27423,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27423,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27423,tc_HOL_Obool),tc_fun(X27423,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X27423,X27422))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).

fof(i_0_6216,plain,
    ! [X27424,X27425,X27426] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27426,X27426),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27426,X27426,X27426),X27425),X27424)),X27425))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27426,X27425)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27426,X27424)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27426,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27426,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27426,tc_HOL_Obool),tc_fun(X27426,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X27426,X27425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).

fof(i_0_6217,plain,
    ! [X28727,X28728,X28729,X28730,X28731,X28732,X28733] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X28733,X28732,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28733)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28733),c_Hoare__Mirabelle_Opeek__and(X28733,X28731,X28730)),X28729),X28728)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28733),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X28733,X28732,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28733)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28733),c_Hoare__Mirabelle_Opeek__and(X28733,X28731,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X28730))),X28727),X28728)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28733),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X28733,X28732,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28733)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28733),X28731),c_Com_Ocom_OCond(X28730,X28729,X28727)),X28728)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28733),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf])]) ).

fof(i_0_6218,plain,
    ! [X17197,X17198,X17199,X17200,X17201,X17202] :
      ( ( hBOOL(hAPP(hAPP(X17197,esk7_6(X17197,X17198,X17199,X17200,X17201,X17202)),esk8_6(X17197,X17198,X17199,X17200,X17201,X17202)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17202,X17201,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17202)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17202),X17197),X17199),X17198)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17202),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17202,X17201,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17202)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17202),X17200),X17199),X17198)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17202),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17200,esk7_6(X17197,X17198,X17199,X17200,X17201,X17202)),esk8_6(X17197,X17198,X17199,X17200,X17201,X17202)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17202,X17201,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17202)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17202),X17197),X17199),X17198)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17202),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17202,X17201,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17202)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17202),X17200),X17199),X17198)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17202),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conseq1])])])]) ).

fof(i_0_6219,plain,
    ! [X17230,X17231,X17232,X17233,X17234,X17235] :
      ( ( hBOOL(hAPP(hAPP(X17231,esk11_6(X17230,X17231,X17232,X17233,X17234,X17235)),esk12_6(X17230,X17231,X17232,X17233,X17234,X17235)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17235,X17234,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17235),X17233),X17232),X17230)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17235),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17235,X17234,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17235),X17233),X17232),X17231)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17235),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17230,esk11_6(X17230,X17231,X17232,X17233,X17234,X17235)),esk12_6(X17230,X17231,X17232,X17233,X17234,X17235)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17235,X17234,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17235),X17233),X17232),X17230)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17235),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17235,X17234,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17235)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17235),X17233),X17232),X17231)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17235),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conseq2])])])]) ).

cnf(i_0_6220,plain,
    ( X2 = X3
    | c_List_Oconcat(X1,X2) != c_List_Oconcat(X1,X3)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk430_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5278]) ).

cnf(i_0_6221,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk429_3(X2,X3,X1)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)
    | c_List_Oconcat(X1,X3) != c_List_Oconcat(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5279]) ).

fof(i_0_6222,plain,
    ! [X25382,X25383,X25384,X25385,X25386] :
      ( ~ class_Groups_Ocomm__monoid__add(X25386)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25385),X25384))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25385,X25386),X25383),hAPP(c_Set_OCollect(X25385),hAPP(hAPP(c_COMBS(X25385,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25385),c_fconj),hAPP(hAPP(c_COMBC(X25385,tc_fun(X25385,tc_HOL_Obool),tc_HOL_Obool),c_member(X25385)),X25384))),hAPP(hAPP(c_COMBC(X25385,tc_fun(X25385,tc_HOL_Obool),tc_HOL_Obool),c_member(X25385)),X25382)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25385,X25386),hAPP(hAPP(c_COMBC(X25385,X25386,X25386),hAPP(hAPP(c_COMBS(X25385,X25386,tc_fun(X25386,X25386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25386,tc_fun(X25386,X25386)),X25385),c_If(X25386)),hAPP(hAPP(c_COMBC(X25385,tc_fun(X25385,tc_HOL_Obool),tc_HOL_Obool),c_member(X25385)),X25382))),X25383)),c_Groups_Ozero__class_Ozero(X25386))),X25384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H])]) ).

cnf(i_0_6223,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))),
    inference(split_conjunct,[status(thm)],[i_0_5280]) ).

cnf(i_0_6224,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Opred(X1),
    inference(split_conjunct,[status(thm)],[i_0_5281]) ).

cnf(i_0_6225,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5282]) ).

fof(i_0_6226,plain,
    ! [X31063,X31064,X31065,X31066,X31067,X31068,X31069,X31070] : hAPP(hAPP(c_List_Ozip(X31070,X31069),hAPP(hAPP(c_List_Omap(X31068,X31070),X31067),X31066)),hAPP(hAPP(c_List_Omap(X31065,X31069),X31064),X31063)) = hAPP(hAPP(c_List_Omap(tc_prod(X31068,X31065),tc_prod(X31070,X31069)),hAPP(c_Product__Type_Oprod_Oprod__case(X31068,X31065,tc_prod(X31070,X31069)),hAPP(hAPP(c_COMBC(X31068,tc_fun(X31065,X31069),tc_fun(X31065,tc_prod(X31070,X31069))),hAPP(hAPP(c_COMBB(tc_fun(X31069,tc_prod(X31070,X31069)),tc_fun(tc_fun(X31065,X31069),tc_fun(X31065,tc_prod(X31070,X31069))),X31068),c_COMBB(X31069,tc_prod(X31070,X31069),X31065)),hAPP(hAPP(c_COMBB(X31070,tc_fun(X31069,tc_prod(X31070,X31069)),X31068),c_Product__Type_OPair(X31070,X31069)),X31067))),X31064))),hAPP(hAPP(c_List_Ozip(X31068,X31065),X31066),X31063)),
    inference(variable_rename,[status(thm)],[fact_zip__map__map]) ).

cnf(i_0_6227,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5283]) ).

cnf(i_0_6228,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5284]) ).

fof(i_0_6229,plain,
    ! [X27099] : c_Wellfounded_Ofinite__psubset(X27099) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X27099,tc_HOL_Obool),tc_fun(X27099,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X27099,tc_HOL_Obool),tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X27099,tc_HOL_Obool),tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27099,tc_HOL_Obool)),c_COMBS(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27099,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X27099,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X27099,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X27099,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X27099)))),
    inference(variable_rename,[status(thm)],[fact_finite__psubset__def]) ).

cnf(i_0_6230,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5285]) ).

cnf(i_0_6231,plain,
    ( hAPP(c_Nat_OSuc,X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5286]) ).

fof(i_0_6232,plain,
    ! [X30159,X30160] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30160),X30159))
        | c_Nitpick_Ocard_H(X30160,X30159) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30160)),c_Hilbert__Choice_OEps(tc_List_Olist(X30160),hAPP(hAPP(c_COMBS(tc_List_Olist(X30160),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30160)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30160),tc_fun(X30160,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30160,tc_HOL_Obool),tc_fun(tc_fun(X30160,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30160)),c_fequal),c_List_Oset(X30160))),X30159))),c_List_Odistinct(X30160)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30160),X30159))
        | c_Nitpick_Ocard_H(X30160,X30159) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5287])]) ).

fof(i_0_6233,plain,
    ! [X25261,X25262] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25262))
      | hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X25262))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25261)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X25262))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X25261))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5288])]) ).

fof(i_0_6234,plain,
    ! [X28081,X28082,X28083,X28084,X28085,X28086,X28087,X28088,X28089] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28089,X28088)),hAPP(hAPP(c_Product__Type_OPair(X28089,X28088),X28087),X28086)),X28085))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28084,X28083)),hAPP(hAPP(c_Product__Type_OPair(X28084,X28083),hAPP(X28082,X28087)),hAPP(X28081,X28086))),hAPP(c_Set_Oimage(tc_prod(X28089,X28088),tc_prod(X28084,X28083),c_Product__Type_Omap__pair(X28089,X28084,X28088,X28083,X28082,X28081)),X28085))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])]) ).

cnf(i_0_6235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5289]) ).

cnf(i_0_6236,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5290]) ).

fof(i_0_6237,plain,
    ! [X32725,X32726,X32727,X32728,X32729,X32730,X32731] : c_New__Random__Sequence_Oneg__decr__bind(X32731,X32730,X32729,X32728,X32727,X32726,X32725) = c_New__DSequence_Oneg__decr__bind(X32731,X32730,hAPP(hAPP(hAPP(X32729,X32727),X32726),X32725),hAPP(hAPP(c_COMBC(X32731,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32730)))),hAPP(hAPP(c_COMBC(X32731,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32730))))),hAPP(hAPP(c_COMBC(X32731,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32730)))))),X32728),X32727)),X32726)),X32725)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(i_0_6238,plain,
    ! [X28287,X28288,X28289,X28290] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28290,tc_fun(X28289,tc_HOL_Obool)),X28288),X28287) = hAPP(c_Set_OCollect(X28289),hAPP(hAPP(c_COMBB(tc_fun(X28290,tc_HOL_Obool),tc_HOL_Obool,X28289),c_HOL_OAll(X28290)),hAPP(hAPP(c_COMBB(tc_fun(X28290,tc_HOL_Obool),tc_fun(X28290,tc_HOL_Obool),X28289),hAPP(c_COMBS(X28290,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28290),c_fimplies),hAPP(hAPP(c_COMBC(X28290,tc_fun(X28290,tc_HOL_Obool),tc_HOL_Obool),c_member(X28290)),X28288)))),hAPP(hAPP(c_COMBC(X28289,tc_fun(X28290,tc_fun(X28289,tc_HOL_Obool)),tc_fun(X28290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28289,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X28290,tc_fun(X28289,tc_HOL_Obool)),tc_fun(X28290,tc_HOL_Obool)),X28289),c_COMBB(tc_fun(X28289,tc_HOL_Obool),tc_HOL_Obool,X28290)),c_member(X28289))),X28287)))),
    inference(variable_rename,[status(thm)],[fact_INTER__def]) ).

fof(i_0_6239,plain,
    ! [X28277,X28278,X28279,X28280,X28281,X28282,X28283,X28284,X28285] :
      ( ( ~ c_Equiv__Relations_Ocongruent(X28280,X28279,X28278,X28277)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28280,X28280)),X28281),X28278))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28280,X28280,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28280,tc_fun(X28280,X28279),tc_fun(X28280,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28279,tc_HOL_Obool),tc_fun(tc_fun(X28280,X28279),tc_fun(X28280,tc_HOL_Obool)),X28280),c_COMBB(X28279,tc_HOL_Obool,X28280)),hAPP(hAPP(c_COMBB(X28279,tc_fun(X28279,tc_HOL_Obool),X28280),c_fequal),X28277))),X28277)),X28281)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28285,X28285)),esk320_4(X28282,X28283,X28284,X28285)),X28283))
        | c_Equiv__Relations_Ocongruent(X28285,X28284,X28283,X28282) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28285,X28285,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28285,tc_fun(X28285,X28284),tc_fun(X28285,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28284,tc_HOL_Obool),tc_fun(tc_fun(X28285,X28284),tc_fun(X28285,tc_HOL_Obool)),X28285),c_COMBB(X28284,tc_HOL_Obool,X28285)),hAPP(hAPP(c_COMBB(X28284,tc_fun(X28284,tc_HOL_Obool),X28285),c_fequal),X28282))),X28282)),esk320_4(X28282,X28283,X28284,X28285)))
        | c_Equiv__Relations_Ocongruent(X28285,X28284,X28283,X28282) ) ),
    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_congruent__def])])])])])]) ).

fof(i_0_6240,plain,
    ! [X25425,X25426,X25427,X25428,X25429] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),hAPP(c_Set_OCollect(X25426),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_HOL_Obool,X25426),c_HOL_OEx(X25428)),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_fun(X25428,tc_HOL_Obool),X25426),hAPP(c_COMBS(X25428,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25428),c_fconj),X25427))),X25425)))))
        | ~ hBOOL(hAPP(X25427,X25429))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),hAPP(c_Set_OCollect(X25426),hAPP(hAPP(c_COMBC(X25426,X25428,tc_HOL_Obool),X25425),X25429))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25428),hAPP(c_Set_OCollect(X25428),X25427))) )
      & ( hBOOL(hAPP(X25427,esk240_4(X25425,X25426,X25427,X25428)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),hAPP(c_Set_OCollect(X25426),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_HOL_Obool,X25426),c_HOL_OEx(X25428)),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_fun(X25428,tc_HOL_Obool),X25426),hAPP(c_COMBS(X25428,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25428),c_fconj),X25427))),X25425)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25428),hAPP(c_Set_OCollect(X25428),X25427))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),hAPP(c_Set_OCollect(X25426),hAPP(hAPP(c_COMBC(X25426,X25428,tc_HOL_Obool),X25425),esk240_4(X25425,X25426,X25427,X25428)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),hAPP(c_Set_OCollect(X25426),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_HOL_Obool,X25426),c_HOL_OEx(X25428)),hAPP(hAPP(c_COMBB(tc_fun(X25428,tc_HOL_Obool),tc_fun(X25428,tc_HOL_Obool),X25426),hAPP(c_COMBS(X25428,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25428),c_fconj),X25427))),X25425)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25428),hAPP(c_Set_OCollect(X25428),X25427))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex])])])])]) ).

fof(i_0_6241,plain,
    ! [X28044,X28045,X28046,X28047,X28048,X28049] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28048),esk302_6(X28044,X28045,X28046,X28047,X28048,X28049)),X28047))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28048,X28049),hAPP(hAPP(c_COMBS(X28048,tc_fun(X28046,tc_HOL_Obool),X28049),hAPP(hAPP(c_COMBB(tc_fun(X28046,X28049),tc_fun(tc_fun(X28046,tc_HOL_Obool),X28049),X28048),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28046,X28049)),X28044)),X28045)),X28047) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28048,X28046),X28049),hAPP(c_Product__Type_Oprod_Oprod__case(X28048,X28046,X28049),X28044)),hAPP(hAPP(c_Product__Type_OSigma(X28048,X28046),X28047),X28045))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28048),X28047))
        | ~ class_Groups_Ocomm__monoid__mult(X28049) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28046),hAPP(X28045,esk302_6(X28044,X28045,X28046,X28047,X28048,X28049))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28048,X28049),hAPP(hAPP(c_COMBS(X28048,tc_fun(X28046,tc_HOL_Obool),X28049),hAPP(hAPP(c_COMBB(tc_fun(X28046,X28049),tc_fun(tc_fun(X28046,tc_HOL_Obool),X28049),X28048),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28046,X28049)),X28044)),X28045)),X28047) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28048,X28046),X28049),hAPP(c_Product__Type_Oprod_Oprod__case(X28048,X28046,X28049),X28044)),hAPP(hAPP(c_Product__Type_OSigma(X28048,X28046),X28047),X28045))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28048),X28047))
        | ~ class_Groups_Ocomm__monoid__mult(X28049) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).

fof(i_0_6242,plain,
    ! [X28051,X28052,X28053,X28054,X28055,X28056] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28055),esk303_6(X28051,X28052,X28053,X28054,X28055,X28056)),X28054))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28055,X28056),hAPP(hAPP(c_COMBS(X28055,tc_fun(X28053,tc_HOL_Obool),X28056),hAPP(hAPP(c_COMBB(tc_fun(X28053,X28056),tc_fun(tc_fun(X28053,tc_HOL_Obool),X28056),X28055),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28053,X28056)),X28051)),X28052)),X28054) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28055,X28053),X28056),hAPP(c_Product__Type_Oprod_Oprod__case(X28055,X28053,X28056),X28051)),hAPP(hAPP(c_Product__Type_OSigma(X28055,X28053),X28054),X28052))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28055),X28054))
        | ~ class_Groups_Ocomm__monoid__add(X28056) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28053),hAPP(X28052,esk303_6(X28051,X28052,X28053,X28054,X28055,X28056))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28055,X28056),hAPP(hAPP(c_COMBS(X28055,tc_fun(X28053,tc_HOL_Obool),X28056),hAPP(hAPP(c_COMBB(tc_fun(X28053,X28056),tc_fun(tc_fun(X28053,tc_HOL_Obool),X28056),X28055),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28053,X28056)),X28051)),X28052)),X28054) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28055,X28053),X28056),hAPP(c_Product__Type_Oprod_Oprod__case(X28055,X28053,X28056),X28051)),hAPP(hAPP(c_Product__Type_OSigma(X28055,X28053),X28054),X28052))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28055),X28054))
        | ~ class_Groups_Ocomm__monoid__add(X28056) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).

fof(i_0_6243,plain,
    ! [X22719,X22720,X22721,X22722,X22723] :
      ( ~ class_Groups_Ocomm__monoid__add(X22723)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22722),X22721))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22722,X22723),X22720),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22722,tc_HOL_Obool)),X22721),X22719)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22722,X22723),hAPP(hAPP(c_COMBC(X22722,X22723,X22723),hAPP(hAPP(c_COMBS(X22722,X22723,tc_fun(X22723,X22723)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22723,tc_fun(X22723,X22723)),X22722),c_If(X22723)),hAPP(hAPP(c_COMBC(X22722,tc_fun(X22722,tc_HOL_Obool),tc_HOL_Obool),c_member(X22722)),X22719))),X22720)),c_Groups_Ozero__class_Ozero(X22723))),X22721) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).

fof(i_0_6244,plain,
    ! [X21036,X21037,X21038,X21039,X21040,X21041] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21041),X21038),X21039))
        | hAPP(c_Set_Ovimage(X21037,X21041,hAPP(hAPP(c_COMBC(X21037,X21041,X21041),hAPP(hAPP(c_COMBC(X21037,X21041,tc_fun(X21041,X21041)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21041,tc_fun(X21041,X21041)),X21037),c_If(X21041)),hAPP(hAPP(c_COMBC(X21037,tc_fun(X21037,tc_HOL_Obool),tc_HOL_Obool),c_member(X21037)),X21036))),X21040)),X21038)),X21039) = c_Orderings_Otop__class_Otop(tc_fun(X21037,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X21041),X21040),X21039)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21041),X21038),X21039))
        | hAPP(c_Set_Ovimage(X21037,X21041,hAPP(hAPP(c_COMBC(X21037,X21041,X21041),hAPP(hAPP(c_COMBC(X21037,X21041,tc_fun(X21041,X21041)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21041,tc_fun(X21041,X21041)),X21037),c_If(X21041)),hAPP(hAPP(c_COMBC(X21037,tc_fun(X21037,tc_HOL_Obool),tc_HOL_Obool),c_member(X21037)),X21036))),X21040)),X21038)),X21039) = X21036
        | ~ hBOOL(hAPP(hAPP(c_member(X21041),X21040),X21039)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21041),X21038),X21039))
        | hAPP(c_Set_Ovimage(X21037,X21041,hAPP(hAPP(c_COMBC(X21037,X21041,X21041),hAPP(hAPP(c_COMBC(X21037,X21041,tc_fun(X21041,X21041)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21041,tc_fun(X21041,X21041)),X21037),c_If(X21041)),hAPP(hAPP(c_COMBC(X21037,tc_fun(X21037,tc_HOL_Obool),tc_HOL_Obool),c_member(X21037)),X21036))),X21040)),X21038)),X21039) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21037,tc_HOL_Obool)),X21036)
        | hBOOL(hAPP(hAPP(c_member(X21041),X21040),X21039)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21041),X21038),X21039))
        | hAPP(c_Set_Ovimage(X21037,X21041,hAPP(hAPP(c_COMBC(X21037,X21041,X21041),hAPP(hAPP(c_COMBC(X21037,X21041,tc_fun(X21041,X21041)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21041,tc_fun(X21041,X21041)),X21037),c_If(X21041)),hAPP(hAPP(c_COMBC(X21037,tc_fun(X21037,tc_HOL_Obool),tc_HOL_Obool),c_member(X21037)),X21036))),X21040)),X21038)),X21039) = c_Orderings_Obot__class_Obot(tc_fun(X21037,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X21041),X21040),X21039)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5291])])]) ).

fof(i_0_6245,plain,
    ! [X23258,X23259,X23260,X23261] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23261,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23261,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk150_4(X23258,X23259,X23260,X23261))),X23260)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23261,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk150_4(X23258,X23259,X23260,X23261)),X23259))),X23258)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23261,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23261,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23260)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23261,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23258))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])]) ).

cnf(i_0_6246,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5292]) ).

fof(i_0_6247,plain,
    ! [X32732,X32733,X32734,X32735,X32736,X32737,X32738] : c_New__Random__Sequence_Opos__decr__bind(X32738,X32737,X32736,X32735,X32734,X32733,X32732) = c_New__DSequence_Opos__decr__bind(X32738,X32737,hAPP(hAPP(hAPP(X32736,X32734),X32733),X32732),hAPP(hAPP(c_COMBC(X32738,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32737))),hAPP(hAPP(c_COMBC(X32738,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32737)))),hAPP(hAPP(c_COMBC(X32738,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32737))))),X32735),X32734)),X32733)),X32732)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

cnf(i_0_6248,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5293]) ).

cnf(i_0_6249,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5294]) ).

cnf(i_0_6250,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_5295]) ).

cnf(i_0_6251,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5296]) ).

cnf(i_0_6252,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5297]) ).

fof(i_0_6253,plain,
    ! [X27774,X27775,X27776,X27777,X27778,X27779] : hAPP(c_Set_Oimage(X27779,tc_prod(X27778,X27777),hAPP(hAPP(c_COMBS(X27779,X27777,tc_prod(X27778,X27777)),hAPP(hAPP(c_COMBB(X27778,tc_fun(X27777,tc_prod(X27778,X27777)),X27779),c_Product__Type_OPair(X27778,X27777)),X27776)),X27775)),X27774) = hAPP(hAPP(c_Product__Type_OSigma(X27778,X27777),hAPP(c_Set_Oimage(X27779,X27778,X27776),X27774)),hAPP(hAPP(c_COMBB(tc_fun(X27779,tc_HOL_Obool),tc_fun(X27777,tc_HOL_Obool),X27778),c_Set_Oimage(X27779,X27777,X27775)),hAPP(hAPP(c_COMBC(X27778,tc_fun(X27779,tc_HOL_Obool),tc_fun(X27779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27779,tc_HOL_Obool),tc_fun(tc_fun(X27779,tc_HOL_Obool),tc_fun(X27779,tc_HOL_Obool)),X27778),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27779,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27778,tc_HOL_Obool),tc_fun(X27779,tc_HOL_Obool),X27778),c_Set_Ovimage(X27779,X27778,X27776)),hAPP(hAPP(c_COMBC(X27778,tc_fun(X27778,tc_HOL_Obool),tc_fun(X27778,tc_HOL_Obool)),c_Set_Oinsert(X27778)),c_Orderings_Obot__class_Obot(tc_fun(X27778,tc_HOL_Obool)))))),X27774))),
    inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma]) ).

cnf(i_0_6254,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5298]) ).

fof(i_0_6255,plain,
    ! [X32977,X32978] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X32978)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X32978),X32977) = c_Lazy__Sequence_Oappend(tc_List_Olist(X32978),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X32978)),c_List_Olist_ONil(X32978)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32978))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32977)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X32978,tc_List_Olist(X32978)),tc_List_Olist(X32978),c_Lazy__Sequence_Oproduct(X32978,tc_List_Olist(X32978),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32978,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32977),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X32978),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32977),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X32978,tc_List_Olist(X32978),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32978))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32978),tc_List_Olist(X32978)),tc_fun(tc_List_Olist(X32978),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32978))),X32978),hAPP(c_COMBB(tc_List_Olist(X32978),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32978)),tc_List_Olist(X32978)),c_Lazy__Sequence_Osingle(tc_List_Olist(X32978)))),c_List_Olist_OCons(X32978))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X32978)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps])]) ).

fof(i_0_6256,plain,
    ! [X28291,X28292] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X28292)
      | c_Complete__Lattice_OSup__class_OSup(X28292,X28291) = c_Complete__Lattice_OInf__class_OInf(X28292,hAPP(c_Set_OCollect(X28292),hAPP(hAPP(c_COMBB(tc_fun(X28292,tc_HOL_Obool),tc_HOL_Obool,X28292),c_HOL_OAll(X28292)),hAPP(hAPP(c_COMBB(tc_fun(X28292,tc_HOL_Obool),tc_fun(X28292,tc_HOL_Obool),X28292),hAPP(c_COMBS(X28292,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28292),c_fimplies),hAPP(hAPP(c_COMBC(X28292,tc_fun(X28292,tc_HOL_Obool),tc_HOL_Obool),c_member(X28292)),X28291)))),hAPP(c_COMBC(X28292,X28292,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X28292)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).

fof(i_0_6257,plain,
    ! [X24014,X24015,X24016,X24017,X24018,X24019] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24018),esk165_6(X24014,X24015,X24016,X24017,X24018,X24019)),X24017))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24018,X24019),X24016),X24017) != X24015
        | ~ hBOOL(hAPP(hAPP(c_member(X24018),X24014),X24017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24019),hAPP(X24016,X24014)),X24015))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24018),X24017))
        | ~ class_Groups_Oordered__ab__group__add(X24019) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24019),c_Groups_Ozero__class_Ozero(X24019)),hAPP(X24016,esk165_6(X24014,X24015,X24016,X24017,X24018,X24019))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24018,X24019),X24016),X24017) != X24015
        | ~ hBOOL(hAPP(hAPP(c_member(X24018),X24014),X24017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24019),hAPP(X24016,X24014)),X24015))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24018),X24017))
        | ~ class_Groups_Oordered__ab__group__add(X24019) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound])])])]) ).

fof(i_0_6258,plain,
    ! [X20292,X20293,X20294,X20295,X20296,X20297] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20296),X20294),X20295))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20296,X20297),hAPP(hAPP(c_COMBC(X20296,X20297,X20297),hAPP(hAPP(c_COMBS(X20296,X20297,tc_fun(X20297,X20297)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20297,tc_fun(X20297,X20297)),X20296),c_If(X20297)),hAPP(hAPP(c_COMBC(X20296,X20296,tc_HOL_Obool),c_fequal),X20294))),X20293)),X20292)),X20295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20297),hAPP(X20293,X20294)),hAPP(hAPP(c_Power_Opower__class_Opower(X20297),X20292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X20296),X20295)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20296),X20295))
        | ~ class_Groups_Ocomm__monoid__mult(X20297) )
      & ( hBOOL(hAPP(hAPP(c_member(X20296),X20294),X20295))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20296,X20297),hAPP(hAPP(c_COMBC(X20296,X20297,X20297),hAPP(hAPP(c_COMBS(X20296,X20297,tc_fun(X20297,X20297)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20297,tc_fun(X20297,X20297)),X20296),c_If(X20297)),hAPP(hAPP(c_COMBC(X20296,X20296,tc_HOL_Obool),c_fequal),X20294))),X20293)),X20292)),X20295) = hAPP(hAPP(c_Power_Opower__class_Opower(X20297),X20292),hAPP(c_Finite__Set_Ocard(X20296),X20295))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20296),X20295))
        | ~ class_Groups_Ocomm__monoid__mult(X20297) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5299])])]) ).

fof(i_0_6259,plain,
    ! [X20092,X20093,X20094,X20095,X20096] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20095),X20093),X20094))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20095,X20096),hAPP(hAPP(c_COMBC(X20095,X20096,X20096),hAPP(hAPP(c_COMBS(X20095,X20096,tc_fun(X20096,X20096)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20096,tc_fun(X20096,X20096)),X20095),c_If(X20096)),hAPP(hAPP(c_COMBC(X20095,X20095,tc_HOL_Obool),c_fequal),X20093))),X20092)),c_Groups_Oone__class_Oone(X20096))),X20094) = hAPP(X20092,X20093)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20095),X20094))
        | ~ class_Groups_Ocomm__monoid__mult(X20096) )
      & ( hBOOL(hAPP(hAPP(c_member(X20095),X20093),X20094))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20095,X20096),hAPP(hAPP(c_COMBC(X20095,X20096,X20096),hAPP(hAPP(c_COMBS(X20095,X20096,tc_fun(X20096,X20096)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20096,tc_fun(X20096,X20096)),X20095),c_If(X20096)),hAPP(hAPP(c_COMBC(X20095,X20095,tc_HOL_Obool),c_fequal),X20093))),X20092)),c_Groups_Oone__class_Oone(X20096))),X20094) = c_Groups_Oone__class_Oone(X20096)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20095),X20094))
        | ~ class_Groups_Ocomm__monoid__mult(X20096) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5300])])]) ).

fof(i_0_6260,plain,
    ! [X22669,X22670,X22671,X22672,X22673] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22672),X22670),X22671))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22672,X22673),hAPP(hAPP(c_COMBC(X22672,X22673,X22673),hAPP(hAPP(c_COMBS(X22672,X22673,tc_fun(X22673,X22673)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22673,tc_fun(X22673,X22673)),X22672),c_If(X22673)),hAPP(hAPP(c_COMBC(X22672,X22672,tc_HOL_Obool),c_fequal),X22670))),X22669)),c_Groups_Ozero__class_Ozero(X22673))),X22671) = hAPP(X22669,X22670)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22672),X22671))
        | ~ class_Groups_Ocomm__monoid__add(X22673) )
      & ( hBOOL(hAPP(hAPP(c_member(X22672),X22670),X22671))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22672,X22673),hAPP(hAPP(c_COMBC(X22672,X22673,X22673),hAPP(hAPP(c_COMBS(X22672,X22673,tc_fun(X22673,X22673)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22673,tc_fun(X22673,X22673)),X22672),c_If(X22673)),hAPP(hAPP(c_COMBC(X22672,X22672,tc_HOL_Obool),c_fequal),X22670))),X22669)),c_Groups_Ozero__class_Ozero(X22673))),X22671) = c_Groups_Ozero__class_Ozero(X22673)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22672),X22671))
        | ~ class_Groups_Ocomm__monoid__add(X22673) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5301])])]) ).

fof(i_0_6261,plain,
    ! [X28293,X28294] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X28294)
      | c_Complete__Lattice_OInf__class_OInf(X28294,X28293) = c_Complete__Lattice_OSup__class_OSup(X28294,hAPP(c_Set_OCollect(X28294),hAPP(hAPP(c_COMBB(tc_fun(X28294,tc_HOL_Obool),tc_HOL_Obool,X28294),c_HOL_OAll(X28294)),hAPP(hAPP(c_COMBB(tc_fun(X28294,tc_HOL_Obool),tc_fun(X28294,tc_HOL_Obool),X28294),hAPP(c_COMBS(X28294,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28294),c_fimplies),hAPP(hAPP(c_COMBC(X28294,tc_fun(X28294,tc_HOL_Obool),tc_HOL_Obool),c_member(X28294)),X28293)))),c_Orderings_Oord__class_Oless__eq(X28294))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).

fof(i_0_6262,plain,
    ! [X21339,X21340,X21341,X21342,X21343,X21344,X21345] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21345,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21344,tc_fun(X21345,tc_HOL_Obool)),X21343),X21342)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21341,tc_fun(X21345,tc_HOL_Obool)),X21340),X21339)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21344,tc_fun(X21345,tc_HOL_Obool)),X21343),hAPP(hAPP(c_COMBB(tc_fun(X21341,tc_fun(X21345,tc_HOL_Obool)),tc_fun(X21345,tc_HOL_Obool),X21344),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21341,tc_fun(X21345,tc_HOL_Obool)),X21340)),hAPP(hAPP(c_COMBC(X21344,tc_fun(X21341,tc_fun(X21345,tc_HOL_Obool)),tc_fun(X21341,tc_fun(X21345,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21345,tc_HOL_Obool),tc_fun(X21345,tc_HOL_Obool)),tc_fun(tc_fun(X21341,tc_fun(X21345,tc_HOL_Obool)),tc_fun(X21341,tc_fun(X21345,tc_HOL_Obool))),X21344),c_COMBB(tc_fun(X21345,tc_HOL_Obool),tc_fun(X21345,tc_HOL_Obool),X21341)),hAPP(hAPP(c_COMBB(tc_fun(X21345,tc_HOL_Obool),tc_fun(tc_fun(X21345,tc_HOL_Obool),tc_fun(X21345,tc_HOL_Obool)),X21344),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21345,tc_HOL_Obool))),X21342))),X21339))),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(i_0_6263,plain,
    ! [X21681,X21682,X21683,X21684,X21685,X21686,X21687] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21687,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21686,tc_fun(X21687,tc_HOL_Obool)),X21685),X21684)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21683,tc_fun(X21687,tc_HOL_Obool)),X21682),X21681)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21686,tc_fun(X21687,tc_HOL_Obool)),X21685),hAPP(hAPP(c_COMBB(tc_fun(X21683,tc_fun(X21687,tc_HOL_Obool)),tc_fun(X21687,tc_HOL_Obool),X21686),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21683,tc_fun(X21687,tc_HOL_Obool)),X21682)),hAPP(hAPP(c_COMBC(X21686,tc_fun(X21683,tc_fun(X21687,tc_HOL_Obool)),tc_fun(X21683,tc_fun(X21687,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21687,tc_HOL_Obool),tc_fun(X21687,tc_HOL_Obool)),tc_fun(tc_fun(X21683,tc_fun(X21687,tc_HOL_Obool)),tc_fun(X21683,tc_fun(X21687,tc_HOL_Obool))),X21686),c_COMBB(tc_fun(X21687,tc_HOL_Obool),tc_fun(X21687,tc_HOL_Obool),X21683)),hAPP(hAPP(c_COMBB(tc_fun(X21687,tc_HOL_Obool),tc_fun(tc_fun(X21687,tc_HOL_Obool),tc_fun(X21687,tc_HOL_Obool)),X21686),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21687,tc_HOL_Obool))),X21684))),X21681))),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2]) ).

cnf(i_0_6264,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5302]) ).

cnf(i_0_6265,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5303]) ).

cnf(i_0_6266,plain,
    hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7)) = hAPP(c_Product__Type_Oapfst(X5,X3,X2,X6),hAPP(c_Product__Type_Oapsnd(X1,X2,X5,X4),X7)),
    inference(split_conjunct,[status(thm)],[i_0_5304]) ).

cnf(i_0_6267,plain,
    c_Product__Type_Oapfst(X1,X2,X3,X4) = c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),
    inference(split_conjunct,[status(thm)],[i_0_5305]) ).

fof(i_0_6268,plain,
    ! [X32750,X32751,X32752,X32753,X32754,X32755,X32756] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X32756,X32755,X32754,X32753),X32752),X32751),X32750) = c_New__DSequence_Oneg__bind(X32756,X32755,hAPP(hAPP(hAPP(X32754,X32752),X32751),X32750),hAPP(hAPP(c_COMBC(X32756,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32755)))),hAPP(hAPP(c_COMBC(X32756,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32755))))),hAPP(hAPP(c_COMBC(X32756,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32755)))))),X32753),X32752)),X32751)),X32750)),
    inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).

fof(i_0_6269,plain,
    ! [X30567,X30568,X30569,X30570,X30571] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30571),tc_List_Olist(X30571))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30571),tc_List_Olist(X30571)),hAPP(hAPP(c_List_Oappend(X30571),X30570),X30569)),hAPP(hAPP(c_List_Oappend(X30571),X30570),X30568))),c_List_Olexord(X30571,X30567)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),esk414_5(X30567,X30568,X30569,X30570,X30571)),esk414_5(X30567,X30568,X30569,X30570,X30571))),X30567))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30571),tc_List_Olist(X30571))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30571),tc_List_Olist(X30571)),X30569),X30568)),c_List_Olexord(X30571,X30567))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5306])])]) ).

fof(i_0_6270,plain,
    ! [X33224,X33225] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X33225,tc_HOL_Obool),X33224) = hAPP(c_Set_OCollect(X33225),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33225,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X33225),c_HOL_OEx(tc_fun(X33225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33225,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33225,tc_HOL_Obool),tc_HOL_Obool),X33225),hAPP(c_COMBS(tc_fun(X33225,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33225,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33225,tc_HOL_Obool),tc_fun(tc_fun(X33225,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33225,tc_HOL_Obool))),X33224)))),c_member(X33225)))),
    inference(variable_rename,[status(thm)],[fact_Union__eq]) ).

fof(i_0_6271,plain,
    ! [X28317,X28318] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X28318,tc_HOL_Obool),X28317) = hAPP(c_Set_OCollect(X28318),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28318,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X28318),c_HOL_OAll(tc_fun(X28318,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28318,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X28318,tc_HOL_Obool),tc_HOL_Obool),X28318),hAPP(c_COMBS(tc_fun(X28318,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X28318,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X28318,tc_HOL_Obool),tc_fun(tc_fun(X28318,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X28318,tc_HOL_Obool))),X28317)))),c_member(X28318)))),
    inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).

fof(i_0_6272,plain,
    ! [X29406,X29407,X29408,X29409,X29410] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),esk356_5(X29406,X29407,X29408,X29409,X29410))),c_Transitive__Closure_Ortrancl(X29410,X29407)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,X29407)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29410,X29410),tc_HOL_Obool)),X29407),X29406)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),esk356_5(X29406,X29407,X29408,X29409,X29410)),esk357_5(X29406,X29407,X29408,X29409,X29410))),X29406))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,X29407)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29410,X29410),tc_HOL_Obool)),X29407),X29406)))) )
      & ( esk356_5(X29406,X29407,X29408,X29409,X29410) != esk357_5(X29406,X29407,X29408,X29409,X29410)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,X29407)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29410,X29410)),hAPP(hAPP(c_Product__Type_OPair(X29410,X29410),X29409),X29408)),c_Transitive__Closure_Ortrancl(X29410,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29410,X29410),tc_HOL_Obool)),X29407),X29406)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE])])])]) ).

fof(i_0_6273,plain,
    ! [X29399,X29400,X29401,X29402,X29403] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),esk354_5(X29399,X29400,X29401,X29402,X29403)),X29401)),c_Transitive__Closure_Ortrancl(X29403,X29400)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,X29400)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29403,X29403),tc_HOL_Obool)),X29400),X29399)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),esk355_5(X29399,X29400,X29401,X29402,X29403)),esk354_5(X29399,X29400,X29401,X29402,X29403))),X29399))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,X29400)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29403,X29403),tc_HOL_Obool)),X29400),X29399)))) )
      & ( esk355_5(X29399,X29400,X29401,X29402,X29403) != esk354_5(X29399,X29400,X29401,X29402,X29403)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,X29400)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),X29402),X29401)),c_Transitive__Closure_Ortrancl(X29403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29403,X29403),tc_HOL_Obool)),X29400),X29399)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE])])])]) ).

fof(i_0_6274,plain,
    ! [X31035,X31036,X31037,X31038,X31039,X31040] : hAPP(hAPP(c_List_Ozip(X31040,X31039),X31038),hAPP(hAPP(c_List_Omap(X31037,X31039),X31036),X31035)) = hAPP(hAPP(c_List_Omap(tc_prod(X31040,X31037),tc_prod(X31040,X31039)),hAPP(c_Product__Type_Oprod_Oprod__case(X31040,X31037,tc_prod(X31040,X31039)),hAPP(hAPP(c_COMBC(X31040,tc_fun(X31037,X31039),tc_fun(X31037,tc_prod(X31040,X31039))),hAPP(hAPP(c_COMBB(tc_fun(X31039,tc_prod(X31040,X31039)),tc_fun(tc_fun(X31037,X31039),tc_fun(X31037,tc_prod(X31040,X31039))),X31040),c_COMBB(X31039,tc_prod(X31040,X31039),X31037)),c_Product__Type_OPair(X31040,X31039))),X31036))),hAPP(hAPP(c_List_Ozip(X31040,X31037),X31038),X31035)),
    inference(variable_rename,[status(thm)],[fact_zip__map2]) ).

cnf(i_0_6275,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5307]) ).

cnf(i_0_6276,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5285]) ).

cnf(i_0_6277,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5286]) ).

fof(i_0_6278,plain,
    ! [X25236,X25237,X25238] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk233_3(X25236,X25237,X25238)),X25238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25236),hAPP(X25237,X25238)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25237,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25236))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_3(X25236,X25237,X25238)),X25238)) )
      & ( hAPP(X25237,esk233_3(X25236,X25237,X25238)) = X25236
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25236),hAPP(X25237,X25238)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25237,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25236))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_3(X25236,X25237,X25238)),X25238)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk233_3(X25236,X25237,X25238)),X25238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25236),hAPP(X25237,X25238)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25237,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25236))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X25237,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk232_3(X25236,X25237,X25238)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X25237,esk232_3(X25236,X25237,X25238))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X25237,esk233_3(X25236,X25237,X25238)) = X25236
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25236),hAPP(X25237,X25238)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25237,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25236))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X25237,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk232_3(X25236,X25237,X25238)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X25237,esk232_3(X25236,X25237,X25238))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val])])])]) ).

fof(i_0_6279,plain,
    ! [X25209,X25210,X25211] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk225_3(X25209,X25210,X25211)),X25211))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25209),hAPP(X25210,X25211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25209))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk224_3(X25209,X25210,X25211)),X25211)) )
      & ( hAPP(X25210,esk225_3(X25209,X25210,X25211)) = X25209
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25209),hAPP(X25210,X25211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25209))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk224_3(X25209,X25210,X25211)),X25211)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk225_3(X25209,X25210,X25211)),X25211))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25209),hAPP(X25210,X25211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X25210,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk224_3(X25209,X25210,X25211)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X25210,esk224_3(X25209,X25210,X25211))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X25210,esk225_3(X25209,X25210,X25211)) = X25209
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25209),hAPP(X25210,X25211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X25210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X25210,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk224_3(X25209,X25210,X25211)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X25210,esk224_3(X25209,X25210,X25211))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__val__lemma])])])]) ).

fof(i_0_6280,plain,
    ! [X29382,X29383,X29384,X29385,X29386] :
      ( ( X29383 = hAPP(c_Nat_OSuc,esk350_5(X29382,X29383,X29384,X29385,X29386))
        | X29383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),esk349_5(X29382,X29383,X29384,X29385,X29386))),X29382))
        | X29383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),esk349_5(X29382,X29383,X29384,X29385,X29386)),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),esk350_5(X29382,X29383,X29384,X29385,X29386)),X29382)))
        | X29383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) )
      & ( X29383 = hAPP(c_Nat_OSuc,esk350_5(X29382,X29383,X29384,X29385,X29386))
        | X29385 = X29384
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),esk349_5(X29382,X29383,X29384,X29385,X29386))),X29382))
        | X29385 = X29384
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),esk349_5(X29382,X29383,X29384,X29385,X29386)),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),esk350_5(X29382,X29383,X29384,X29385,X29386)),X29382)))
        | X29385 = X29384
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29386,X29386)),hAPP(hAPP(c_Product__Type_OPair(X29386,X29386),X29385),X29384)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29386,X29386),tc_HOL_Obool),X29383),X29382))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5308])])])]) ).

fof(i_0_6281,plain,
    ! [X20427,X20428,X20429,X20430] :
      ( ~ c_Fun_Oinj__on(X20430,X20429,X20428,c_Orderings_Otop__class_Otop(tc_fun(X20430,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20430,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20430,X20429,X20428),hAPP(hAPP(c_Set_Oinsert(X20429),X20427),c_Orderings_Obot__class_Obot(tc_fun(X20429,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X20430),c_HOL_OThe(X20430,hAPP(hAPP(c_COMBC(X20430,X20429,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20429,tc_fun(X20429,tc_HOL_Obool),X20430),c_fequal),X20428)),X20427))),c_Orderings_Obot__class_Obot(tc_fun(X20430,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).

fof(i_0_6282,plain,
    ! [X32771,X32772,X32773,X32774,X32775,X32776,X32777] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X32777,X32776,X32775,X32774),X32773),X32772),X32771) = c_New__DSequence_Opos__bind(X32777,X32776,hAPP(hAPP(hAPP(X32775,X32773),X32772),X32771),hAPP(hAPP(c_COMBC(X32777,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32776))),hAPP(hAPP(c_COMBC(X32777,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32776)))),hAPP(hAPP(c_COMBC(X32777,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32776))))),X32774),X32773)),X32772)),X32771)),
    inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).

fof(i_0_6283,plain,
    ! [X34103,X34104] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34104,X34103) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34104),X34103))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34103),X34104)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34104),X34103))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34104,X34103) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34103),X34104))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34104,X34103) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5309])])]) ).

fof(i_0_6284,plain,
    ! [X34101,X34102] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34102,X34101) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34102),X34101))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34101),X34102)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34102),X34101))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34102,X34101) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34101),X34102))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34102,X34101) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5310])])]) ).

fof(i_0_6285,plain,
    ! [X34099,X34100] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34100,X34099)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34100),X34099))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34099),X34100)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34100),X34099))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34100,X34099) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34099),X34100))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34100,X34099) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5311])])]) ).

fof(i_0_6286,plain,
    ! [X34097,X34098] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34098,X34097)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34098),X34097))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34097),X34098)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34098),X34097))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34098,X34097) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34097),X34098))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34098,X34097) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5312])])]) ).

fof(i_0_6287,plain,
    ! [X26384,X26385,X26386,X26387] : c_Nitpick_Oprod(X26387,X26386,X26385,X26384) = hAPP(c_Set_OCollect(tc_prod(X26387,X26386)),hAPP(c_Product__Type_Oprod_Oprod__case(X26387,X26386,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26387,tc_fun(X26386,tc_HOL_Obool),tc_fun(X26386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X26386,tc_HOL_Obool),tc_fun(X26386,tc_HOL_Obool)),X26387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X26386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26387),c_fconj),hAPP(hAPP(c_COMBC(X26387,tc_fun(X26387,tc_HOL_Obool),tc_HOL_Obool),c_member(X26387)),X26385)))),hAPP(hAPP(c_COMBC(X26386,tc_fun(X26386,tc_HOL_Obool),tc_HOL_Obool),c_member(X26386)),X26384)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).

cnf(i_0_6288,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5313]) ).

fof(i_0_6289,plain,
    ! [X28504,X28505,X28506,X28507,X28508,X28509,X28510,X28511,X28512,X28513,X28514] : hAPP(c_Product__Type_Omap__pair(X28514,X28513,X28512,X28511,X28510,X28509),hAPP(c_Product__Type_Omap__pair(X28508,X28514,X28507,X28512,X28506,X28505),X28504)) = hAPP(c_Product__Type_Omap__pair(X28508,X28513,X28507,X28511,hAPP(c_Fun_Ocomp(X28514,X28513,X28508,X28510),X28506),hAPP(c_Fun_Ocomp(X28512,X28511,X28507,X28509),X28505)),X28504),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(i_0_6290,plain,
    ! [X27315,X27316,X27317,X27318] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27318),X27317)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27316),X27315)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27318),X27315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27316),X27317))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27318),X27315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27316),X27317)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27318),X27317)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27316),X27315)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less])]) ).

fof(i_0_6291,plain,
    ! [X27319,X27320,X27321,X27322] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27322),X27321)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27320),X27319)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27322),X27319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27320),X27321))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27322),X27319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27320),X27321)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27322),X27321)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27320),X27319)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le])]) ).

cnf(i_0_6292,plain,
    ( c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),c_List_OdropWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5314]) ).

cnf(i_0_6293,plain,
    c_List_OdropWhile(X1,X2,X3) = hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3),
    inference(split_conjunct,[status(thm)],[i_0_5315]) ).

fof(i_0_6294,plain,
    ! [X28739,X28740,X28741,X28742,X28743,X28744] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28743),esk330_6(X28739,X28740,X28741,X28742,X28743,X28744)),X28742))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28739,X28744),X28740),hAPP(c_Set_Oimage(X28743,X28739,X28741),X28742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28743,X28744),hAPP(c_Fun_Ocomp(X28739,X28744,X28743,X28740),X28741)),X28742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28743),X28742))
        | ~ class_Groups_Ocomm__monoid__add(X28744) )
      & ( hBOOL(hAPP(hAPP(c_member(X28743),esk331_6(X28739,X28740,X28741,X28742,X28743,X28744)),X28742))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28739,X28744),X28740),hAPP(c_Set_Oimage(X28743,X28739,X28741),X28742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28743,X28744),hAPP(c_Fun_Ocomp(X28739,X28744,X28743,X28740),X28741)),X28742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28743),X28742))
        | ~ class_Groups_Ocomm__monoid__add(X28744) )
      & ( esk330_6(X28739,X28740,X28741,X28742,X28743,X28744) != esk331_6(X28739,X28740,X28741,X28742,X28743,X28744)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28739,X28744),X28740),hAPP(c_Set_Oimage(X28743,X28739,X28741),X28742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28743,X28744),hAPP(c_Fun_Ocomp(X28739,X28744,X28743,X28740),X28741)),X28742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28743),X28742))
        | ~ class_Groups_Ocomm__monoid__add(X28744) )
      & ( hAPP(X28741,esk330_6(X28739,X28740,X28741,X28742,X28743,X28744)) = hAPP(X28741,esk331_6(X28739,X28740,X28741,X28742,X28743,X28744))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28739,X28744),X28740),hAPP(c_Set_Oimage(X28743,X28739,X28741),X28742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28743,X28744),hAPP(c_Fun_Ocomp(X28739,X28744,X28743,X28740),X28741)),X28742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28743),X28742))
        | ~ class_Groups_Ocomm__monoid__add(X28744) )
      & ( hAPP(X28740,hAPP(X28741,esk330_6(X28739,X28740,X28741,X28742,X28743,X28744))) != c_Groups_Ozero__class_Ozero(X28744)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28739,X28744),X28740),hAPP(c_Set_Oimage(X28743,X28739,X28741),X28742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28743,X28744),hAPP(c_Fun_Ocomp(X28739,X28744,X28743,X28740),X28741)),X28742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28743),X28742))
        | ~ class_Groups_Ocomm__monoid__add(X28744) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero])])])]) ).

fof(i_0_6295,plain,
    ! [X25372,X25373,X25374,X25375,X25376,X25377] : hAPP(c_Set_Oimage(X25377,X25376,hAPP(hAPP(c_COMBS(X25377,X25376,X25376),hAPP(hAPP(c_COMBS(X25377,X25376,tc_fun(X25376,X25376)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25376,tc_fun(X25376,X25376)),X25377),c_If(X25376)),X25375)),X25374)),X25373)),X25372) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25376,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25377,X25376,X25374),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25377,tc_HOL_Obool)),X25372),hAPP(c_Set_OCollect(X25377),X25375)))),hAPP(c_Set_Oimage(X25377,X25376,X25373),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25377,tc_HOL_Obool)),X25372),hAPP(c_Set_OCollect(X25377),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25377),c_fNot),X25375))))),
    inference(variable_rename,[status(thm)],[fact_if__image__distrib]) ).

cnf(i_0_6296,plain,
    hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X1,X3,X6),X7)) = hAPP(c_Product__Type_Oapsnd(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
    inference(split_conjunct,[status(thm)],[i_0_5316]) ).

cnf(i_0_6297,plain,
    hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X1,X3,X6),X7)) = hAPP(c_Product__Type_Oapfst(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
    inference(split_conjunct,[status(thm)],[i_0_5317]) ).

fof(i_0_6298,plain,
    ! [X27300,X27301,X27302,X27303] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27303),X27302)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27301),X27300)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27303),X27301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27302),X27300))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27303),X27300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27302),X27301)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_mult]) ).

fof(i_0_6299,plain,
    ! [X25627,X25628,X25629,X25630,X25631,X25632] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25631),esk254_6(X25627,X25628,X25629,X25630,X25631,X25632)),X25630))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25632,X25631,c_Groups_Otimes__class_Otimes(X25632)),X25629),X25627),X25630) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25632,X25631,c_Groups_Otimes__class_Otimes(X25632)),X25628),X25627),X25630)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25631),X25630))
        | ~ class_Groups_Oab__semigroup__mult(X25632) )
      & ( hAPP(X25629,esk254_6(X25627,X25628,X25629,X25630,X25631,X25632)) != hAPP(X25628,esk254_6(X25627,X25628,X25629,X25630,X25631,X25632))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25632,X25631,c_Groups_Otimes__class_Otimes(X25632)),X25629),X25627),X25630) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25632,X25631,c_Groups_Otimes__class_Otimes(X25632)),X25628),X25627),X25630)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25631),X25630))
        | ~ class_Groups_Oab__semigroup__mult(X25632) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__cong])])])]) ).

cnf(i_0_6300,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5318]) ).

cnf(i_0_6301,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5318]) ).

fof(i_0_6302,plain,
    ! [X28143,X28144,X28145,X28146] :
      ( ~ c_Wellfounded_Owf(X28146,X28145)
      | ~ c_Fun_Oinj__on(X28146,X28144,X28143,c_Orderings_Otop__class_Otop(tc_fun(X28146,tc_HOL_Obool)))
      | c_Wellfounded_Owf(X28144,hAPP(c_Set_Oimage(tc_prod(X28146,X28146),tc_prod(X28144,X28144),c_Product__Type_Omap__pair(X28146,X28144,X28146,X28144,X28143,X28143)),X28145)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).

fof(i_0_6303,plain,
    ! [X25245,X25246,X25247,X25248,X25249,X25250] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25249),esk235_6(X25245,X25246,X25247,X25248,X25249,X25250)),X25250))
        | c_Fun_Oinj__on(X25248,X25247,X25246,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25249,tc_fun(X25248,tc_HOL_Obool)),X25250),X25245))
        | X25250 = c_Orderings_Obot__class_Obot(tc_fun(X25249,tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X25248,X25247,X25246,hAPP(X25245,esk235_6(X25245,X25246,X25247,X25248,X25249,X25250)))
        | c_Fun_Oinj__on(X25248,X25247,X25246,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25249,tc_fun(X25248,tc_HOL_Obool)),X25250),X25245))
        | X25250 = c_Orderings_Obot__class_Obot(tc_fun(X25249,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__INTER])])])]) ).

fof(i_0_6304,plain,
    ! [X31353,X31354,X31355,X31356,X31357] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31356),esk421_5(X31353,X31354,X31355,X31356,X31357)),hAPP(c_List_Oset(X31356),X31355)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31357),hAPP(c_List_Omonoid__add__class_Olistsum(X31357),hAPP(hAPP(c_List_Omap(X31356,X31357),X31354),X31355))),hAPP(c_List_Omonoid__add__class_Olistsum(X31357),hAPP(hAPP(c_List_Omap(X31356,X31357),X31353),X31355))))
        | ~ class_Groups_Omonoid__add(X31357)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31357) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31357),hAPP(X31354,esk421_5(X31353,X31354,X31355,X31356,X31357))),hAPP(X31353,esk421_5(X31353,X31354,X31355,X31356,X31357))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31357),hAPP(c_List_Omonoid__add__class_Olistsum(X31357),hAPP(hAPP(c_List_Omap(X31356,X31357),X31354),X31355))),hAPP(c_List_Omonoid__add__class_Olistsum(X31357),hAPP(hAPP(c_List_Omap(X31356,X31357),X31353),X31355))))
        | ~ class_Groups_Omonoid__add(X31357)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31357) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mono])])])]) ).

fof(i_0_6305,plain,
    ! [X32505,X32506,X32507,X32508,X32509] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_5(X32505,X32506,X32507,X32508,X32509)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32509)),X32508)))
        | c_List_Olist__all2(X32509,X32507,X32505,X32508,X32506)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32509)),X32508) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32507)),X32506) )
      & ( ~ hBOOL(hAPP(hAPP(X32505,hAPP(hAPP(c_List_Onth(X32509),X32508),esk459_5(X32505,X32506,X32507,X32508,X32509))),hAPP(hAPP(c_List_Onth(X32507),X32506),esk459_5(X32505,X32506,X32507,X32508,X32509))))
        | c_List_Olist__all2(X32509,X32507,X32505,X32508,X32506)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32509)),X32508) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32507)),X32506) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__all__nthI])])])]) ).

fof(i_0_6306,plain,
    ! [X31506,X31507,X31508,X31509,X31510,X31511,X31512,X31513,X31514,X31515,X31516] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31510)),X31507) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31509)),X31506)
        | ~ c_List_Olist__all2(X31510,X31509,X31508,X31507,X31506) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31511),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31510)),X31507)))
        | hBOOL(hAPP(hAPP(X31508,hAPP(hAPP(c_List_Onth(X31510),X31507),X31511)),hAPP(hAPP(c_List_Onth(X31509),X31506),X31511)))
        | ~ c_List_Olist__all2(X31510,X31509,X31508,X31507,X31506) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk424_5(X31512,X31513,X31514,X31515,X31516)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31516)),X31513)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31516)),X31513) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31515)),X31512)
        | c_List_Olist__all2(X31516,X31515,X31514,X31513,X31512) )
      & ( ~ hBOOL(hAPP(hAPP(X31514,hAPP(hAPP(c_List_Onth(X31516),X31513),esk424_5(X31512,X31513,X31514,X31515,X31516))),hAPP(hAPP(c_List_Onth(X31515),X31512),esk424_5(X31512,X31513,X31514,X31515,X31516))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31516)),X31513) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31515)),X31512)
        | c_List_Olist__all2(X31516,X31515,X31514,X31513,X31512) ) ),
    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_list__all2__conv__all__nth])])])])])]) ).

fof(i_0_6307,plain,
    ! [X18643,X18644,X18645,X18646,X18647] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18646),esk37_5(X18643,X18644,X18645,X18646,X18647)),X18645))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18647),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18646,X18647),X18644),X18645)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18646,X18647),X18643),X18645)))
        | X18645 = c_Orderings_Obot__class_Obot(tc_fun(X18646,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18646),X18645))
        | ~ class_Groups_Ocomm__monoid__add(X18647)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18647) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18647),hAPP(X18644,esk37_5(X18643,X18644,X18645,X18646,X18647))),hAPP(X18643,esk37_5(X18643,X18644,X18645,X18646,X18647))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18647),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18646,X18647),X18644),X18645)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18646,X18647),X18643),X18645)))
        | X18645 = c_Orderings_Obot__class_Obot(tc_fun(X18646,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18646),X18645))
        | ~ class_Groups_Ocomm__monoid__add(X18647)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18647) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono])])])]) ).

fof(i_0_6308,plain,
    ! [X19325,X19326,X19327,X19328,X19329] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19328),esk66_5(X19325,X19326,X19327,X19328,X19329)),X19327))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19329),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19328,X19329),X19326),X19327)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19328,X19329),X19325),X19327)))
        | ~ class_Groups_Ocomm__monoid__add(X19329)
        | ~ class_Groups_Oordered__ab__semigroup__add(X19329) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19329),hAPP(X19326,esk66_5(X19325,X19326,X19327,X19328,X19329))),hAPP(X19325,esk66_5(X19325,X19326,X19327,X19328,X19329))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19329),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19328,X19329),X19326),X19327)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19328,X19329),X19325),X19327)))
        | ~ class_Groups_Ocomm__monoid__add(X19329)
        | ~ class_Groups_Oordered__ab__semigroup__add(X19329) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono])])])]) ).

fof(i_0_6309,plain,
    ! [X25393,X25394,X25395,X25396,X25397,X25398] :
      ( ~ class_Groups_Ocomm__monoid__add(X25398)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25397),X25396))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25397,X25398),hAPP(hAPP(c_COMBS(X25397,X25398,X25398),hAPP(hAPP(c_COMBS(X25397,X25398,tc_fun(X25398,X25398)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25398,tc_fun(X25398,X25398)),X25397),c_If(X25398)),X25395)),X25394)),X25393)),X25396) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25398),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25397,X25398),X25394),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25397,tc_HOL_Obool)),X25396),hAPP(c_Set_OCollect(X25397),X25395)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25397,X25398),X25393),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25397,tc_HOL_Obool)),X25396),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25397,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25397),X25395))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cases])]) ).

cnf(i_0_6310,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5302]) ).

cnf(i_0_6311,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5303]) ).

fof(i_0_6312,plain,
    ! [X17252,X17253,X17254,X17255,X17256] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17256,X17255,X17254)
      | hAPP(X17253,hAPP(hAPP(X17255,esk13_5(X17252,X17253,X17254,X17255,X17256)),esk14_5(X17252,X17253,X17254,X17255,X17256))) != hAPP(hAPP(X17255,hAPP(X17253,esk13_5(X17252,X17253,X17254,X17255,X17256))),hAPP(X17253,esk14_5(X17252,X17253,X17254,X17255,X17256)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17256),X17252))
      | X17252 = c_Orderings_Obot__class_Obot(tc_fun(X17256,tc_HOL_Obool))
      | hAPP(X17253,hAPP(X17254,X17252)) = hAPP(X17254,hAPP(c_Set_Oimage(X17256,X17256,X17253),X17252)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).

cnf(i_0_6313,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
    | c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
    | X3 = c_List_Olist_ONil(tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5319]) ).

cnf(i_0_6314,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
    | c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5319]) ).

cnf(i_0_6315,plain,
    ( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))
    | X2 = c_List_Olist_ONil(tc_List_Olist(X1))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk434_3(X3,X1,X2))) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_5319]) ).

cnf(i_0_6316,plain,
    ( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk434_3(X3,X1,X2))) != X3
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5319]) ).

cnf(i_0_6317,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_5320]) ).

cnf(i_0_6318,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk267_3(X1,X2,X3)),esk268_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk268_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk267_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk268_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5321]) ).

fof(i_0_6319,plain,
    ! [X20097,X20098,X20099,X20100,X20101] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20100),X20098),X20099))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20100,X20101),hAPP(hAPP(c_COMBC(X20100,X20101,X20101),hAPP(hAPP(c_COMBS(X20100,X20101,tc_fun(X20101,X20101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20101,tc_fun(X20101,X20101)),X20100),c_If(X20101)),hAPP(c_fequal,X20098))),X20097)),c_Groups_Oone__class_Oone(X20101))),X20099) = hAPP(X20097,X20098)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20100),X20099))
        | ~ class_Groups_Ocomm__monoid__mult(X20101) )
      & ( hBOOL(hAPP(hAPP(c_member(X20100),X20098),X20099))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20100,X20101),hAPP(hAPP(c_COMBC(X20100,X20101,X20101),hAPP(hAPP(c_COMBS(X20100,X20101,tc_fun(X20101,X20101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20101,tc_fun(X20101,X20101)),X20100),c_If(X20101)),hAPP(c_fequal,X20098))),X20097)),c_Groups_Oone__class_Oone(X20101))),X20099) = c_Groups_Oone__class_Oone(X20101)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20100),X20099))
        | ~ class_Groups_Ocomm__monoid__mult(X20101) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5322])])]) ).

fof(i_0_6320,plain,
    ! [X22674,X22675,X22676,X22677,X22678] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22677),X22675),X22676))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22677,X22678),hAPP(hAPP(c_COMBC(X22677,X22678,X22678),hAPP(hAPP(c_COMBS(X22677,X22678,tc_fun(X22678,X22678)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22678,tc_fun(X22678,X22678)),X22677),c_If(X22678)),hAPP(c_fequal,X22675))),X22674)),c_Groups_Ozero__class_Ozero(X22678))),X22676) = hAPP(X22674,X22675)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22677),X22676))
        | ~ class_Groups_Ocomm__monoid__add(X22678) )
      & ( hBOOL(hAPP(hAPP(c_member(X22677),X22675),X22676))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22677,X22678),hAPP(hAPP(c_COMBC(X22677,X22678,X22678),hAPP(hAPP(c_COMBS(X22677,X22678,tc_fun(X22678,X22678)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22678,tc_fun(X22678,X22678)),X22677),c_If(X22678)),hAPP(c_fequal,X22675))),X22674)),c_Groups_Ozero__class_Ozero(X22678))),X22676) = c_Groups_Ozero__class_Ozero(X22678)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22677),X22676))
        | ~ class_Groups_Ocomm__monoid__add(X22678) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5323])])]) ).

fof(i_0_6321,plain,
    ! [X31564,X31565,X31566] : hAPP(c_List_Oset(tc_List_Olist(X31566)),c_Enum_On__lists(X31566,X31565,X31564)) = hAPP(c_Set_OCollect(tc_List_Olist(X31566)),hAPP(hAPP(c_COMBS(tc_List_Olist(X31566),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X31566)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X31566),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31566)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31566)))),X31565))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31566),tc_fun(X31566,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X31566,tc_HOL_Obool),tc_fun(tc_fun(X31566,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X31566)),c_Orderings_Oord__class_Oless__eq(tc_fun(X31566,tc_HOL_Obool))),c_List_Oset(X31566))),hAPP(c_List_Oset(X31566),X31564)))),
    inference(variable_rename,[status(thm)],[fact_set__n__lists]) ).

fof(i_0_6322,plain,
    ! [X28525,X28526,X28527,X28528,X28529,X28530,X28531,X28532,X28533,X28534] : hAPP(c_Fun_Ocomp(tc_prod(X28534,X28533),tc_prod(X28532,X28531),tc_prod(X28530,X28529),c_Product__Type_Omap__pair(X28534,X28532,X28533,X28531,X28528,X28527)),c_Product__Type_Omap__pair(X28530,X28534,X28529,X28533,X28526,X28525)) = c_Product__Type_Omap__pair(X28530,X28532,X28529,X28531,hAPP(c_Fun_Ocomp(X28534,X28532,X28530,X28528),X28526),hAPP(c_Fun_Ocomp(X28533,X28531,X28529,X28527),X28525)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(i_0_6323,plain,
    ! [X28515,X28516,X28517,X28518,X28519,X28520,X28521,X28522,X28523,X28524] : c_Product__Type_Omap__pair(X28524,X28523,X28522,X28521,hAPP(c_Fun_Ocomp(X28520,X28523,X28524,X28519),X28518),hAPP(c_Fun_Ocomp(X28517,X28521,X28522,X28516),X28515)) = hAPP(c_Fun_Ocomp(tc_prod(X28520,X28517),tc_prod(X28523,X28521),tc_prod(X28524,X28522),c_Product__Type_Omap__pair(X28520,X28523,X28517,X28521,X28519,X28516)),c_Product__Type_Omap__pair(X28524,X28520,X28522,X28517,X28518,X28515)),
    inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).

fof(i_0_6324,plain,
    ! [X29749,X29750,X29751,X29752,X29753,X29754,X29755,X29756,X29757] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29752)),X29751) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29752)),X29750)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29752),tc_List_Olist(X29752))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29752),tc_List_Olist(X29752)),X29751),X29750)),c_List_Olistrel(X29752,X29749))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29752)),X29751)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29752,X29752)),hAPP(hAPP(c_Product__Type_OPair(X29752,X29752),hAPP(hAPP(c_List_Onth(X29752),X29751),X29753)),hAPP(hAPP(c_List_Onth(X29752),X29750),X29753))),X29749))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29752),tc_List_Olist(X29752))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29752),tc_List_Olist(X29752)),X29751),X29750)),c_List_Olistrel(X29752,X29749))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk386_4(X29754,X29755,X29756,X29757)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29757)),X29756)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29757)),X29756) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29757)),X29755)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29757),tc_List_Olist(X29757))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29757),tc_List_Olist(X29757)),X29756),X29755)),c_List_Olistrel(X29757,X29754))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29757,X29757)),hAPP(hAPP(c_Product__Type_OPair(X29757,X29757),hAPP(hAPP(c_List_Onth(X29757),X29756),esk386_4(X29754,X29755,X29756,X29757))),hAPP(hAPP(c_List_Onth(X29757),X29755),esk386_4(X29754,X29755,X29756,X29757)))),X29754))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29757)),X29756) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29757)),X29755)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29757),tc_List_Olist(X29757))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29757),tc_List_Olist(X29757)),X29756),X29755)),c_List_Olistrel(X29757,X29754))) ) ),
    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_listrel__iff__nth])])])])])]) ).

cnf(i_0_6325,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk269_3(X1,X2,X3)),esk270_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk270_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk269_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk270_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5324]) ).

fof(i_0_6326,plain,
    ! [X29700,X29701,X29702,X29703,X29704] :
      ( ( X29703 = hAPP(hAPP(c_List_Olist_OCons(X29704),esk382_5(X29700,X29701,X29702,X29703,X29704)),esk383_5(X29700,X29701,X29702,X29703,X29704))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29704),tc_List_Olist(X29704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29704),tc_List_Olist(X29704)),X29703),hAPP(hAPP(c_List_Olist_OCons(X29704),X29702),X29701))),c_List_Olistrel(X29704,X29700))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29704,X29704)),hAPP(hAPP(c_Product__Type_OPair(X29704,X29704),esk382_5(X29700,X29701,X29702,X29703,X29704)),X29702)),X29700))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29704),tc_List_Olist(X29704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29704),tc_List_Olist(X29704)),X29703),hAPP(hAPP(c_List_Olist_OCons(X29704),X29702),X29701))),c_List_Olistrel(X29704,X29700))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29704),tc_List_Olist(X29704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29704),tc_List_Olist(X29704)),esk383_5(X29700,X29701,X29702,X29703,X29704)),X29701)),c_List_Olistrel(X29704,X29700)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29704),tc_List_Olist(X29704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29704),tc_List_Olist(X29704)),X29703),hAPP(hAPP(c_List_Olist_OCons(X29704),X29702),X29701))),c_List_Olistrel(X29704,X29700))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5325])])])]) ).

cnf(i_0_6327,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5320]) ).

fof(i_0_6328,plain,
    ! [X29419,X29420,X29421,X29422,X29423] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29423,X29423)),hAPP(hAPP(c_Product__Type_OPair(X29423,X29423),X29422),esk359_5(X29419,X29420,X29421,X29422,X29423))),X29419))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29423,X29423)),hAPP(hAPP(c_Product__Type_OPair(X29423,X29423),X29422),X29421)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29423,X29423),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29420)),X29419))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29423,X29423)),hAPP(hAPP(c_Product__Type_OPair(X29423,X29423),esk359_5(X29419,X29420,X29421,X29422,X29423)),X29421)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29423,X29423),tc_HOL_Obool),X29420),X29419)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29423,X29423)),hAPP(hAPP(c_Product__Type_OPair(X29423,X29423),X29422),X29421)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29423,X29423),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29420)),X29419))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5326])])])]) ).

fof(i_0_6329,plain,
    ! [X29413,X29414,X29415,X29416,X29417] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29417,X29417)),hAPP(hAPP(c_Product__Type_OPair(X29417,X29417),X29416),esk358_5(X29413,X29414,X29415,X29416,X29417))),X29413))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29417,X29417)),hAPP(hAPP(c_Product__Type_OPair(X29417,X29417),X29416),X29415)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29417,X29417),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29414)),X29413))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29417,X29417)),hAPP(hAPP(c_Product__Type_OPair(X29417,X29417),esk358_5(X29413,X29414,X29415,X29416,X29417)),X29415)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29417,X29417),tc_HOL_Obool),X29414),X29413)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29417,X29417)),hAPP(hAPP(c_Product__Type_OPair(X29417,X29417),X29416),X29415)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29417,X29417),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29414)),X29413))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2])])])]) ).

cnf(i_0_6330,plain,
    c_Nitpick_Otimes__frac(X1,X2,X3) = hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2)),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X1),X2)),hAPP(c_Nitpick_Odenom(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_5327]) ).

fof(i_0_6331,plain,
    ! [X29389,X29390,X29391,X29392,X29393] :
      ( ( X29390 = hAPP(c_Nat_OSuc,esk352_5(X29389,X29390,X29391,X29392,X29393))
        | X29390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),esk351_5(X29389,X29390,X29391,X29392,X29393))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),esk352_5(X29389,X29390,X29391,X29392,X29393)),X29389)))
        | X29390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),esk351_5(X29389,X29390,X29391,X29392,X29393)),X29391)),X29389))
        | X29390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) )
      & ( X29390 = hAPP(c_Nat_OSuc,esk352_5(X29389,X29390,X29391,X29392,X29393))
        | X29392 = X29391
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),esk351_5(X29389,X29390,X29391,X29392,X29393))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),esk352_5(X29389,X29390,X29391,X29392,X29393)),X29389)))
        | X29392 = X29391
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),esk351_5(X29389,X29390,X29391,X29392,X29393)),X29391)),X29389))
        | X29392 = X29391
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29393,X29393)),hAPP(hAPP(c_Product__Type_OPair(X29393,X29393),X29392),X29391)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29393,X29393),tc_HOL_Obool),X29390),X29389))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5328])])])]) ).

fof(i_0_6332,plain,
    ! [X29425,X29426,X29427,X29428,X29429] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29429,X29429)),hAPP(hAPP(c_Product__Type_OPair(X29429,X29429),X29428),esk360_5(X29425,X29426,X29427,X29428,X29429))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29429,X29429),tc_HOL_Obool),X29426),X29425)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29429,X29429)),hAPP(hAPP(c_Product__Type_OPair(X29429,X29429),X29428),X29427)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29429,X29429),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29426)),X29425))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29429,X29429)),hAPP(hAPP(c_Product__Type_OPair(X29429,X29429),esk360_5(X29425,X29426,X29427,X29428,X29429)),X29427)),X29425))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29429,X29429)),hAPP(hAPP(c_Product__Type_OPair(X29429,X29429),X29428),X29427)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29429,X29429),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29426)),X29425))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5329])])])]) ).

cnf(i_0_6333,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5330]) ).

cnf(i_0_6334,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5331]) ).

cnf(i_0_6335,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5332]) ).

cnf(i_0_6336,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5333]) ).

cnf(i_0_6337,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5334]) ).

cnf(i_0_6338,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5335]) ).

cnf(i_0_6339,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_5336]) ).

cnf(i_0_6340,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5337]) ).

cnf(i_0_6341,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5338]) ).

cnf(i_0_6342,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5339]) ).

fof(i_0_6343,plain,
    ! [X25490,X25491,X25492] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X25492),X25491),X25490) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25492,tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool)),X25491),hAPP(hAPP(c_COMBC(X25492,tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25492,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool)),X25492),c_Set_Oinsert(tc_fun(X25492,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25492,tc_HOL_Obool),tc_fun(X25492,tc_HOL_Obool),X25492),c_Relation_OImage(X25492,X25492,X25490)),hAPP(hAPP(c_COMBC(X25492,tc_fun(X25492,tc_HOL_Obool),tc_fun(X25492,tc_HOL_Obool)),c_Set_Oinsert(X25492)),c_Orderings_Obot__class_Obot(tc_fun(X25492,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25492,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_quotient__def]) ).

cnf(i_0_6344,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))
    | ~ class_Rings_Osemiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5340]) ).

cnf(i_0_6345,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5341]) ).

cnf(i_0_6346,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5342]) ).

cnf(i_0_6347,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5343]) ).

cnf(i_0_6348,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5344]) ).

cnf(i_0_6349,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5345]) ).

cnf(i_0_6350,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5346]) ).

cnf(i_0_6351,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5347]) ).

cnf(i_0_6352,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),
    inference(split_conjunct,[status(thm)],[i_0_5348]) ).

cnf(i_0_6353,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).

fof(i_0_6354,plain,
    ! [X27198,X27199,X27200,X27201,X27202] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27200,X27202)),hAPP(hAPP(c_Product__Type_OPair(X27200,X27202),esk280_5(X27198,X27199,X27200,X27201,X27202)),X27201)),X27199))
        | ~ hBOOL(hAPP(hAPP(c_member(X27202),X27201),hAPP(c_Relation_OImage(X27200,X27202,X27199),X27198))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27200),esk280_5(X27198,X27199,X27200,X27201,X27202)),X27198))
        | ~ hBOOL(hAPP(hAPP(c_member(X27202),X27201),hAPP(c_Relation_OImage(X27200,X27202,X27199),X27198))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5349])])])]) ).

fof(i_0_6355,plain,
    ! [X26441,X26442,X26443,X26444,X26445,X26447,X26448,X26449,X26450,X26451,X26452] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26443),esk260_5(X26441,X26442,X26443,X26444,X26445)),X26441))
        | ~ hBOOL(hAPP(hAPP(c_member(X26445),X26444),hAPP(c_Relation_OImage(X26443,X26445,X26442),X26441))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X26443,X26445)),hAPP(hAPP(c_Product__Type_OPair(X26443,X26445),esk260_5(X26441,X26442,X26443,X26444,X26445)),X26444)),X26442))
        | ~ hBOOL(hAPP(hAPP(c_member(X26445),X26444),hAPP(c_Relation_OImage(X26443,X26445,X26442),X26441))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26449),X26452),X26447))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26449,X26451)),hAPP(hAPP(c_Product__Type_OPair(X26449,X26451),X26452),X26450)),X26448))
        | hBOOL(hAPP(hAPP(c_member(X26451),X26450),hAPP(c_Relation_OImage(X26449,X26451,X26448),X26447))) ) ),
    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_Image__iff])])])])])]) ).

fof(i_0_6356,plain,
    ! [X17224,X17225,X17226,X17227] :
      ( ~ c_Finite__Set_Ofolding__one(X17227,X17226,X17225)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17227),X17224))
      | X17224 = c_Orderings_Obot__class_Obot(tc_fun(X17227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X17227),hAPP(hAPP(X17226,esk9_4(X17224,X17225,X17226,X17227)),esk10_4(X17224,X17225,X17226,X17227))),hAPP(hAPP(c_Set_Oinsert(X17227),esk9_4(X17224,X17225,X17226,X17227)),hAPP(hAPP(c_Set_Oinsert(X17227),esk10_4(X17224,X17225,X17226,X17227)),c_Orderings_Obot__class_Obot(tc_fun(X17227,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X17227),hAPP(X17225,X17224)),X17224)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed])])]) ).

cnf(i_0_6357,plain,
    c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X2),X3) = c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X3)),c_Enum_On__lists(X1,X2,X3))),
    inference(split_conjunct,[status(thm)],[i_0_5350]) ).

cnf(i_0_6358,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))),
    inference(split_conjunct,[status(thm)],[i_0_5351]) ).

fof(i_0_6359,plain,
    ! [X33196,X33197,X33198,X33199] : hAPP(c_Relation_OImage(X33199,X33198,hAPP(c_Set_OCollect(tc_prod(X33199,X33198)),hAPP(c_Product__Type_Oprod_Oprod__case(X33199,X33198,tc_HOL_Obool),X33197))),X33196) = hAPP(c_Set_OCollect(X33198),hAPP(hAPP(c_COMBB(tc_fun(X33199,tc_HOL_Obool),tc_HOL_Obool,X33198),c_HOL_OEx(X33199)),hAPP(hAPP(c_COMBB(tc_fun(X33199,tc_HOL_Obool),tc_fun(X33199,tc_HOL_Obool),X33198),hAPP(c_COMBS(X33199,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33199),c_fconj),hAPP(hAPP(c_COMBC(X33199,tc_fun(X33199,tc_HOL_Obool),tc_HOL_Obool),c_member(X33199)),X33196)))),hAPP(c_COMBC(X33199,X33198,tc_HOL_Obool),X33197)))),
    inference(variable_rename,[status(thm)],[fact_Image__Collect__split]) ).

cnf(i_0_6360,plain,
    ( hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_5275]) ).

fof(i_0_6361,plain,
    ! [X25486,X25487,X25488,X25489] :
      ( ~ c_Fun_Oinj__on(X25489,tc_fun(tc_fun(X25489,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X25489,tc_fun(tc_prod(X25489,X25489),tc_HOL_Obool),tc_fun(tc_fun(X25489,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25489,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X25489,X25489),tc_HOL_Obool),tc_fun(tc_fun(X25489,tc_HOL_Obool),tc_HOL_Obool)),X25489),c_Equiv__Relations_Oquotient(X25489)),hAPP(hAPP(c_COMBC(X25489,tc_fun(X25489,tc_HOL_Obool),tc_fun(X25489,tc_HOL_Obool)),c_Set_Oinsert(X25489)),c_Orderings_Obot__class_Obot(tc_fun(X25489,tc_HOL_Obool))))),X25488),X25487)
      | ~ hBOOL(hAPP(hAPP(c_member(X25489),X25486),X25487))
      | hAPP(hAPP(c_Equiv__Relations_Oquotient(X25489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25489,tc_HOL_Obool)),X25487),hAPP(hAPP(c_Set_Oinsert(X25489),X25486),c_Orderings_Obot__class_Obot(tc_fun(X25489,tc_HOL_Obool))))),X25488) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X25489,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25489),X25487),X25488)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25489),hAPP(hAPP(c_Set_Oinsert(X25489),X25486),c_Orderings_Obot__class_Obot(tc_fun(X25489,tc_HOL_Obool)))),X25488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).

fof(i_0_6362,plain,
    ! [X28273,X28274,X28275,X28276] : hAPP(c_Set_OCollect(X28276),hAPP(hAPP(c_COMBB(tc_fun(X28275,tc_HOL_Obool),tc_HOL_Obool,X28276),c_HOL_OAll(X28275)),hAPP(hAPP(c_COMBB(tc_fun(X28275,tc_HOL_Obool),tc_fun(X28275,tc_HOL_Obool),X28276),hAPP(c_COMBS(X28275,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28275),c_fimplies),hAPP(hAPP(c_COMBC(X28275,tc_fun(X28275,tc_HOL_Obool),tc_HOL_Obool),c_member(X28275)),X28274)))),X28273))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28275,tc_fun(X28276,tc_HOL_Obool)),X28274),hAPP(hAPP(c_COMBB(tc_fun(X28276,tc_HOL_Obool),tc_fun(X28276,tc_HOL_Obool),X28275),c_Set_OCollect(X28276)),hAPP(c_COMBC(X28276,X28275,tc_HOL_Obool),X28273))),
    inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).

fof(i_0_6363,plain,
    ! [X30531,X30532,X30533,X30534] : c_List_Osublist(X30534,hAPP(hAPP(c_List_Oappend(X30534),X30533),X30532),X30531) = hAPP(hAPP(c_List_Oappend(X30534),c_List_Osublist(X30534,X30533,X30531)),c_List_Osublist(X30534,X30532,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30534)),X30533)))),X30531)))),
    inference(variable_rename,[status(thm)],[fact_sublist__append]) ).

fof(i_0_6364,plain,
    ! [X32491,X32492,X32493,X32494,X32495] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),hAPP(hAPP(c_List_Otake(X32495),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),X32494)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32493)),X32492))),X32494)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32493)),hAPP(hAPP(c_List_Otake(X32493),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),X32494)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32493)),X32492))),X32492))
        | hBOOL(hAPP(X32491,hAPP(hAPP(c_List_Ozip(X32495,X32493),X32494),X32492))) )
      & ( ~ hBOOL(hAPP(X32491,hAPP(hAPP(c_List_Ozip(X32495,X32493),hAPP(hAPP(c_List_Otake(X32495),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),X32494)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32493)),X32492))),X32494)),hAPP(hAPP(c_List_Otake(X32493),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),X32494)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32493)),X32492))),X32492))))
        | hBOOL(hAPP(X32491,hAPP(hAPP(c_List_Ozip(X32495,X32493),X32494),X32492))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])]) ).

cnf(i_0_6365,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5352]) ).

cnf(i_0_6366,plain,
    ( hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))
    | hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),X5) != hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X6),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_5353]) ).

cnf(i_0_6367,plain,
    ( hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5)) = hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))
    | hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),X5) != hAPP(c_Product__Type_Oapfst(X1,X2,X3,X6),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_5354]) ).

cnf(i_0_6368,plain,
    c_Relation_OId(X1) = hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_5355]) ).

cnf(i_0_6369,plain,
    hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7))),
    inference(split_conjunct,[status(thm)],[i_0_5356]) ).

cnf(i_0_6370,plain,
    hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))),
    inference(split_conjunct,[status(thm)],[i_0_5357]) ).

fof(i_0_6371,plain,
    ! [X25475,X25476,X25477] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25477),X25476))
      | ~ c_Fun_Oinj__on(X25477,tc_fun(tc_fun(X25477,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X25477,tc_fun(tc_prod(X25477,X25477),tc_HOL_Obool),tc_fun(tc_fun(X25477,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25477,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X25477,X25477),tc_HOL_Obool),tc_fun(tc_fun(X25477,tc_HOL_Obool),tc_HOL_Obool)),X25477),c_Equiv__Relations_Oquotient(X25477)),hAPP(hAPP(c_COMBC(X25477,tc_fun(X25477,tc_HOL_Obool),tc_fun(X25477,tc_HOL_Obool)),c_Set_Oinsert(X25477)),c_Orderings_Obot__class_Obot(tc_fun(X25477,tc_HOL_Obool))))),X25475),X25476)
      | hAPP(c_Finite__Set_Ocard(tc_fun(X25477,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25477),X25476),X25475)) = hAPP(c_Finite__Set_Ocard(X25477),X25476) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).

fof(i_0_6372,plain,
    ! [X22787,X22788,X22789,X22790] :
      ( ~ class_Rings_Ocomm__semiring__1(X22790)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22790),c_Groups_Oone__class_Oone(X22790)),c_Groups_Oone__class_Oone(X22790))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X22790),hAPP(hAPP(c_COMBB(X22790,X22790,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X22790),X22789)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X22790,X22790),hAPP(hAPP(c_COMBB(X22790,tc_fun(X22790,X22790),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X22790)),c_Nat_Osemiring__1__class_Oof__nat(X22790))),X22788))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22787))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22790),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22790),X22787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22790),X22789),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22790),X22789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22790),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22790),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22787),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X22788)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).

fof(i_0_6373,plain,
    ! [X34109,X34110] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34110),X34109))
      | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34109,X34110) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty])]) ).

fof(i_0_6374,plain,
    ! [X34107,X34108] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34108),X34107))
      | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34107,X34108) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty])]) ).

fof(i_0_6375,plain,
    ! [X34105,X34106] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34106),X34105))
      | c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X34105,X34106) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty])]) ).

cnf(i_0_6376,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5358]) ).

fof(i_0_6377,plain,
    ! [X27590,X27591] :
      ( ( c_Wellfounded_Owf(X27591,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590))
        | ~ c_FunDef_Oreduction__pair(X27591,X27590) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27591,X27591,X27591),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590)))
        | ~ c_FunDef_Oreduction__pair(X27591,X27590) )
      & ( ~ c_Wellfounded_Owf(X27591,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27591,X27591,X27591),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool),tc_fun(tc_prod(X27591,X27591),tc_HOL_Obool)),X27590)))
        | c_FunDef_Oreduction__pair(X27591,X27590) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])]) ).

cnf(i_0_6378,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_5359]) ).

cnf(i_0_6379,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5360]) ).

cnf(i_0_6380,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_5361]) ).

fof(i_0_6381,plain,
    ! [X21274,X21275,X21276,X21277,X21278,X21279,X21280,X21281,X21282,X21283,X21284] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21278,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21277,tc_fun(X21278,tc_HOL_Obool)),X21276),X21275)),X21274))
        | ~ hBOOL(hAPP(hAPP(c_member(X21277),X21279),X21276))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21278,tc_HOL_Obool)),hAPP(X21275,X21279)),X21274)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21283),esk100_5(X21280,X21281,X21282,X21283,X21284)),X21282))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21284,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21283,tc_fun(X21284,tc_HOL_Obool)),X21282),X21281)),X21280)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21284,tc_HOL_Obool)),hAPP(X21281,esk100_5(X21280,X21281,X21282,X21283,X21284))),X21280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21284,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21283,tc_fun(X21284,tc_HOL_Obool)),X21282),X21281)),X21280)) ) ),
    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_UN__subset__iff])])])])])]) ).

fof(i_0_6382,plain,
    ! [X22974,X22975,X22976,X22977,X22978] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22977),esk140_5(X22974,X22975,X22976,X22977,X22978)),X22976))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22978),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22977,X22978),X22975),X22976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22978),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22978),hAPP(c_Finite__Set_Ocard(X22977),X22976))),X22974)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X22978)
        | ~ class_Rings_Osemiring__1(X22978) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22978),hAPP(X22975,esk140_5(X22974,X22975,X22976,X22977,X22978))),X22974))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22978),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22977,X22978),X22975),X22976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22978),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22978),hAPP(c_Finite__Set_Ocard(X22977),X22976))),X22974)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X22978)
        | ~ class_Rings_Osemiring__1(X22978) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])]) ).

cnf(i_0_6383,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat)))),
    inference(split_conjunct,[status(thm)],[i_0_5362]) ).

fof(i_0_6384,plain,
    ! [X28127,X28128,X28129,X28130,X28131,X28132] : c_Product__Type_Omap__pair(X28132,X28131,X28130,X28129,X28128,X28127) = hAPP(c_Product__Type_Oprod_Oprod__case(X28132,X28130,tc_prod(X28131,X28129)),hAPP(hAPP(c_COMBC(X28132,tc_fun(X28130,X28129),tc_fun(X28130,tc_prod(X28131,X28129))),hAPP(hAPP(c_COMBB(tc_fun(X28129,tc_prod(X28131,X28129)),tc_fun(tc_fun(X28130,X28129),tc_fun(X28130,tc_prod(X28131,X28129))),X28132),c_COMBB(X28129,tc_prod(X28131,X28129),X28130)),hAPP(hAPP(c_COMBB(X28131,tc_fun(X28129,tc_prod(X28131,X28129)),X28132),c_Product__Type_OPair(X28131,X28129)),X28128))),X28127)),
    inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).

fof(i_0_6385,plain,
    ! [X24935,X24936,X24937] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24937))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24936),X24935))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24937))),X24935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).

fof(i_0_6386,plain,
    ! [X21402,X21403,X21404,X21405,X21406,X21407] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21405,X21406),X21404),X21403)),X21402))
        | ~ hBOOL(hAPP(hAPP(c_member(X21405),X21407),X21404))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(X21403,X21407)),X21402))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21406) )
      & ( hBOOL(hAPP(hAPP(c_member(X21405),esk101_5(X21402,X21403,X21404,X21405,X21406)),X21404))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21405,X21406),X21404),X21403)),X21402))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21406) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(X21403,esk101_5(X21402,X21403,X21404,X21405,X21406))),X21402))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21405,X21406),X21404),X21403)),X21402))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21406) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__le__iff])])])])]) ).

cnf(i_0_6387,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5318]) ).

cnf(i_0_6388,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I4_J]) ).

cnf(i_0_6389,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I4_J]) ).

fof(i_0_6390,plain,
    ! [X29793,X29794,X29795,X29796,X29798,X29799,X29800,X29801,X29802] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_4(X29793,X29794,X29795,X29796)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29794))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29794)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( hAPP(hAPP(c_List_Otake(X29796),esk390_4(X29793,X29794,X29795,X29796)),X29795) = hAPP(hAPP(c_List_Otake(X29796),esk390_4(X29793,X29794,X29795,X29796)),X29794)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29794)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29796,X29796)),hAPP(hAPP(c_Product__Type_OPair(X29796,X29796),hAPP(hAPP(c_List_Onth(X29796),X29795),esk390_4(X29793,X29794,X29795,X29796))),hAPP(hAPP(c_List_Onth(X29796),X29794),esk390_4(X29793,X29794,X29795,X29796)))),X29793))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29794)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_4(X29793,X29794,X29795,X29796)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29794))))
        | hAPP(hAPP(c_List_Otake(X29796),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),X29794) = X29795
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( hAPP(hAPP(c_List_Otake(X29796),esk390_4(X29793,X29794,X29795,X29796)),X29795) = hAPP(hAPP(c_List_Otake(X29796),esk390_4(X29793,X29794,X29795,X29796)),X29794)
        | hAPP(hAPP(c_List_Otake(X29796),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),X29794) = X29795
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29796,X29796)),hAPP(hAPP(c_Product__Type_OPair(X29796,X29796),hAPP(hAPP(c_List_Onth(X29796),X29795),esk390_4(X29793,X29794,X29795,X29796))),hAPP(hAPP(c_List_Onth(X29796),X29794),esk390_4(X29793,X29794,X29795,X29796)))),X29793))
        | hAPP(hAPP(c_List_Otake(X29796),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29796)),X29795)),X29794) = X29795
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29796),tc_List_Olist(X29796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29796),tc_List_Olist(X29796)),X29795),X29794)),c_List_Olexord(X29796,X29793))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29801)),X29800)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29801)),X29799)))
        | hAPP(hAPP(c_List_Otake(X29801),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29801)),X29800)),X29799) != X29800
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29801),tc_List_Olist(X29801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29801),tc_List_Olist(X29801)),X29800),X29799)),c_List_Olexord(X29801,X29798))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29802),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29801)),X29800)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29801)),X29799))))
        | hAPP(hAPP(c_List_Otake(X29801),X29802),X29800) != hAPP(hAPP(c_List_Otake(X29801),X29802),X29799)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29801,X29801)),hAPP(hAPP(c_Product__Type_OPair(X29801,X29801),hAPP(hAPP(c_List_Onth(X29801),X29800),X29802)),hAPP(hAPP(c_List_Onth(X29801),X29799),X29802))),X29798))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29801),tc_List_Olist(X29801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29801),tc_List_Olist(X29801)),X29800),X29799)),c_List_Olexord(X29801,X29798))) ) ),
    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_lexord__take__index__conv])])])])])]) ).

cnf(i_0_6391,plain,
    c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5363]) ).

fof(i_0_6392,plain,
    ! [X27963,X27964,X27965,X27966] : hAPP(c_Set_OCollect(tc_prod(X27966,X27965)),hAPP(c_Product__Type_Oprod_Oprod__case(X27966,X27965,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X27966,tc_fun(X27965,tc_HOL_Obool),tc_fun(X27965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27965,tc_HOL_Obool),tc_fun(X27965,tc_HOL_Obool)),X27966),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27965)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27966),c_fconj),X27964))),X27963))) = hAPP(hAPP(c_Product__Type_OSigma(X27966,X27965),hAPP(c_Set_OCollect(X27966),X27964)),hAPP(hAPP(c_COMBB(tc_fun(X27965,tc_HOL_Obool),tc_fun(X27965,tc_HOL_Obool),X27966),c_Set_OCollect(X27965)),X27963)),
    inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(i_0_6393,plain,
    ! [X25263,X25264] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25264))
      | hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X25264))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X25263))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])]) ).

fof(i_0_6394,plain,
    ! [X28555,X28556,X28557,X28558] : c_Hilbert__Choice_OEps(tc_prod(X28558,X28557),hAPP(c_Product__Type_Oprod_Oprod__case(X28558,X28557,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28558,tc_fun(X28557,tc_HOL_Obool),tc_fun(X28557,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28557,tc_HOL_Obool),tc_fun(X28557,tc_HOL_Obool)),X28558),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28557)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28558),c_fconj),hAPP(c_fequal,X28556)))),hAPP(c_fequal,X28555)))) = hAPP(hAPP(c_Product__Type_OPair(X28558,X28557),X28556),X28555),
    inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).

fof(i_0_6395,plain,
    ! [X26758,X26759,X26760,X26761] : c_HOL_OThe(tc_prod(X26761,X26760),hAPP(c_Product__Type_Oprod_Oprod__case(X26761,X26760,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26761,tc_fun(X26760,tc_HOL_Obool),tc_fun(X26760,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X26760,tc_HOL_Obool),tc_fun(X26760,tc_HOL_Obool)),X26761),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X26760)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26761),c_fconj),hAPP(c_fequal,X26759)))),hAPP(c_fequal,X26758)))) = hAPP(hAPP(c_Product__Type_OPair(X26761,X26760),X26759),X26758),
    inference(variable_rename,[status(thm)],[fact_The__split__eq]) ).

cnf(i_0_6396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5352]) ).

fof(i_0_6397,plain,
    ! [X17643,X17644,X17645,X17646,X17647,X17648] :
      ( ~ class_Groups_Ocomm__monoid__add(X17648)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17647,X17648),hAPP(hAPP(c_COMBC(X17647,tc_fun(X17646,tc_HOL_Obool),X17648),hAPP(hAPP(c_COMBB(tc_fun(X17646,X17648),tc_fun(tc_fun(X17646,tc_HOL_Obool),X17648),X17647),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17646,X17648)),X17645)),X17644)),X17643) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17646,X17648),hAPP(hAPP(c_COMBC(X17646,tc_fun(X17647,tc_HOL_Obool),X17648),hAPP(hAPP(c_COMBB(tc_fun(X17647,X17648),tc_fun(tc_fun(X17647,tc_HOL_Obool),X17648),X17646),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17647,X17648)),hAPP(c_COMBC(X17647,X17646,X17648),X17645))),X17643)),X17644) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).

fof(i_0_6398,plain,
    ! [X27959,X27960,X27961,X27962] : hAPP(c_Set_OCollect(tc_prod(X27962,X27961)),hAPP(c_Product__Type_Oprod_Oprod__case(X27962,X27961,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27962,tc_fun(X27961,tc_HOL_Obool),tc_fun(X27961,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27961,tc_HOL_Obool),tc_fun(X27961,tc_HOL_Obool)),X27962),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27962),c_fconj),X27960))),X27959))) = hAPP(hAPP(c_Product__Type_OSigma(X27962,X27961),hAPP(c_Set_OCollect(X27962),X27960)),hAPP(c_COMBK(tc_fun(X27961,tc_HOL_Obool),X27962),hAPP(c_Set_OCollect(X27961),X27959))),
    inference(variable_rename,[status(thm)],[fact_Collect__split]) ).

fof(i_0_6399,plain,
    ! [X19726,X19727,X19728,X19729] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19729),X19728))
      | hAPP(c_Set_Oimage(X19729,X19727,X19726),X19728) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X19727,tc_HOL_Obool),X19729,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19727,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19729,tc_fun(X19727,tc_HOL_Obool),tc_fun(X19727,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X19727,tc_fun(tc_fun(X19727,tc_HOL_Obool),tc_fun(X19727,tc_HOL_Obool)),X19729),c_Set_Oinsert(X19727)),X19726)),c_Orderings_Obot__class_Obot(tc_fun(X19727,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X19727,tc_HOL_Obool))),X19728) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])]) ).

cnf(i_0_6400,plain,
    c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5364]) ).

fof(i_0_6401,plain,
    ! [X19308,X19309,X19310,X19311] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19311),X19310))
      | ~ hBOOL(hAPP(hAPP(c_member(X19311),X19309),X19310))
      | ~ hBOOL(hAPP(hAPP(c_member(X19311),X19308),X19310))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19311),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19311,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19311,tc_HOL_Obool)),X19310),hAPP(hAPP(c_Set_Oinsert(X19311),X19309),c_Orderings_Obot__class_Obot(tc_fun(X19311,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X19311),X19308),c_Orderings_Obot__class_Obot(tc_fun(X19311,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X19311),X19310))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff2__less])]) ).

cnf(i_0_6402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5365]) ).

fof(i_0_6403,plain,
    ! [X27259,X27260] : c_Relation_OId__on(X27260,X27259) = hAPP(c_Product__Type_Oprod_Oprod__case(X27260,X27260,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X27260,tc_HOL_Obool,tc_fun(X27260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X27260,tc_HOL_Obool)),X27260),c_COMBC(X27260,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27260,tc_HOL_Obool),tc_fun(X27260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27260),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27260),c_fconj)),c_fequal))),X27259)),
    inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).

fof(i_0_6404,plain,
    ! [X26380] : c_Int_Oint__ge__less__than(X26380) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26380)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(i_0_6405,plain,
    ! [X28855,X28856,X28857,X28858,X28859,X28860,X28861,X28862,X28863] : hAPP(hAPP(c_Product__Type_Oscomp(X28863,X28862,X28861,X28860),hAPP(hAPP(c_Product__Type_Oscomp(X28863,X28859,X28858,tc_prod(X28862,X28861)),X28857),X28856)),X28855) = hAPP(hAPP(c_Product__Type_Oscomp(X28863,X28859,X28858,X28860),X28857),hAPP(hAPP(c_COMBC(X28859,tc_fun(X28862,tc_fun(X28861,X28860)),tc_fun(X28858,X28860)),hAPP(hAPP(c_COMBB(tc_fun(X28858,tc_prod(X28862,X28861)),tc_fun(tc_fun(X28862,tc_fun(X28861,X28860)),tc_fun(X28858,X28860)),X28859),c_Product__Type_Oscomp(X28858,X28862,X28861,X28860)),X28856)),X28855)),
    inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).

fof(i_0_6406,plain,
    ! [X27232,X27233,X27234,X27235] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27235),X27234))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27233),X27235)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27232),X27234)),c_FunDef_Omax__weak))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27233),X27232)),X27234)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).

fof(i_0_6407,plain,
    ! [X27222,X27223,X27224,X27225] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27225),X27224))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27223),X27225)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27222),X27224)),c_FunDef_Omax__strict))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27223),X27222)),X27224)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__insertI])]) ).

cnf(i_0_6408,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5337]) ).

cnf(i_0_6409,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5338]) ).

fof(i_0_6410,plain,
    ! [X32073,X32074,X32075,X32076,X32077] :
      ( ~ class_Orderings_Olinorder(X32077)
      | c_List_Olinorder__class_Osorted(X32077,hAPP(hAPP(c_List_Omap(X32076,X32077),X32075),hAPP(c_List_Ofilter(X32076,hAPP(hAPP(c_COMBC(X32076,X32077,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32077,tc_fun(X32077,tc_HOL_Obool),X32076),c_fequal),X32075)),hAPP(X32074,X32073))),X32073))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).

fof(i_0_6411,plain,
    ! [X29719,X29720,X29721,X29722,X29723] :
      ( ( X29720 = hAPP(hAPP(c_List_Olist_OCons(X29723),esk384_5(X29719,X29720,X29721,X29722,X29723)),esk385_5(X29719,X29720,X29721,X29722,X29723))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29723),tc_List_Olist(X29723))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29723),tc_List_Olist(X29723)),hAPP(hAPP(c_List_Olist_OCons(X29723),X29722),X29721)),X29720)),c_List_Olistrel(X29723,X29719))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29723,X29723)),hAPP(hAPP(c_Product__Type_OPair(X29723,X29723),X29722),esk384_5(X29719,X29720,X29721,X29722,X29723))),X29719))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29723),tc_List_Olist(X29723))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29723),tc_List_Olist(X29723)),hAPP(hAPP(c_List_Olist_OCons(X29723),X29722),X29721)),X29720)),c_List_Olistrel(X29723,X29719))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29723),tc_List_Olist(X29723))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29723),tc_List_Olist(X29723)),X29721),esk385_5(X29719,X29720,X29721,X29722,X29723))),c_List_Olistrel(X29723,X29719)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29723),tc_List_Olist(X29723))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29723),tc_List_Olist(X29723)),hAPP(hAPP(c_List_Olist_OCons(X29723),X29722),X29721)),X29720)),c_List_Olistrel(X29723,X29719))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5366])])])]) ).

cnf(i_0_6412,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5367]) ).

fof(i_0_6413,plain,
    ! [X28734,X28735,X28736,X28737,X28738] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X28738,X28737,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28738)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28738),c_Hoare__Mirabelle_Opeek__and(X28738,X28736,X28735)),X28734),X28736)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28738),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X28738,X28737,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28738)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28738),X28736),c_Com_Ocom_OWhile(X28735,X28734)),c_Hoare__Mirabelle_Opeek__and(X28738,X28736,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X28735)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28738),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Loop])]) ).

cnf(i_0_6414,plain,
    c_List_Osublist(X1,X2,X3) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_5368]) ).

fof(i_0_6415,plain,
    ! [X28812,X28813,X28814,X28815,X28816,X28818,X28819,X28820,X28821,X28823] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28815),X28814))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool)),X28814),X28813)),c_Wellfounded_Omax__ext(X28815,X28812))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28815),X28813))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool)),X28814),X28813)),c_Wellfounded_Omax__ext(X28815,X28812))) )
      & ( X28813 != c_Orderings_Obot__class_Obot(tc_fun(X28815,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool)),X28814),X28813)),c_Wellfounded_Omax__ext(X28815,X28812))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28815),esk336_5(X28812,X28813,X28814,X28815,X28816)),X28813))
        | ~ hBOOL(hAPP(hAPP(c_member(X28815),X28816),X28814))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool)),X28814),X28813)),c_Wellfounded_Omax__ext(X28815,X28812))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28815,X28815)),hAPP(hAPP(c_Product__Type_OPair(X28815,X28815),X28816),esk336_5(X28812,X28813,X28814,X28815,X28816))),X28812))
        | ~ hBOOL(hAPP(hAPP(c_member(X28815),X28816),X28814))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28815,tc_HOL_Obool),tc_fun(X28815,tc_HOL_Obool)),X28814),X28813)),c_Wellfounded_Omax__ext(X28815,X28812))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28821),esk337_4(X28818,X28819,X28820,X28821)),X28820))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28821),X28820))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28821),X28819))
        | X28819 = c_Orderings_Obot__class_Obot(tc_fun(X28821,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28821,tc_HOL_Obool),tc_fun(X28821,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28821,tc_HOL_Obool),tc_fun(X28821,tc_HOL_Obool)),X28820),X28819)),c_Wellfounded_Omax__ext(X28821,X28818))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28821),X28823),X28819))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28821,X28821)),hAPP(hAPP(c_Product__Type_OPair(X28821,X28821),esk337_4(X28818,X28819,X28820,X28821)),X28823)),X28818))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28821),X28820))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28821),X28819))
        | X28819 = c_Orderings_Obot__class_Obot(tc_fun(X28821,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28821,tc_HOL_Obool),tc_fun(X28821,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28821,tc_HOL_Obool),tc_fun(X28821,tc_HOL_Obool)),X28820),X28819)),c_Wellfounded_Omax__ext(X28821,X28818))) ) ),
    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_max__ext_Osimps])])])])])]) ).

fof(i_0_6416,plain,
    ! [X27572,X27573,X27574] :
      ( ( ~ c_Wellfounded_Owf(X27574,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),X27573),X27572))
        | c_Wellfounded_Owf(X27574,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27574,X27574,X27574),X27573),X27573)),hAPP(hAPP(c_Relation_Orel__comp(X27574,X27574,X27574),X27572),X27573))),X27572)) )
      & ( ~ c_Wellfounded_Owf(X27574,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27574,X27574,X27574),X27573),X27573)),hAPP(hAPP(c_Relation_Orel__comp(X27574,X27574,X27574),X27572),X27573))),X27572))
        | c_Wellfounded_Owf(X27574,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27574,X27574),tc_HOL_Obool)),X27573),X27572)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).

fof(i_0_6417,plain,
    ! [X28133,X28134,X28135,X28136,X28137,X28138,X28139,X28140,X28141,X28142] :
      ( hAPP(c_Set_Oimage(X28142,X28141,X28140),X28139) != X28138
      | hAPP(c_Set_Oimage(X28137,X28136,X28135),X28134) != X28133
      | hAPP(c_Set_Oimage(tc_prod(X28142,X28137),tc_prod(X28141,X28136),c_Product__Type_Omap__pair(X28142,X28141,X28137,X28136,X28140,X28135)),hAPP(hAPP(c_Product__Type_OSigma(X28142,X28137),X28139),hAPP(c_COMBK(tc_fun(X28137,tc_HOL_Obool),X28142),X28134))) = hAPP(hAPP(c_Product__Type_OSigma(X28141,X28136),X28138),hAPP(c_COMBK(tc_fun(X28136,tc_HOL_Obool),X28141),X28133)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).

fof(i_0_6418,plain,
    ! [X27236,X27237,X27238,X27239] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27239),X27238))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27239),X27237)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27238),X27236)),c_FunDef_Omin__weak))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27238),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27237),X27236))),c_FunDef_Omin__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).

fof(i_0_6419,plain,
    ! [X27218,X27219,X27220,X27221] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27221),X27220))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27221),X27219)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27220),X27218)),c_FunDef_Omin__strict))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27220),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27219),X27218))),c_FunDef_Omin__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).

fof(i_0_6420,plain,
    ! [X18201,X18202,X18203,X18204,X18205] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X18205),X18203),X18202) = hAPP(hAPP(c_Set_Oinsert(X18205),esk32_5(X18201,X18202,X18203,X18204,X18205)),esk33_5(X18201,X18202,X18203,X18204,X18205))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18205,X18204,hAPP(hAPP(c_Set_Oinsert(X18205),X18203),X18202)),X18201)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18205,X18205,X18204,esk32_5(X18201,X18202,X18203,X18204,X18205),esk33_5(X18201,X18202,X18203,X18204,X18205)),X18201))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18205,X18204,hAPP(hAPP(c_Set_Oinsert(X18205),X18203),X18202)),X18201)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18205),esk32_5(X18201,X18202,X18203,X18204,X18205)),esk33_5(X18201,X18202,X18203,X18204,X18205)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18205,X18204,hAPP(hAPP(c_Set_Oinsert(X18205),X18203),X18202)),X18201)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE])])])]) ).

fof(i_0_6421,plain,
    ! [X18187,X18188,X18189,X18190,X18191,X18194,X18195,X18196,X18197,X18198,X18199,X18200] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X18191),X18189),X18188) = hAPP(hAPP(c_Set_Oinsert(X18191),esk30_5(X18187,X18188,X18189,X18190,X18191)),esk31_5(X18187,X18188,X18189,X18190,X18191))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18191,X18190,hAPP(hAPP(c_Set_Oinsert(X18191),X18189),X18188)),X18187)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18191,X18191,X18190,esk30_5(X18187,X18188,X18189,X18190,X18191),esk31_5(X18187,X18188,X18189,X18190,X18191)),X18187))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18191,X18190,hAPP(hAPP(c_Set_Oinsert(X18191),X18189),X18188)),X18187)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18191),esk30_5(X18187,X18188,X18189,X18190,X18191)),esk31_5(X18187,X18188,X18189,X18190,X18191)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18191,X18190,hAPP(hAPP(c_Set_Oinsert(X18191),X18189),X18188)),X18187)) )
      & ( hAPP(hAPP(c_Set_Oinsert(X18198),X18196),X18195) != hAPP(hAPP(c_Set_Oinsert(X18198),X18199),X18200)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18198,X18198,X18197,X18199,X18200),X18194))
        | hBOOL(hAPP(hAPP(c_member(X18198),X18199),X18200))
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18198,X18197,hAPP(hAPP(c_Set_Oinsert(X18198),X18196),X18195)),X18194)) ) ),
    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)],[i_0_5369])])])])])]) ).

fof(i_0_6422,plain,
    ! [X30106,X30107,X30108,X30109,X30112,X30113,X30114,X30115,X30116,X30117] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30109,X30109)),hAPP(hAPP(c_Product__Type_OPair(X30109,X30109),hAPP(hAPP(c_List_Onth(X30109),X30108),esk400_4(X30106,X30107,X30108,X30109))),esk399_4(X30106,X30107,X30108,X30109))),X30106))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30109),tc_List_Olist(X30109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30109),tc_List_Olist(X30109)),X30108),X30107)),c_List_Olistrel1(X30109,X30106))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk400_4(X30106,X30107,X30108,X30109)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30109)),X30108)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30109),tc_List_Olist(X30109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30109),tc_List_Olist(X30109)),X30108),X30107)),c_List_Olistrel1(X30109,X30106))) )
      & ( X30107 = hAPP(hAPP(c_List_Olist__update(X30109,X30108),esk400_4(X30106,X30107,X30108,X30109)),esk399_4(X30106,X30107,X30108,X30109))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30109),tc_List_Olist(X30109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30109),tc_List_Olist(X30109)),X30108),X30107)),c_List_Olistrel1(X30109,X30106))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30115,X30115)),hAPP(hAPP(c_Product__Type_OPair(X30115,X30115),hAPP(hAPP(c_List_Onth(X30115),X30114),X30117)),X30116)),X30112))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30117),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30115)),X30114)))
        | X30113 != hAPP(hAPP(c_List_Olist__update(X30115,X30114),X30117),X30116)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30115),tc_List_Olist(X30115))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30115),tc_List_Olist(X30115)),X30114),X30113)),c_List_Olistrel1(X30115,X30112))) ) ),
    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_listrel1__iff__update])])])])])]) ).

fof(i_0_6423,plain,
    ! [X28075,X28076,X28077,X28078,X28079,X28080] :
      ( hAPP(c_Set_Oimage(X28080,X28079,X28078),c_Orderings_Otop__class_Otop(tc_fun(X28080,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28079,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X28077,X28076,X28075),c_Orderings_Otop__class_Otop(tc_fun(X28077,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28076,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(tc_prod(X28080,X28077),tc_prod(X28079,X28076),c_Product__Type_Omap__pair(X28080,X28079,X28077,X28076,X28078,X28075)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28080,X28077),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28079,X28076),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).

fof(i_0_6424,plain,
    ! [X17528,X17529,X17530] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17530),X17529))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17530,tc_HOL_Obool)),X17528),X17529) = hAPP(hAPP(c_Finite__Set_Ofold(X17530,tc_fun(X17530,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17530,tc_HOL_Obool),tc_fun(tc_fun(X17530,tc_HOL_Obool),tc_fun(X17530,tc_HOL_Obool)),X17530),hAPP(c_COMBC(tc_fun(X17530,tc_HOL_Obool),tc_fun(X17530,tc_HOL_Obool),tc_fun(X17530,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X17530,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X17530,tc_fun(X17530,tc_HOL_Obool),tc_fun(X17530,tc_HOL_Obool)),c_Set_Oinsert(X17530)),c_Orderings_Obot__class_Obot(tc_fun(X17530,tc_HOL_Obool))))),X17528),X17529) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).

cnf(i_0_6425,plain,
    ( hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X1),X4) = hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X5),X4)
    | hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5353]) ).

cnf(i_0_6426,plain,
    ( hAPP(c_Product__Type_Oapfst(X2,X6,X3,X1),X4) = hAPP(c_Product__Type_Oapfst(X2,X6,X3,X5),X4)
    | hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5354]) ).

cnf(i_0_6427,plain,
    c_Nitpick_Ouminus__frac(X1,X2) = c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(c_Nitpick_Odenom(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_5370]) ).

cnf(i_0_6428,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Oapsnd(X3,X2,X1,X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5371]) ).

cnf(i_0_6429,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Oapfst(X3,X1,X2,X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Ofst(X3,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5372]) ).

fof(i_0_6430,plain,
    ! [X28108,X28109,X28110,X28111,X28112,X28113,X28114] : hAPP(c_Product__Type_Ofst(X28114,X28113),hAPP(c_Product__Type_Omap__pair(X28112,X28114,X28111,X28113,X28110,X28109),X28108)) = hAPP(X28110,hAPP(c_Product__Type_Ofst(X28112,X28111),X28108)),
    inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).

fof(i_0_6431,plain,
    ! [X28101,X28102,X28103,X28104,X28105,X28106,X28107] : hAPP(c_Product__Type_Osnd(X28107,X28106),hAPP(c_Product__Type_Omap__pair(X28105,X28107,X28104,X28106,X28103,X28102),X28101)) = hAPP(X28102,hAPP(c_Product__Type_Osnd(X28105,X28104),X28101)),
    inference(variable_rename,[status(thm)],[fact_snd__prod__fun]) ).

cnf(i_0_6432,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Oapsnd(X3,X2,X1,X4),X5)) = hAPP(c_Product__Type_Ofst(X1,X3),X5),
    inference(split_conjunct,[status(thm)],[i_0_5373]) ).

cnf(i_0_6433,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Oapfst(X3,X1,X2,X4),X5)) = hAPP(c_Product__Type_Osnd(X3,X2),X5),
    inference(split_conjunct,[status(thm)],[i_0_5374]) ).

fof(i_0_6434,plain,
    ! [X29759,X29760,X29761,X29762] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29762,X29762)),hAPP(hAPP(c_Product__Type_OPair(X29762,X29762),esk387_4(X29759,X29760,X29761,X29762)),esk388_4(X29759,X29760,X29761,X29762))),X29761))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29760),X29759)),c_List_Olexord(X29762,X29761)))
        | X29760 = X29759
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29759),X29760)),c_List_Olexord(X29762,X29761))) )
      & ( esk387_4(X29759,X29760,X29761,X29762) != esk388_4(X29759,X29760,X29761,X29762)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29760),X29759)),c_List_Olexord(X29762,X29761)))
        | X29760 = X29759
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29759),X29760)),c_List_Olexord(X29762,X29761))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29762,X29762)),hAPP(hAPP(c_Product__Type_OPair(X29762,X29762),esk388_4(X29759,X29760,X29761,X29762)),esk387_4(X29759,X29760,X29761,X29762))),X29761))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29760),X29759)),c_List_Olexord(X29762,X29761)))
        | X29760 = X29759
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29762),tc_List_Olist(X29762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29762),tc_List_Olist(X29762)),X29759),X29760)),c_List_Olexord(X29762,X29761))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).

fof(i_0_6435,plain,
    ! [X27308,X27309,X27310,X27311] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27311),X27310)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27309),X27308)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27311),X27309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27310),X27308))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_add]) ).

fof(i_0_6436,plain,
    ! [X27257,X27258] : c_Relation_OId__on(X27258,X27257) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27258,tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool)),X27257),hAPP(hAPP(c_COMBC(X27258,tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool),tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X27258,X27258),tc_fun(tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool),tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool)),X27258),c_Set_Oinsert(tc_prod(X27258,X27258))),hAPP(hAPP(c_COMBS(X27258,X27258,tc_prod(X27258,X27258)),c_Product__Type_OPair(X27258,X27258)),c_COMBI(X27258)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27258,X27258),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).

cnf(i_0_6437,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_5375]) ).

fof(i_0_6438,plain,
    ! [X32810,X32811,X32812] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32812,X32812,hAPP(hAPP(c_COMBB(tc_fun(X32812,tc_HOL_Obool),tc_fun(X32812,tc_HOL_Obool),X32812),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32812),c_fNot)),c_fequal)),X32811),X32810))
        | X32811 != X32810 )
      & ( X32811 = X32810
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32812,X32812,hAPP(hAPP(c_COMBB(tc_fun(X32812,tc_HOL_Obool),tc_fun(X32812,tc_HOL_Obool),X32812),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32812),c_fNot)),c_fequal)),X32811),X32810)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])]) ).

cnf(i_0_6439,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat)))),
    inference(split_conjunct,[status(thm)],[i_0_5376]) ).

cnf(i_0_6440,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),c_Int_Onat)))),
    inference(split_conjunct,[status(thm)],[i_0_5377]) ).

fof(i_0_6441,plain,
    ! [X31049,X31050,X31051,X31052,X31053,X31054,X31055,X31056] : hAPP(hAPP(c_List_Omap(tc_prod(X31056,X31055),X31054),X31053),hAPP(hAPP(c_List_Ozip(X31056,X31055),hAPP(hAPP(c_List_Omap(X31052,X31056),X31051),X31050)),X31049)) = hAPP(hAPP(c_List_Omap(tc_prod(X31052,X31055),X31054),hAPP(c_Product__Type_Oprod_Oprod__case(X31052,X31055,X31054),hAPP(hAPP(c_COMBB(tc_fun(X31055,tc_prod(X31056,X31055)),tc_fun(X31055,X31054),X31052),hAPP(c_COMBB(tc_prod(X31056,X31055),X31054,X31055),X31053)),hAPP(hAPP(c_COMBB(X31056,tc_fun(X31055,tc_prod(X31056,X31055)),X31052),c_Product__Type_OPair(X31056,X31055)),X31051)))),hAPP(hAPP(c_List_Ozip(X31052,X31055),X31050),X31049)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).

fof(i_0_6442,plain,
    ! [X32476,X32477,X32478,X32479] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32478,X32479)),X32477),X32476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32478,X32479)),X32477),X32476))
        | ~ class_Orderings_Oorder(X32479)
        | ~ class_Enum_Oenum(X32478) )
      & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32478),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32478),c_fNot),hAPP(hAPP(c_COMBS(X32478,X32479,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32479,tc_fun(X32479,tc_HOL_Obool),X32478),c_fequal),X32477)),X32476))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32478,X32479)),X32477),X32476))
        | ~ class_Orderings_Oorder(X32479)
        | ~ class_Enum_Oenum(X32478) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32478,X32479)),X32477),X32476))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32478),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32478),c_fNot),hAPP(hAPP(c_COMBS(X32478,X32479,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32479,tc_fun(X32479,tc_HOL_Obool),X32478),c_fequal),X32477)),X32476))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32478,X32479)),X32477),X32476))
        | ~ class_Orderings_Oorder(X32479)
        | ~ class_Enum_Oenum(X32478) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J])])]) ).

fof(i_0_6443,plain,
    ! [X30353,X30354,X30355,X30356] : c_List_Osublist(X30356,hAPP(hAPP(c_List_Olist_OCons(X30356),X30355),X30354),X30353) = hAPP(hAPP(c_List_Oappend(X30356),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X30356)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30353)),hAPP(hAPP(c_List_Olist_OCons(X30356),X30355),c_List_Olist_ONil(X30356))),c_List_Olist_ONil(X30356))),c_List_Osublist(X30356,X30354,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X30353)))),
    inference(variable_rename,[status(thm)],[fact_sublist__Cons]) ).

cnf(i_0_6444,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5378]) ).

fof(i_0_6445,plain,
    ! [X32127,X32128,X32129,X32130] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32130),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32130))),X32129)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32128),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32130))),c_List_Otranspose(X32130,X32129))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32127),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32130))),hAPP(c_List_Ofilter(tc_List_Olist(X32130),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32130)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32128)),c_Nat_Osize__class_Osize(tc_List_Olist(X32130)))),X32129))))
      | hAPP(hAPP(c_List_Onth(X32130),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32130)),c_List_Otranspose(X32130,X32129)),X32128)),X32127) = hAPP(hAPP(c_List_Onth(X32130),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32130)),X32129),X32127)),X32128) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted])]) ).

cnf(i_0_6446,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5379]) ).

cnf(i_0_6447,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5358]) ).

cnf(i_0_6448,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5380]) ).

cnf(i_0_6449,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5381]) ).

cnf(i_0_6450,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5382]) ).

cnf(i_0_6451,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5360]) ).

cnf(i_0_6452,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5383]) ).

cnf(i_0_6453,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5384]) ).

cnf(i_0_6454,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5385]) ).

fof(i_0_6455,plain,
    ! [X21802,X21803,X21804,X21805,X21806,X21808] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21805),esk114_5(X21802,X21803,X21804,X21805,X21806)),X21804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21805,X21806),X21804),X21803)),X21802))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21806)
        | ~ class_Orderings_Olinorder(X21806) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21806),hAPP(X21803,esk114_5(X21802,X21803,X21804,X21805,X21806))),X21802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21805,X21806),X21804),X21803)),X21802))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21806)
        | ~ class_Orderings_Olinorder(X21806) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21805),X21808),X21804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21806),hAPP(X21803,X21808)),X21802))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21805,X21806),X21804),X21803)),X21802))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21806)
        | ~ class_Orderings_Olinorder(X21806) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__less__iff])])])])]) ).

fof(i_0_6456,plain,
    ! [X21185,X21186,X21187,X21188,X21189,X21191,X21192,X21193,X21194,X21195,X21196,X21197,X21200] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21189),esk92_5(X21185,X21186,X21187,X21188,X21189)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21188,tc_fun(X21189,tc_HOL_Obool)),X21187),X21186)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21188),X21191),X21187))
        | ~ hBOOL(hAPP(hAPP(c_member(X21189),X21192),hAPP(X21186,X21191)))
        | hBOOL(hAPP(X21185,X21192)) )
      & ( ~ hBOOL(hAPP(X21185,esk92_5(X21185,X21186,X21187,X21188,X21189)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21188),X21191),X21187))
        | ~ hBOOL(hAPP(hAPP(c_member(X21189),X21192),hAPP(X21186,X21191)))
        | hBOOL(hAPP(X21185,X21192)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21196),esk93_5(X21193,X21194,X21195,X21196,X21197)),X21195))
        | ~ hBOOL(hAPP(hAPP(c_member(X21197),X21200),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21196,tc_fun(X21197,tc_HOL_Obool)),X21195),X21194)))
        | hBOOL(hAPP(X21193,X21200)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21197),esk94_5(X21193,X21194,X21195,X21196,X21197)),hAPP(X21194,esk93_5(X21193,X21194,X21195,X21196,X21197))))
        | ~ hBOOL(hAPP(hAPP(c_member(X21197),X21200),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21196,tc_fun(X21197,tc_HOL_Obool)),X21195),X21194)))
        | hBOOL(hAPP(X21193,X21200)) )
      & ( ~ hBOOL(hAPP(X21193,esk94_5(X21193,X21194,X21195,X21196,X21197)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21197),X21200),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21196,tc_fun(X21197,tc_HOL_Obool)),X21195),X21194)))
        | hBOOL(hAPP(X21193,X21200)) ) ),
    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_ball__UN])])])])])]) ).

cnf(i_0_6457,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J]) ).

fof(i_0_6458,plain,
    ! [X27273,X27274,X27275,X27276,X27277,X27278] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool)),X27277),X27276)),c_Wellfounded_Omax__ext(X27278,X27275)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool)),X27274),X27273)),c_Wellfounded_Omax__ext(X27278,X27275)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27278,tc_HOL_Obool),tc_fun(X27278,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27278,tc_HOL_Obool)),X27277),X27274)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27278,tc_HOL_Obool)),X27276),X27273))),c_Wellfounded_Omax__ext(X27278,X27275))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).

fof(i_0_6459,plain,
    ! [X28068,X28069,X28070,X28071,X28072] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28072),esk306_5(X28068,X28069,X28070,X28071,X28072)),X28069))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28072,X28071)),X28070),hAPP(hAPP(c_Product__Type_OSigma(X28072,X28071),X28069),X28068))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28071),esk307_5(X28068,X28069,X28070,X28071,X28072)),hAPP(X28068,esk306_5(X28068,X28069,X28070,X28071,X28072))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28072,X28071)),X28070),hAPP(hAPP(c_Product__Type_OSigma(X28072,X28071),X28069),X28068))) )
      & ( X28070 = hAPP(hAPP(c_Product__Type_OPair(X28072,X28071),esk306_5(X28068,X28069,X28070,X28071,X28072)),esk307_5(X28068,X28069,X28070,X28071,X28072))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28072,X28071)),X28070),hAPP(hAPP(c_Product__Type_OSigma(X28072,X28071),X28069),X28068))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).

fof(i_0_6460,plain,
    ! [X31019,X31020,X31021,X31022,X31023,X31024,X31025] : hAPP(c_List_Ofoldl(X31025,X31024,X31023,X31022),hAPP(hAPP(c_List_Omap(X31021,X31024),X31020),X31019)) = hAPP(c_List_Ofoldl(X31025,X31021,hAPP(hAPP(c_COMBC(X31025,tc_fun(X31021,X31024),tc_fun(X31021,X31025)),hAPP(hAPP(c_COMBB(tc_fun(X31024,X31025),tc_fun(tc_fun(X31021,X31024),tc_fun(X31021,X31025)),X31025),c_COMBB(X31024,X31025,X31021)),X31023)),X31020),X31022),X31019),
    inference(variable_rename,[status(thm)],[fact_foldl__map]) ).

fof(i_0_6461,plain,
    ! [X27357,X27358,X27359,X27360,X27361,X27362,X27363] : hAPP(hAPP(c_Relation_Orel__comp(X27363,X27362,X27361),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27360,tc_fun(tc_prod(X27363,X27362),tc_HOL_Obool)),X27359),X27358)),X27357) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27360,tc_fun(tc_prod(X27363,X27361),tc_HOL_Obool)),X27359),hAPP(hAPP(c_COMBC(X27360,tc_fun(tc_prod(X27362,X27361),tc_HOL_Obool),tc_fun(tc_prod(X27363,X27361),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27363,X27362),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27362,X27361),tc_HOL_Obool),tc_fun(tc_prod(X27363,X27361),tc_HOL_Obool)),X27360),c_Relation_Orel__comp(X27363,X27362,X27361)),X27358)),X27357)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(i_0_6462,plain,
    ! [X25914,X25915] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25915),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25914)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25915)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25914) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25915),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25914)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25915)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25914),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25915)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5386])]) ).

cnf(i_0_6463,plain,
    c_List_OdropWhile(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),c_List_OdropWhile(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5387]) ).

fof(i_0_6464,plain,
    ! [X25311,X25312,X25313] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),X25312)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),hAPP(hAPP(c_COMBS(X25313,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25313),c_fdisj),X25312)),X25311)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),X25311)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),hAPP(hAPP(c_COMBS(X25313,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25313),c_fdisj),X25312)),X25311)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),X25312)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),X25311)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25313),hAPP(c_Set_OCollect(X25313),hAPP(hAPP(c_COMBS(X25313,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25313),c_fdisj),X25312)),X25311)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).

fof(i_0_6465,plain,
    ! [X33582,X33583,X33584,X33585,X33586] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33585),esk529_5(X33582,X33583,X33584,X33585,X33586)),hAPP(c_Set_Oimage(X33586,X33585,X33584),c_Orderings_Otop__class_Otop(tc_fun(X33586,tc_HOL_Obool)))))
        | hBOOL(hAPP(X33583,X33582))
        | ~ c_Fun_Oinj__on(X33586,X33585,X33584,c_Orderings_Otop__class_Otop(tc_fun(X33586,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X33583,hAPP(c_Hilbert__Choice_Oinv__into(X33586,X33585,c_Orderings_Otop__class_Otop(tc_fun(X33586,tc_HOL_Obool)),X33584),esk529_5(X33582,X33583,X33584,X33585,X33586))))
        | hBOOL(hAPP(X33583,X33582))
        | ~ c_Fun_Oinj__on(X33586,X33585,X33584,c_Orderings_Otop__class_Otop(tc_fun(X33586,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__transfer])])])]) ).

fof(i_0_6466,plain,
    ! [X32570,X32571,X32572] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32571,X32572)),X32570))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32571),hAPP(hAPP(c_COMBB(tc_fun(X32572,tc_HOL_Obool),tc_HOL_Obool,X32571),c_Enum_Oenum__class_Oenum__all(X32572)),hAPP(hAPP(c_COMBB(tc_fun(X32572,tc_prod(X32571,X32572)),tc_fun(X32572,tc_HOL_Obool),X32571),hAPP(c_COMBB(tc_prod(X32571,X32572),tc_HOL_Obool,X32572),X32570)),c_Product__Type_OPair(X32571,X32572)))))
        | ~ class_Enum_Oenum(X32572)
        | ~ class_Enum_Oenum(X32571) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32571),hAPP(hAPP(c_COMBB(tc_fun(X32572,tc_HOL_Obool),tc_HOL_Obool,X32571),c_Enum_Oenum__class_Oenum__all(X32572)),hAPP(hAPP(c_COMBB(tc_fun(X32572,tc_prod(X32571,X32572)),tc_fun(X32572,tc_HOL_Obool),X32571),hAPP(c_COMBB(tc_prod(X32571,X32572),tc_HOL_Obool,X32572),X32570)),c_Product__Type_OPair(X32571,X32572)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32571,X32572)),X32570))
        | ~ class_Enum_Oenum(X32572)
        | ~ class_Enum_Oenum(X32571) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])]) ).

fof(i_0_6467,plain,
    ! [X32480,X32481,X32482] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32481,X32482)),X32480))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32481),hAPP(hAPP(c_COMBB(tc_fun(X32482,tc_HOL_Obool),tc_HOL_Obool,X32481),c_Enum_Oenum__class_Oenum__ex(X32482)),hAPP(hAPP(c_COMBB(tc_fun(X32482,tc_prod(X32481,X32482)),tc_fun(X32482,tc_HOL_Obool),X32481),hAPP(c_COMBB(tc_prod(X32481,X32482),tc_HOL_Obool,X32482),X32480)),c_Product__Type_OPair(X32481,X32482)))))
        | ~ class_Enum_Oenum(X32482)
        | ~ class_Enum_Oenum(X32481) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32481),hAPP(hAPP(c_COMBB(tc_fun(X32482,tc_HOL_Obool),tc_HOL_Obool,X32481),c_Enum_Oenum__class_Oenum__ex(X32482)),hAPP(hAPP(c_COMBB(tc_fun(X32482,tc_prod(X32481,X32482)),tc_fun(X32482,tc_HOL_Obool),X32481),hAPP(c_COMBB(tc_prod(X32481,X32482),tc_HOL_Obool,X32482),X32480)),c_Product__Type_OPair(X32481,X32482)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32481,X32482)),X32480))
        | ~ class_Enum_Oenum(X32482)
        | ~ class_Enum_Oenum(X32481) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])]) ).

fof(i_0_6468,plain,
    ! [X31382,X31383,X31384,X31385] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X31385,X31384),X31382))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31385,hAPP(hAPP(c_COMBS(X31385,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31385),c_fconj),X31384)),X31383)),X31382)) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31385,X31383),X31382))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31385,hAPP(hAPP(c_COMBS(X31385,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31385),c_fconj),X31384)),X31383)),X31382)) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X31385,X31384),X31382))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31385,X31383),X31382))
        | hBOOL(hAPP(c_List_Olistsp(X31385,hAPP(hAPP(c_COMBS(X31385,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31385),c_fconj),X31384)),X31383)),X31382)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).

fof(i_0_6469,plain,
    ! [X25553,X25554] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25554))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X25553)),hAPP(c_Int_Onat,X25554)) = hAPP(c_Int_Onat,X25553) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X25554))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X25553)),hAPP(c_Int_Onat,X25554)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25553),X25554)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5388])]) ).

cnf(i_0_6470,plain,
    ( c_List_OdropWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5389]) ).

cnf(i_0_6471,plain,
    ( hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk548_3(X3,X2,X1)),X4)) = hAPP(X2,esk548_3(X3,X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk547_3(X3,X2,X1)))),hAPP(X2,esk547_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5390]) ).

fof(i_0_6472,plain,
    ! [X18216,X18217,X18218,X18219,X18220] :
      ( ~ class_Groups_Oab__semigroup__mult(X18220)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18220,X18220,c_Groups_Otimes__class_Otimes(X18220),X18219,X18218),X18217))
      | ~ hBOOL(hAPP(hAPP(c_member(X18220),X18216),X18218))
      | hBOOL(hAPP(hAPP(c_member(X18220),X18219),X18218))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18220,X18220,c_Groups_Otimes__class_Otimes(X18220),X18216,hAPP(hAPP(c_Set_Oinsert(X18220),X18219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18220,tc_HOL_Obool)),X18218),hAPP(hAPP(c_Set_Oinsert(X18220),X18216),c_Orderings_Obot__class_Obot(tc_fun(X18220,tc_HOL_Obool)))))),X18217)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5391])]) ).

fof(i_0_6473,plain,
    ! [X31366,X31367,X31368,X31369] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31369)),X31368),c_List_Olists(X31369,X31367)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31369)),X31368),c_List_Olists(X31369,X31366)))
      | hBOOL(hAPP(c_List_Olistsp(X31369,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31369,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X31369,tc_fun(X31369,tc_HOL_Obool),tc_HOL_Obool),c_member(X31369)),X31367)),hAPP(hAPP(c_COMBC(X31369,tc_fun(X31369,tc_HOL_Obool),tc_HOL_Obool),c_member(X31369)),X31366))),X31368)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).

fof(i_0_6474,plain,
    ! [X25851,X25852,X25853,X25854,X25855,X25856,X25857,X25858,X25859,X25860] :
      ( ~ c_Equiv__Relations_Oequiv(X25860,X25859,X25858)
      | ~ c_Equiv__Relations_Oequiv(X25857,X25856,X25855)
      | ~ c_Equiv__Relations_Ocongruent2(X25860,X25857,tc_fun(X25854,tc_HOL_Obool),X25858,X25855,X25853)
      | ~ hBOOL(hAPP(hAPP(c_member(X25860),X25852),X25859))
      | ~ hBOOL(hAPP(hAPP(c_member(X25857),X25851),X25856))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25860,tc_fun(X25854,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25860,X25860,X25858),hAPP(hAPP(c_Set_Oinsert(X25860),X25852),c_Orderings_Obot__class_Obot(tc_fun(X25860,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X25857,tc_fun(X25854,tc_HOL_Obool)),tc_fun(X25854,tc_HOL_Obool),X25860),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25857,tc_fun(X25854,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25857,X25857,X25855),hAPP(hAPP(c_Set_Oinsert(X25857),X25851),c_Orderings_Obot__class_Obot(tc_fun(X25857,tc_HOL_Obool)))))),X25853)) = hAPP(hAPP(X25853,X25852),X25851) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).

fof(i_0_6475,plain,
    ! [X29548,X29549,X29550] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29550)),c_List_Osublist(X29550,X29549,X29548)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29550)),X29549)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29548)))),
    inference(variable_rename,[status(thm)],[fact_length__sublist]) ).

cnf(i_0_6476,plain,
    c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_5392]) ).

fof(i_0_6477,plain,
    ! [X31862,X31863,X31864] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31864)),hAPP(c_List_Ofilter(X31864,X31863),X31862)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31864)),X31862)))),hAPP(hAPP(c_COMBB(X31864,tc_HOL_Obool,tc_Nat_Onat),X31863),hAPP(c_List_Onth(X31864),X31862))))),
    inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).

fof(i_0_6478,plain,
    ! [X20179,X20180,X20181,X20182,X20183] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20183)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20182),X20181))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20183,X20182,c_Groups_Otimes__class_Otimes(X20183)),hAPP(hAPP(c_COMBS(X20182,X20183,X20183),hAPP(hAPP(c_COMBB(X20183,tc_fun(X20183,X20183),X20182),c_Groups_Otimes__class_Otimes(X20183)),X20180)),X20179)),c_Groups_Oone__class_Oone(X20183)),X20181) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20183),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20183,X20182,c_Groups_Otimes__class_Otimes(X20183)),X20180),c_Groups_Oone__class_Oone(X20183)),X20181)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20183,X20182,c_Groups_Otimes__class_Otimes(X20183)),X20179),c_Groups_Oone__class_Oone(X20183)),X20181)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).

fof(i_0_6479,plain,
    ! [X33822,X33823,X33824,X33825,X33826,X33827] :
      ( ~ c_Fun_Oinj__on(X33827,X33826,X33825,X33824)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33826,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33827,X33826,X33825),X33824)),X33823))
      | ~ c_Fun_Oinj__on(X33826,X33827,X33822,X33823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33827,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33826,X33827,X33822),X33823)),X33824))
      | c_Fun_Obij__betw(X33827,X33826,esk539_6(X33822,X33823,X33824,X33825,X33826,X33827),X33824,X33823) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantor__Bernstein])])]) ).

fof(i_0_6480,plain,
    ! [X30553,X30554,X30555,X30556,X30557,X30558] :
      ( ( X30557 = X30555
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),X30557),X30555)),c_List_Olistrel1(X30558,X30553)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30558,X30558)),hAPP(hAPP(c_Product__Type_OPair(X30558,X30558),X30556),X30554)),X30553))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),X30557),X30555)),c_List_Olistrel1(X30558,X30553)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) )
      & ( X30557 = X30555
        | X30556 = X30554
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30558,X30558)),hAPP(hAPP(c_Product__Type_OPair(X30558,X30558),X30556),X30554)),X30553))
        | X30556 = X30554
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),X30557),X30555)),c_List_Olistrel1(X30558,X30553)))
        | X30556 != X30554
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) )
      & ( X30557 != X30555
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30558,X30558)),hAPP(hAPP(c_Product__Type_OPair(X30558,X30558),X30556),X30554)),X30553))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30558),tc_List_Olist(X30558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30558),tc_List_Olist(X30558)),hAPP(hAPP(c_List_Oappend(X30558),X30557),hAPP(hAPP(c_List_Olist_OCons(X30558),X30556),c_List_Olist_ONil(X30558)))),hAPP(hAPP(c_List_Oappend(X30558),X30555),hAPP(hAPP(c_List_Olist_OCons(X30558),X30554),c_List_Olist_ONil(X30558))))),c_List_Olistrel1(X30558,X30553))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).

fof(i_0_6481,plain,
    ! [X31447,X31448,X31449,X31450,X31451,X31452,X31453] :
      ( ( ~ c_List_Olist__all2(X31453,X31452,X31451,X31450,hAPP(hAPP(c_List_Omap(X31449,X31452),X31448),X31447))
        | c_List_Olist__all2(X31453,X31449,hAPP(hAPP(c_COMBC(X31453,tc_fun(X31449,X31452),tc_fun(X31449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31452,tc_HOL_Obool),tc_fun(tc_fun(X31449,X31452),tc_fun(X31449,tc_HOL_Obool)),X31453),c_COMBB(X31452,tc_HOL_Obool,X31449)),X31451)),X31448),X31450,X31447) )
      & ( ~ c_List_Olist__all2(X31453,X31449,hAPP(hAPP(c_COMBC(X31453,tc_fun(X31449,X31452),tc_fun(X31449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31452,tc_HOL_Obool),tc_fun(tc_fun(X31449,X31452),tc_fun(X31449,tc_HOL_Obool)),X31453),c_COMBB(X31452,tc_HOL_Obool,X31449)),X31451)),X31448),X31450,X31447)
        | c_List_Olist__all2(X31453,X31452,X31451,X31450,hAPP(hAPP(c_List_Omap(X31449,X31452),X31448),X31447)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])]) ).

fof(i_0_6482,plain,
    ! [X23263,X23264,X23265,X23266] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23266,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk151_4(X23263,X23264,X23265,X23266))),X23265) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23266,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk151_4(X23263,X23264,X23265,X23266)),X23264))),X23263)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23266,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23265) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23266,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23263) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).

fof(i_0_6483,plain,
    ! [X27603,X27604,X27605,X27606,X27608] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27606),esk292_4(X27603,X27604,X27605,X27606)),X27605))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27606,tc_HOL_Obool),tc_fun(X27606,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27606,tc_HOL_Obool),tc_fun(X27606,tc_HOL_Obool)),X27605),X27604)),c_Wellfounded_Omax__ext(X27606,X27603)))
        | X27604 = c_Orderings_Obot__class_Obot(tc_fun(X27606,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27606),X27604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27606),X27605)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27606),X27608),X27604))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27606,X27606)),hAPP(hAPP(c_Product__Type_OPair(X27606,X27606),esk292_4(X27603,X27604,X27605,X27606)),X27608)),X27603))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27606,tc_HOL_Obool),tc_fun(X27606,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27606,tc_HOL_Obool),tc_fun(X27606,tc_HOL_Obool)),X27605),X27604)),c_Wellfounded_Omax__ext(X27606,X27603)))
        | X27604 = c_Orderings_Obot__class_Obot(tc_fun(X27606,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27606),X27604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27606),X27605)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros])])])])]) ).

fof(i_0_6484,plain,
    ! [X27518,X27519,X27520,X27521,X27522,X27523,X27524,X27526,X27527,X27528,X27529,X27530,X27531,X27532,X27533] :
      ( ( hBOOL(hAPP(hAPP(X27521,X27519),esk287_4(X27518,X27519,X27520,X27521)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27524,X27523,X27522,X27521,X27520),X27519),X27518)) )
      & ( hBOOL(hAPP(hAPP(X27520,esk287_4(X27518,X27519,X27520,X27521)),X27518))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27524,X27523,X27522,X27521,X27520),X27519),X27518)) )
      & ( ~ hBOOL(hAPP(hAPP(X27529,X27527),X27530))
        | ~ hBOOL(hAPP(hAPP(X27528,X27530),X27526))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27533,X27532,X27531,X27529,X27528),X27527),X27526)) ) ),
    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_pred__comp_Oequations])])])])])]) ).

fof(i_0_6485,plain,
    ! [X28824,X28825,X28826] :
      ( ~ c_Wellfounded_Owf(X28826,X28825)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28826,X28826)),hAPP(hAPP(c_Product__Type_OPair(X28826,X28826),hAPP(X28824,hAPP(c_Nat_OSuc,esk338_3(X28824,X28825,X28826)))),hAPP(X28824,esk338_3(X28824,X28825,X28826)))),X28825)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])]) ).

fof(i_0_6486,plain,
    ! [X27575,X27576,X27577,X27579,X27580,X27582] :
      ( ( ~ c_Wellfounded_Owf(X27576,X27575)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27576,X27576)),hAPP(hAPP(c_Product__Type_OPair(X27576,X27576),hAPP(X27577,hAPP(c_Nat_OSuc,esk289_3(X27575,X27576,X27577)))),hAPP(X27577,esk289_3(X27575,X27576,X27577)))),X27575)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27580,X27580)),hAPP(hAPP(c_Product__Type_OPair(X27580,X27580),hAPP(esk290_2(X27579,X27580),hAPP(c_Nat_OSuc,X27582))),hAPP(esk290_2(X27579,X27580),X27582))),X27579))
        | c_Wellfounded_Owf(X27580,X27579) ) ),
    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_wf__iff__no__infinite__down__chain])])])])]) ).

fof(i_0_6487,plain,
    ! [X25897,X25898,X25899,X25900,X25901,X25902,X25903,X25904,X25905] :
      ( ~ c_Equiv__Relations_Oequiv(X25905,X25904,X25903)
      | ~ c_Equiv__Relations_Oequiv(X25902,X25901,X25900)
      | ~ c_Equiv__Relations_Ocongruent2(X25905,X25902,tc_fun(X25899,tc_HOL_Obool),X25903,X25900,X25898)
      | ~ hBOOL(hAPP(hAPP(c_member(X25902),X25897),X25901))
      | c_Equiv__Relations_Ocongruent(X25905,tc_fun(X25899,tc_HOL_Obool),X25903,hAPP(hAPP(c_COMBB(tc_fun(X25902,tc_fun(X25899,tc_HOL_Obool)),tc_fun(X25899,tc_HOL_Obool),X25905),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25902,tc_fun(X25899,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25902,X25902,X25900),hAPP(hAPP(c_Set_Oinsert(X25902),X25897),c_Orderings_Obot__class_Obot(tc_fun(X25902,tc_HOL_Obool)))))),X25898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN])]) ).

cnf(i_0_6488,plain,
    ( c_Nitpick_Oless__eq__frac(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5393]) ).

cnf(i_0_6489,plain,
    ( c_Nitpick_Oless__frac(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5394]) ).

fof(i_0_6490,plain,
    ! [X17511,X17512,X17513,X17514,X17515,X17516,X17517] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17517,X17516,X17515,X17514,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17517,tc_HOL_Obool)),X17513),hAPP(hAPP(c_Set_Oinsert(X17517),X17512),c_Orderings_Obot__class_Obot(tc_fun(X17517,tc_HOL_Obool))))),X17511))
      | ~ hBOOL(hAPP(hAPP(c_member(X17517),X17512),X17513))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17517,X17516,X17515,X17514,X17513),hAPP(hAPP(X17515,X17512),X17511))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).

fof(i_0_6491,plain,
    ! [X22813,X22814,X22815,X22816,X22817] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22816),esk138_5(X22813,X22814,X22815,X22816,X22817)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22816,tc_HOL_Obool)),X22815),X22814)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22817),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22816,X22817),X22813),X22814)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22816,X22817),X22813),X22815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22816,tc_HOL_Obool)),X22814),X22815))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22816),X22815))
        | ~ class_Groups_Ocomm__monoid__add(X22817)
        | ~ class_Groups_Oordered__ab__semigroup__add(X22817) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22817),c_Groups_Ozero__class_Ozero(X22817)),hAPP(X22813,esk138_5(X22813,X22814,X22815,X22816,X22817))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22817),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22816,X22817),X22813),X22814)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22816,X22817),X22813),X22815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22816,tc_HOL_Obool)),X22814),X22815))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22816),X22815))
        | ~ class_Groups_Ocomm__monoid__add(X22817)
        | ~ class_Groups_Oordered__ab__semigroup__add(X22817) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono3])])])]) ).

fof(i_0_6492,plain,
    ! [X22749,X22750,X22751,X22752,X22753] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22752),esk133_5(X22749,X22750,X22751,X22752,X22753)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22752,tc_HOL_Obool)),X22751),X22750)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22753),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22752,X22753),X22749),X22750)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22752,X22753),X22749),X22751)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22752,tc_HOL_Obool)),X22750),X22751))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22752),X22751))
        | ~ class_Groups_Oordered__comm__monoid__add(X22753) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22753),c_Groups_Ozero__class_Ozero(X22753)),hAPP(X22749,esk133_5(X22749,X22750,X22751,X22752,X22753))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22753),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22752,X22753),X22749),X22750)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22752,X22753),X22749),X22751)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22752,tc_HOL_Obool)),X22750),X22751))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22752),X22751))
        | ~ class_Groups_Oordered__comm__monoid__add(X22753) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono2])])])]) ).

fof(i_0_6493,plain,
    ! [X21825,X21826,X21827,X21828] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21828,tc_fun(X21827,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X21828,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21827,tc_HOL_Obool),tc_fun(X21827,tc_HOL_Obool),X21828),hAPP(c_COMBC(X21827,tc_fun(X21827,tc_HOL_Obool),tc_HOL_Obool),c_member(X21827))),X21826)),X21825))
        | hBOOL(hAPP(hAPP(c_member(X21827),X21825),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21828,tc_fun(X21827,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X21828,tc_HOL_Obool))),X21826))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21827),X21825),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21828,tc_fun(X21827,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X21828,tc_HOL_Obool))),X21826)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21828,tc_fun(X21827,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X21828,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21827,tc_HOL_Obool),tc_fun(X21827,tc_HOL_Obool),X21828),hAPP(c_COMBC(X21827,tc_fun(X21827,tc_HOL_Obool),tc_HOL_Obool),c_member(X21827))),X21826)),X21825)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).

fof(i_0_6494,plain,
    ! [X20912,X20913,X20914,X20915] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20915,tc_fun(X20914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20915,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20914,tc_HOL_Obool),tc_fun(X20914,tc_HOL_Obool),X20915),hAPP(c_COMBC(X20914,tc_fun(X20914,tc_HOL_Obool),tc_HOL_Obool),c_member(X20914))),X20913)),X20912))
        | hBOOL(hAPP(hAPP(c_member(X20914),X20912),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20915,tc_fun(X20914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20915,tc_HOL_Obool))),X20913))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20914),X20912),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20915,tc_fun(X20914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20915,tc_HOL_Obool))),X20913)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20915,tc_fun(X20914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20915,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20914,tc_HOL_Obool),tc_fun(X20914,tc_HOL_Obool),X20915),hAPP(c_COMBC(X20914,tc_fun(X20914,tc_HOL_Obool),tc_HOL_Obool),c_member(X20914))),X20913)),X20912)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).

fof(i_0_6495,plain,
    ! [X18521,X18522,X18523,X18524,X18525,X18526] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),X18525),X18524)),X18523)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),X18522),X18524)),X18521)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18526),X18525),X18522)),X18524)),X18523)),X18521))
        | ~ class_Rings_Oordered__ring(X18526) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18526),X18525),X18522)),X18524)),X18523)),X18521))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),X18525),X18524)),X18523)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),X18522),X18524)),X18521)))
        | ~ class_Rings_Oordered__ring(X18526) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).

fof(i_0_6496,plain,
    ! [X18533,X18534,X18535,X18536,X18537,X18538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),X18537),X18536)),X18535)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),X18534),X18536)),X18533)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18538),X18537),X18534)),X18536)),X18535)),X18533))
        | ~ class_Rings_Oordered__ring(X18538) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18538),X18537),X18534)),X18536)),X18535)),X18533))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),X18537),X18536)),X18535)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),X18534),X18536)),X18533)))
        | ~ class_Rings_Oordered__ring(X18538) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).

cnf(i_0_6497,plain,
    ( X2 = X3
    | ~ class_Rings_Olinordered__semidom(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5395]) ).

fof(i_0_6498,plain,
    ! [X17504,X17505,X17506,X17507,X17508,X17509,X17510] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17510),X17509),X17508))
      | ~ c_Nitpick_Ofold__graph_H(X17510,X17507,X17506,X17505,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17510,tc_HOL_Obool)),X17508),hAPP(hAPP(c_Set_Oinsert(X17510),X17509),c_Orderings_Obot__class_Obot(tc_fun(X17510,tc_HOL_Obool)))),X17504)
      | c_Nitpick_Ofold__graph_H(X17510,X17507,X17506,X17505,X17508,hAPP(hAPP(X17506,X17509),X17504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).

fof(i_0_6499,plain,
    ! [X33876,X33877,X33878,X33879,X33880] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33880),esk549_5(X33876,X33877,X33878,X33879,X33880)),X33879))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33878,tc_HOL_Obool)),X33877),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33880,tc_fun(X33878,tc_HOL_Obool)),X33879),X33876))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33878,tc_HOL_Obool)),X33877),hAPP(X33876,esk549_5(X33876,X33877,X33878,X33879,X33880))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33878,tc_HOL_Obool)),X33877),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33880,tc_fun(X33878,tc_HOL_Obool)),X33879),X33876))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__greatest])])])]) ).

fof(i_0_6500,plain,
    ! [X21637,X21638,X21639,X21640,X21641,X21642,X21643,X21644,X21645,X21646,X21647] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21641,tc_HOL_Obool)),X21640),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21639,tc_fun(X21641,tc_HOL_Obool)),X21638),X21637)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21639),X21642),X21638))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21641,tc_HOL_Obool)),X21640),hAPP(X21637,X21642))) )
      & ( hBOOL(hAPP(hAPP(c_member(X21645),esk107_5(X21643,X21644,X21645,X21646,X21647)),X21644))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21647,tc_HOL_Obool)),X21646),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21645,tc_fun(X21647,tc_HOL_Obool)),X21644),X21643))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21647,tc_HOL_Obool)),X21646),hAPP(X21643,esk107_5(X21643,X21644,X21645,X21646,X21647))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21647,tc_HOL_Obool)),X21646),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21645,tc_fun(X21647,tc_HOL_Obool)),X21644),X21643))) ) ),
    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_INT__subset__iff])])])])])]) ).

fof(i_0_6501,plain,
    ! [X33041,X33042,X33043,X33044,X33045] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33045),esk492_5(X33041,X33042,X33043,X33044,X33045)),X33044))
        | c_Relation_Orefl__on(X33043,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33045,tc_fun(X33043,tc_HOL_Obool)),X33044),X33042),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33045,tc_fun(tc_prod(X33043,X33043),tc_HOL_Obool)),X33044),X33041)) )
      & ( ~ c_Relation_Orefl__on(X33043,hAPP(X33042,esk492_5(X33041,X33042,X33043,X33044,X33045)),hAPP(X33041,esk492_5(X33041,X33042,X33043,X33044,X33045)))
        | c_Relation_Orefl__on(X33043,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33045,tc_fun(X33043,tc_HOL_Obool)),X33044),X33042),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33045,tc_fun(tc_prod(X33043,X33043),tc_HOL_Obool)),X33044),X33041)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__INTER])])])]) ).

fof(i_0_6502,plain,
    ! [X33835,X33836,X33837,X33838,X33839] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33839),esk542_5(X33835,X33836,X33837,X33838,X33839)),X33838))
        | c_Relation_Orefl__on(X33837,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33839,tc_fun(X33837,tc_HOL_Obool)),X33838),X33836),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33839,tc_fun(tc_prod(X33837,X33837),tc_HOL_Obool)),X33838),X33835)) )
      & ( ~ c_Relation_Orefl__on(X33837,hAPP(X33836,esk542_5(X33835,X33836,X33837,X33838,X33839)),hAPP(X33835,esk542_5(X33835,X33836,X33837,X33838,X33839)))
        | c_Relation_Orefl__on(X33837,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33839,tc_fun(X33837,tc_HOL_Obool)),X33838),X33836),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33839,tc_fun(tc_prod(X33837,X33837),tc_HOL_Obool)),X33838),X33835)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__UNION])])])]) ).

fof(i_0_6503,plain,
    ! [X26572,X26573,X26574,X26575] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26575,X26574),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26573),X26572)))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26575),X26574),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X26572),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26573)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26573)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X26572),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26574),X26572))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zminus1__lemma])]) ).

cnf(i_0_6504,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(split_conjunct,[status(thm)],[i_0_5396]) ).

fof(i_0_6505,plain,
    ! [X21615,X21616,X21617,X21618,X21619,X21620,X21621,X21622,X21623,X21624,X21625] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21619),X21618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21617,tc_fun(X21619,tc_HOL_Obool)),X21616),X21615)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21617),X21620),X21616))
        | hBOOL(hAPP(hAPP(c_member(X21619),X21618),hAPP(X21615,X21620))) )
      & ( hBOOL(hAPP(hAPP(c_member(X21623),esk106_5(X21621,X21622,X21623,X21624,X21625)),X21622))
        | hBOOL(hAPP(hAPP(c_member(X21625),X21624),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21623,tc_fun(X21625,tc_HOL_Obool)),X21622),X21621))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21625),X21624),hAPP(X21621,esk106_5(X21621,X21622,X21623,X21624,X21625))))
        | hBOOL(hAPP(hAPP(c_member(X21625),X21624),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21623,tc_fun(X21625,tc_HOL_Obool)),X21622),X21621))) ) ),
    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_INT__iff])])])])])]) ).

fof(i_0_6506,plain,
    ! [X28319,X28320,X28321,X28322,X28323,X28324] : hAPP(c_Set_Ovimage(X28324,tc_prod(X28323,X28322),X28321),hAPP(hAPP(c_Product__Type_OSigma(X28323,X28322),X28320),hAPP(c_COMBK(tc_fun(X28322,tc_HOL_Obool),X28323),X28319))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28324,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28324,X28323,hAPP(c_Fun_Ocomp(tc_prod(X28323,X28322),X28323,X28324,c_Product__Type_Ofst(X28323,X28322)),X28321)),X28320)),hAPP(c_Set_Ovimage(X28324,X28322,hAPP(c_Fun_Ocomp(tc_prod(X28323,X28322),X28322,X28324,c_Product__Type_Osnd(X28323,X28322)),X28321)),X28319)),
    inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).

fof(i_0_6507,plain,
    ! [X33024,X33025] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33025)),X33024) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33025,tc_Lazy__Sequence_Olazy__sequence(X33025)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33025,tc_Lazy__Sequence_Olazy__sequence(X33025),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33025),tc_Nat_Onat),X33025),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33025),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X33025)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33025)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X33025),X33024)),
    inference(variable_rename,[status(thm)],[fact_size__code]) ).

fof(i_0_6508,plain,
    ! [X27110,X27111,X27112,X27113,X27114,X27115,X27116,X27117] :
      ( ( X27115 = X27113
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27117,X27117)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27117),X27115),X27113)),X27111))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X27117,X27116),tc_prod(X27117,X27116))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X27117,X27116),tc_prod(X27117,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27115),X27114)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27113),X27112))),c_Wellfounded_Olex__prod(X27117,X27116,X27111,X27110))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27116,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27116,X27116),X27114),X27112)),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27117,X27117)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27117),X27115),X27113)),X27111))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X27117,X27116),tc_prod(X27117,X27116))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X27117,X27116),tc_prod(X27117,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27115),X27114)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27113),X27112))),c_Wellfounded_Olex__prod(X27117,X27116,X27111,X27110))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27117,X27117)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27117),X27115),X27113)),X27111))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X27117,X27116),tc_prod(X27117,X27116))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X27117,X27116),tc_prod(X27117,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27115),X27114)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27113),X27112))),c_Wellfounded_Olex__prod(X27117,X27116,X27111,X27110))) )
      & ( X27115 != X27113
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27116,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27116,X27116),X27114),X27112)),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X27117,X27116),tc_prod(X27117,X27116))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X27117,X27116),tc_prod(X27117,X27116)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27115),X27114)),hAPP(hAPP(c_Product__Type_OPair(X27117,X27116),X27113),X27112))),c_Wellfounded_Olex__prod(X27117,X27116,X27111,X27110))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_6509,plain,
    ! [X22059,X22060,X22061,X22062,X22063,X22064,X22065,X22066,X22067,X22068,X22069] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22063,tc_fun(X22062,tc_HOL_Obool)),X22061),X22060),X22059))
        | ~ hBOOL(hAPP(hAPP(c_member(X22063),X22064),X22061))
        | hBOOL(hAPP(hAPP(X22060,X22064),X22059)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22069),esk120_5(X22065,X22066,X22067,X22068,X22069)),X22067))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22069,tc_fun(X22068,tc_HOL_Obool)),X22067),X22066),X22065)) )
      & ( ~ hBOOL(hAPP(hAPP(X22066,esk120_5(X22065,X22066,X22067,X22068,X22069)),X22065))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22069,tc_fun(X22068,tc_HOL_Obool)),X22067),X22066),X22065)) ) ),
    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_INF1__iff])])])])])]) ).

fof(i_0_6510,plain,
    ! [X25363,X25364] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X25364)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25363))))),
    inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(i_0_6511,plain,
    ! [X24938,X24939,X24940] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24940))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24938),X24939))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24940)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).

fof(i_0_6512,plain,
    ! [X21781,X21782,X21783,X21784,X21785,X21786] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21783,X21785),X21782),X21781)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21783),X21786),X21782))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(X21781,X21786)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21785) )
      & ( hBOOL(hAPP(hAPP(c_member(X21783),esk113_5(X21781,X21782,X21783,X21784,X21785)),X21782))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21783,X21785),X21782),X21781)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21785) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(X21781,esk113_5(X21781,X21782,X21783,X21784,X21785))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21783,X21785),X21782),X21781)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21785) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__INF__iff])])])])]) ).

fof(i_0_6513,plain,
    ! [X32520,X32521,X32522,X32523,X32524] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32523),esk462_5(X32520,X32521,X32522,X32523,X32524)),hAPP(c_List_Oset(X32523),X32522)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32523,X32524,X32521),X32520),X32522) = hAPP(hAPP(c_List_Olist_OCons(X32523),X32520),X32522)
        | ~ class_Orderings_Olinorder(X32524) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32524),hAPP(X32521,X32520)),hAPP(X32521,esk462_5(X32520,X32521,X32522,X32523,X32524))))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32523,X32524,X32521),X32520),X32522) = hAPP(hAPP(c_List_Olist_OCons(X32523),X32520),X32522)
        | ~ class_Orderings_Olinorder(X32524) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__is__Cons])])])]) ).

fof(i_0_6514,plain,
    ! [X23570,X23571,X23572,X23573,X23574] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23573),esk157_5(X23570,X23571,X23572,X23573,X23574)),X23572))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23573,X23574),X23571),X23572) != c_Groups_Ozero__class_Ozero(X23574)
        | ~ hBOOL(hAPP(hAPP(c_member(X23573),X23570),X23572))
        | hAPP(X23571,X23570) = c_Groups_Ozero__class_Ozero(X23574)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23573),X23572))
        | ~ class_Groups_Oordered__ab__group__add(X23574) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23574),c_Groups_Ozero__class_Ozero(X23574)),hAPP(X23571,esk157_5(X23570,X23571,X23572,X23573,X23574))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23573,X23574),X23571),X23572) != c_Groups_Ozero__class_Ozero(X23574)
        | ~ hBOOL(hAPP(hAPP(c_member(X23573),X23570),X23572))
        | hAPP(X23571,X23570) = c_Groups_Ozero__class_Ozero(X23574)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23573),X23572))
        | ~ class_Groups_Oordered__ab__group__add(X23574) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0])])])]) ).

cnf(i_0_6515,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[i_0_5397]) ).

fof(i_0_6516,plain,
    ! [X33538,X33539,X33540,X33541,X33542] : hAPP(c_Hilbert__Choice_Oinv__into(X33542,X33541,X33540,X33539),X33538) = c_Hilbert__Choice_OEps(X33542,hAPP(hAPP(c_COMBS(X33542,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33542),c_fconj),hAPP(hAPP(c_COMBC(X33542,tc_fun(X33542,tc_HOL_Obool),tc_HOL_Obool),c_member(X33542)),X33540))),hAPP(hAPP(c_COMBC(X33542,X33541,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X33541,tc_fun(X33541,tc_HOL_Obool),X33542),c_fequal),X33539)),X33538))),
    inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).

fof(i_0_6517,plain,
    ! [X17531,X17532,X17533,X17534,X17535] : hAPP(c_Fun_Othe__inv__into(X17535,X17534,X17533,X17532),X17531) = c_HOL_OThe(X17535,hAPP(hAPP(c_COMBS(X17535,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17535),c_fconj),hAPP(hAPP(c_COMBC(X17535,tc_fun(X17535,tc_HOL_Obool),tc_HOL_Obool),c_member(X17535)),X17533))),hAPP(hAPP(c_COMBC(X17535,X17534,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17534,tc_fun(X17534,tc_HOL_Obool),X17535),c_fequal),X17532)),X17531))),
    inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).

cnf(i_0_6518,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5398]) ).

fof(i_0_6519,plain,
    ! [X30559,X30560,X30561,X30562] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30562,X30562)),hAPP(hAPP(c_Product__Type_OPair(X30562,X30562),esk410_4(X30559,X30560,X30561,X30562)),esk411_4(X30559,X30560,X30561,X30562))),X30559))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30562),tc_List_Olist(X30562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30562),tc_List_Olist(X30562)),X30561),X30560)),c_List_Olistrel1(X30562,X30559))) )
      & ( X30561 = hAPP(hAPP(c_List_Oappend(X30562),esk412_4(X30559,X30560,X30561,X30562)),hAPP(hAPP(c_List_Olist_OCons(X30562),esk410_4(X30559,X30560,X30561,X30562)),esk413_4(X30559,X30560,X30561,X30562)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30562),tc_List_Olist(X30562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30562),tc_List_Olist(X30562)),X30561),X30560)),c_List_Olistrel1(X30562,X30559))) )
      & ( X30560 = hAPP(hAPP(c_List_Oappend(X30562),esk412_4(X30559,X30560,X30561,X30562)),hAPP(hAPP(c_List_Olist_OCons(X30562),esk411_4(X30559,X30560,X30561,X30562)),esk413_4(X30559,X30560,X30561,X30562)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30562),tc_List_Olist(X30562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30562),tc_List_Olist(X30562)),X30561),X30560)),c_List_Olistrel1(X30562,X30559))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).

fof(i_0_6520,plain,
    ! [X18114,X18115,X18116,X18117,X18118,X18119,X18120] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18120,X18119,X18118)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18120,X18119,X18118,X18117,X18116),X18115))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18120,X18119,X18118,X18117,X18116),X18114))
      | X18114 = X18115 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).

fof(i_0_6521,plain,
    ! [X31113,X31114,X31115,X31116,X31117] :
      ( ~ class_Groups_Ocomm__monoid__add(X31117)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31117),hAPP(hAPP(c_List_Omap(X31116,X31117),hAPP(hAPP(c_COMBS(X31116,X31117,X31117),hAPP(hAPP(c_COMBB(X31117,tc_fun(X31117,X31117),X31116),c_Groups_Oplus__class_Oplus(X31117)),X31115)),X31114)),X31113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31117),hAPP(c_List_Omonoid__add__class_Olistsum(X31117),hAPP(hAPP(c_List_Omap(X31116,X31117),X31115),X31113))),hAPP(c_List_Omonoid__add__class_Olistsum(X31117),hAPP(hAPP(c_List_Omap(X31116,X31117),X31114),X31113))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).

fof(i_0_6522,plain,
    ! [X31118,X31119,X31120,X31121,X31122] :
      ( ~ class_Groups_Oab__group__add(X31122)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31122),hAPP(hAPP(c_List_Omap(X31121,X31122),hAPP(hAPP(c_COMBS(X31121,X31122,X31122),hAPP(hAPP(c_COMBB(X31122,tc_fun(X31122,X31122),X31121),c_Groups_Ominus__class_Ominus(X31122)),X31120)),X31119)),X31118)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X31122),hAPP(c_List_Omonoid__add__class_Olistsum(X31122),hAPP(hAPP(c_List_Omap(X31121,X31122),X31120),X31118))),hAPP(c_List_Omonoid__add__class_Olistsum(X31122),hAPP(hAPP(c_List_Omap(X31121,X31122),X31119),X31118))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).

fof(i_0_6523,plain,
    ! [X24539,X24540,X24541,X24542] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X24542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24541,tc_fun(tc_fun(X24542,tc_HOL_Obool),tc_HOL_Obool)),X24540),hAPP(hAPP(c_COMBB(tc_fun(X24542,tc_HOL_Obool),tc_fun(tc_fun(X24542,tc_HOL_Obool),tc_HOL_Obool),X24541),c_Set_OPow(X24542)),X24539))),hAPP(c_Set_OPow(X24542),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24541,tc_fun(X24542,tc_HOL_Obool)),X24540),X24539)))),
    inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).

fof(i_0_6524,plain,
    ! [X20210,X20211,X20212,X20213,X20214] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20213),X20212)),X20211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20214),X20212)),X20210)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20213),X20214)),X20212)),X20211)),X20210))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20214),X20213)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20213),X20214)),X20212)),X20211)),X20210))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20213),X20212)),X20211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20214),X20212)),X20210)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20214),X20213)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).

fof(i_0_6525,plain,
    ! [X20215,X20216,X20217,X20218,X20219] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20218),X20217)),X20216)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20219),X20217)),X20215)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20218),X20219)),X20217)),X20216)),X20215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20219),X20218)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20218),X20219)),X20217)),X20216)),X20215))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20218),X20217)),X20216)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20219),X20217)),X20215)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20219),X20218)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).

fof(i_0_6526,plain,
    ! [X31131,X31132,X31133,X31134,X31135] :
      ( ~ class_Rings_Osemiring__0(X31135)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31135),hAPP(hAPP(c_List_Omap(X31134,X31135),hAPP(hAPP(c_COMBC(X31134,X31135,X31135),hAPP(hAPP(c_COMBB(X31135,tc_fun(X31135,X31135),X31134),c_Groups_Otimes__class_Otimes(X31135)),X31133)),X31132)),X31131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31135),hAPP(c_List_Omonoid__add__class_Olistsum(X31135),hAPP(hAPP(c_List_Omap(X31134,X31135),X31133),X31131))),X31132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).

fof(i_0_6527,plain,
    ! [X26381] : c_Int_Oint__ge__less__than2(X26381) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26381)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(i_0_6528,plain,
    ! [X21431,X21432,X21433,X21434,X21435] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21434),esk103_5(X21431,X21432,X21433,X21434,X21435)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21434,tc_HOL_Obool)),X21433),X21432)))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21434,tc_HOL_Obool)),X21433),X21432)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21435),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),X21433)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),X21432))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21434),X21432))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21434),X21433))
        | ~ class_Groups_Ocomm__monoid__mult(X21435) )
      & ( hAPP(X21431,esk103_5(X21431,X21432,X21433,X21434,X21435)) != c_Groups_Oone__class_Oone(X21435)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21434,tc_HOL_Obool)),X21433),X21432)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21435),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),X21433)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21435,X21434,c_Groups_Otimes__class_Otimes(X21435)),X21431),c_Groups_Oone__class_Oone(X21435)),X21432))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21434),X21432))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21434),X21433))
        | ~ class_Groups_Ocomm__monoid__mult(X21435) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one])])])]) ).

fof(i_0_6529,plain,
    ! [X20829,X20830,X20831,X20832] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20832,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X20832,tc_fun(X20832,tc_HOL_Obool),tc_HOL_Obool),c_member(X20832)),X20831)),hAPP(hAPP(c_COMBC(X20832,tc_fun(X20832,tc_HOL_Obool),tc_HOL_Obool),c_member(X20832)),X20830)),X20829))
        | hBOOL(hAPP(hAPP(c_member(X20832),X20829),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20832,tc_HOL_Obool)),X20831),X20830))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20832),X20829),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20832,tc_HOL_Obool)),X20831),X20830)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20832,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X20832,tc_fun(X20832,tc_HOL_Obool),tc_HOL_Obool),c_member(X20832)),X20831)),hAPP(hAPP(c_COMBC(X20832,tc_fun(X20832,tc_HOL_Obool),tc_HOL_Obool),c_member(X20832)),X20830)),X20829)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).

fof(i_0_6530,plain,
    ! [X19659,X19660,X19661,X19662] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19662,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X19662,tc_fun(X19662,tc_HOL_Obool),tc_HOL_Obool),c_member(X19662)),X19661)),hAPP(hAPP(c_COMBC(X19662,tc_fun(X19662,tc_HOL_Obool),tc_HOL_Obool),c_member(X19662)),X19660)),X19659))
        | hBOOL(hAPP(hAPP(c_member(X19662),X19659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19662,tc_HOL_Obool)),X19661),X19660))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19662),X19659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19662,tc_HOL_Obool)),X19661),X19660)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19662,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X19662,tc_fun(X19662,tc_HOL_Obool),tc_HOL_Obool),c_member(X19662)),X19661)),hAPP(hAPP(c_COMBC(X19662,tc_fun(X19662,tc_HOL_Obool),tc_HOL_Obool),c_member(X19662)),X19660)),X19659)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).

fof(i_0_6531,plain,
    ! [X25308,X25309,X25310] : hAPP(hAPP(c_Set_Oinsert(X25310),X25309),hAPP(c_Set_OCollect(X25310),X25308)) = hAPP(c_Set_OCollect(X25310),hAPP(hAPP(c_COMBS(X25310,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25310),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25310),c_fNot),hAPP(hAPP(c_COMBC(X25310,X25310,tc_HOL_Obool),c_fequal),X25309)))),X25308)),
    inference(variable_rename,[status(thm)],[fact_insert__Collect]) ).

cnf(i_0_6532,plain,
    ( c_Nitpick_Oof__frac(X2,X1,X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Onum(X2),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Odenom(X2),X3)))
    | ~ class_Rings_Oinverse(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5399]) ).

fof(i_0_6533,plain,
    ! [X26581,X26582,X26583,X26584,X26585,X26586] :
      ( ~ c_Equiv__Relations_Oequiv(X26586,X26585,X26584)
      | ~ hBOOL(hAPP(hAPP(c_member(X26586),X26583),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26586,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26586,X26586,X26584),hAPP(hAPP(c_Set_Oinsert(X26586),X26582),c_Orderings_Obot__class_Obot(tc_fun(X26586,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26586,X26586,X26584),hAPP(hAPP(c_Set_Oinsert(X26586),X26581),c_Orderings_Obot__class_Obot(tc_fun(X26586,tc_HOL_Obool)))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X26586,X26586)),hAPP(hAPP(c_Product__Type_OPair(X26586,X26586),X26582),X26581)),X26584)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).

fof(i_0_6534,plain,
    ! [X32455,X32456] : c_List_Omeasures(X32456,X32455) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X32456),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X32456,tc_List_Olist(tc_fun(X32456,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32456,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X32456,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X32456),c_List_Omap(tc_fun(X32456,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X32456,tc_Nat_Onat),X32456,tc_Nat_Onat),c_COMBI(tc_fun(X32456,tc_Nat_Onat))))),X32455)),
    inference(variable_rename,[status(thm)],[fact_measures__def]) ).

fof(i_0_6535,plain,
    ! [X26873,X26874,X26875,X26876,X26877,X26878,X26879] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26879,X26878),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26877),X26876)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26875,X26878),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26874),X26873)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26878))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26879),X26875),X26878),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26877),X26874)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26876),X26873)),X26878))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26876),X26873),X26878)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).

fof(i_0_6536,plain,
    ! [X33183,X33184,X33185,X33186] : c_Random__Sequence_Omap(X33186,X33185,X33184,X33183) = c_Random__Sequence_Obind(X33186,X33185,X33183,hAPP(c_Fun_Ocomp(X33185,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33185)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X33186,c_Random__Sequence_Osingle(X33185)),X33184)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(i_0_6537,plain,
    ! [X24004,X24005,X24006,X24007,X24008] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24007),esk164_5(X24004,X24005,X24006,X24007,X24008)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24008),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),X24006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),X24005))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24007),X24005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24007),X24006))
        | ~ class_Fields_Ofield(X24008) )
      & ( hAPP(X24004,esk164_5(X24004,X24005,X24006,X24007,X24008)) = c_Groups_Ozero__class_Ozero(X24008)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24008),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),X24006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),X24005))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24007,X24008),X24004),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24007),X24005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24007),X24006))
        | ~ class_Fields_Ofield(X24008) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un])])])]) ).

fof(i_0_6538,plain,
    ! [X26565,X26566,X26567,X26568,X26569,X26570,X26571] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26571,X26570),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26569),X26568)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26567,X26570),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26566),X26565)))
      | X26570 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26571),X26567),X26570),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26569),X26566)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26568),X26565)),X26570))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26568),X26565),X26570)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).

fof(i_0_6539,plain,
    ! [X27827,X27828,X27829,X27830,X27831,X27832] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27832)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27831,X27832),hAPP(hAPP(c_COMBC(X27831,tc_fun(X27830,tc_HOL_Obool),X27832),hAPP(hAPP(c_COMBB(tc_fun(X27830,X27832),tc_fun(tc_fun(X27830,tc_HOL_Obool),X27832),X27831),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27830,X27832)),X27829)),X27828)),X27827) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27831,X27830),X27832),hAPP(c_Product__Type_Oprod_Oprod__case(X27831,X27830,X27832),X27829)),hAPP(hAPP(c_Product__Type_OSigma(X27831,X27830),X27827),hAPP(c_COMBK(tc_fun(X27830,tc_HOL_Obool),X27831),X27828))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).

fof(i_0_6540,plain,
    ! [X27808,X27809,X27810,X27811,X27812,X27813] :
      ( ~ class_Groups_Ocomm__monoid__add(X27813)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27812,X27813),hAPP(hAPP(c_COMBC(X27812,tc_fun(X27811,tc_HOL_Obool),X27813),hAPP(hAPP(c_COMBB(tc_fun(X27811,X27813),tc_fun(tc_fun(X27811,tc_HOL_Obool),X27813),X27812),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27811,X27813)),X27810)),X27809)),X27808) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27812,X27811),X27813),hAPP(c_Product__Type_Oprod_Oprod__case(X27812,X27811,X27813),X27810)),hAPP(hAPP(c_Product__Type_OSigma(X27812,X27811),X27808),hAPP(c_COMBK(tc_fun(X27811,tc_HOL_Obool),X27812),X27809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).

fof(i_0_6541,plain,
    ! [X29487,X29488,X29489,X29490] :
      ( ( X29488 = hAPP(hAPP(c_Product__Type_OPair(X29490,X29489),esk377_4(X29487,X29488,X29489,X29490)),esk376_4(X29487,X29488,X29489,X29490))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29490,X29489)),X29488),hAPP(c_Relation_Oconverse(X29489,X29490),X29487))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29489,X29490)),hAPP(hAPP(c_Product__Type_OPair(X29489,X29490),esk376_4(X29487,X29488,X29489,X29490)),esk377_4(X29487,X29488,X29489,X29490))),X29487))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29490,X29489)),X29488),hAPP(c_Relation_Oconverse(X29489,X29490),X29487))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5400])])])]) ).

fof(i_0_6542,plain,
    ! [X28147,X28148,X28149,X28150,X28151,X28152,X28153,X28154] :
      ( ~ c_Fun_Oinj__on(X28154,X28153,X28152,X28151)
      | ~ c_Fun_Oinj__on(X28150,X28149,X28148,X28147)
      | c_Fun_Oinj__on(tc_prod(X28154,X28150),tc_prod(X28153,X28149),c_Product__Type_Omap__pair(X28154,X28153,X28150,X28149,X28152,X28148),hAPP(hAPP(c_Product__Type_OSigma(X28154,X28150),X28151),hAPP(c_COMBK(tc_fun(X28150,tc_HOL_Obool),X28154),X28147))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).

fof(i_0_6543,plain,
    ! [X26842,X26843,X26844,X26845,X26846] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26846,X26845),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26844),X26843)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26845))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26842),X26846),X26845),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26842),X26844)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26842),X26843)),X26845))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26842),X26843),X26845)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).

fof(i_0_6544,plain,
    ! [X26591,X26592,X26593,X26594,X26595] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26595,X26594),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26593),X26592)))
      | X26594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26591),X26595),X26594),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26591),X26593)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26591),X26592)),X26594))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26591),X26592),X26594)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).

fof(i_0_6545,plain,
    ! [X32855,X32856,X32857,X32858] : c_Lazy__Sequence_Oproduct(X32858,X32857,X32856,X32855) = hAPP(c_Lazy__Sequence_Obind(X32858,tc_prod(X32858,X32857),X32856),hAPP(hAPP(c_COMBB(tc_fun(X32857,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32858,X32857))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32858,X32857)),X32858),c_Lazy__Sequence_Obind(X32857,tc_prod(X32858,X32857),X32855)),hAPP(hAPP(c_COMBB(tc_fun(X32857,tc_prod(X32858,X32857)),tc_fun(X32857,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32858,X32857))),X32858),hAPP(c_COMBB(tc_prod(X32858,X32857),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32858,X32857)),X32857),c_Lazy__Sequence_Osingle(tc_prod(X32858,X32857)))),c_Product__Type_OPair(X32858,X32857)))),
    inference(variable_rename,[status(thm)],[fact_]) ).

fof(i_0_6546,plain,
    ! [X24119,X24120,X24121,X24122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24121),X24120))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24122),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X24122,X24122),hAPP(hAPP(c_COMBB(X24122,tc_fun(X24122,X24122),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X24122)),X24119)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24122,tc_Nat_Onat),X24119),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24121,X24120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24122),hAPP(X24119,X24121)),hAPP(X24119,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24120),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ class_Groups_Oab__group__add(X24122) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24121),X24120))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24122),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X24122,X24122),hAPP(hAPP(c_COMBB(X24122,tc_fun(X24122,X24122),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X24122)),X24119)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24122,tc_Nat_Onat),X24119),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24121,X24120)) = c_Groups_Ozero__class_Ozero(X24122)
        | ~ class_Groups_Oab__group__add(X24122) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5401])])]) ).

fof(i_0_6547,plain,
    ! [X28007,X28008,X28009,X28010] :
      ( c_Fun_Oinj__on(X28010,tc_prod(X28009,X28010),esk300_4(X28007,X28008,X28009,X28010),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28009,tc_fun(X28010,tc_HOL_Obool)),X28008),X28007))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28009,X28010),tc_HOL_Obool)),hAPP(c_Set_Oimage(X28010,tc_prod(X28009,X28010),esk300_4(X28007,X28008,X28009,X28010)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28009,tc_fun(X28010,tc_HOL_Obool)),X28008),X28007))),hAPP(hAPP(c_Product__Type_OSigma(X28009,X28010),X28008),X28007))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).

fof(i_0_6548,plain,
    ! [X18500,X18501,X18502,X18503,X18504] :
      ( ~ class_Groups_Oab__semigroup__mult(X18504)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18504,X18504,c_Groups_Otimes__class_Otimes(X18504),X18503,X18502),X18501))
      | hBOOL(hAPP(hAPP(c_member(X18504),X18503),X18502))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18504,X18504,c_Groups_Otimes__class_Otimes(X18504),X18500,hAPP(hAPP(c_Set_Oinsert(X18504),X18503),X18502)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18504),X18500),X18501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5402])]) ).

fof(i_0_6549,plain,
    ! [X31873,X31874,X31875,X31876] : hAPP(hAPP(c_List_Omap(tc_prod(X31876,tc_Nat_Onat),X31876),c_Product__Type_Ofst(X31876,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31876,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31876,tc_Nat_Onat)),X31875),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X31876,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X31876,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X31876,tc_Nat_Onat),X31874),X31873))) = hAPP(hAPP(c_List_Omap(tc_prod(X31876,tc_Nat_Onat),X31876),c_Product__Type_Ofst(X31876,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31876,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31876,tc_Nat_Onat)),X31875),c_Product__Type_Osnd(X31876,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X31876,tc_Nat_Onat),X31874),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X31873)))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(i_0_6550,plain,
    ! [X28637,X28638,X28639,X28640,X28641,X28642] : hAPP(c_Fun_Ocomp(tc_prod(X28642,X28641),X28642,tc_prod(X28640,X28639),c_Product__Type_Ofst(X28642,X28641)),c_Product__Type_Omap__pair(X28640,X28642,X28639,X28641,X28638,X28637)) = hAPP(c_Fun_Ocomp(X28640,X28642,tc_prod(X28640,X28639),X28638),c_Product__Type_Ofst(X28640,X28639)),
    inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(i_0_6551,plain,
    ! [X28643,X28644,X28645,X28646,X28647,X28648] : hAPP(c_Fun_Ocomp(tc_prod(X28648,X28647),X28647,tc_prod(X28646,X28645),c_Product__Type_Osnd(X28648,X28647)),c_Product__Type_Omap__pair(X28646,X28648,X28645,X28647,X28644,X28643)) = hAPP(c_Fun_Ocomp(X28645,X28647,tc_prod(X28646,X28645),X28643),c_Product__Type_Osnd(X28646,X28645)),
    inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(i_0_6552,plain,
    ! [X21718,X21719,X21720,X21721,X21722,X21723] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21723,tc_fun(X21722,tc_HOL_Obool)),X21721),hAPP(hAPP(c_COMBC(X21723,tc_fun(X21720,tc_fun(X21722,tc_HOL_Obool)),tc_fun(X21722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21720,tc_HOL_Obool),tc_fun(tc_fun(X21720,tc_fun(X21722,tc_HOL_Obool)),tc_fun(X21722,tc_HOL_Obool)),X21723),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21720,tc_fun(X21722,tc_HOL_Obool))),X21719)),X21718)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21720,tc_fun(X21722,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21723,tc_fun(X21720,tc_HOL_Obool)),X21721),X21719)),X21718),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(i_0_6553,plain,
    ! [X21201,X21202,X21203,X21204,X21205,X21206] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21206,tc_fun(X21205,tc_HOL_Obool)),X21204),hAPP(hAPP(c_COMBC(X21206,tc_fun(X21203,tc_fun(X21205,tc_HOL_Obool)),tc_fun(X21205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21203,tc_HOL_Obool),tc_fun(tc_fun(X21203,tc_fun(X21205,tc_HOL_Obool)),tc_fun(X21205,tc_HOL_Obool)),X21206),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21203,tc_fun(X21205,tc_HOL_Obool))),X21202)),X21201)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21203,tc_fun(X21205,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21206,tc_fun(X21203,tc_HOL_Obool)),X21204),X21202)),X21201),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(i_0_6554,plain,
    ! [X21724,X21725,X21726,X21727,X21728,X21729] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21729,tc_fun(X21728,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21727,tc_fun(X21729,tc_HOL_Obool)),X21726),X21725)),X21724) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21727,tc_fun(X21728,tc_HOL_Obool)),X21726),hAPP(hAPP(c_COMBC(X21727,tc_fun(X21729,tc_fun(X21728,tc_HOL_Obool)),tc_fun(X21728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21729,tc_HOL_Obool),tc_fun(tc_fun(X21729,tc_fun(X21728,tc_HOL_Obool)),tc_fun(X21728,tc_HOL_Obool)),X21727),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21729,tc_fun(X21728,tc_HOL_Obool))),X21725)),X21724)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(i_0_6555,plain,
    ! [X21179,X21180,X21181,X21182,X21183,X21184] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21184,tc_fun(X21183,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21182,tc_fun(X21184,tc_HOL_Obool)),X21181),X21180)),X21179) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21182,tc_fun(X21183,tc_HOL_Obool)),X21181),hAPP(hAPP(c_COMBC(X21182,tc_fun(X21184,tc_fun(X21183,tc_HOL_Obool)),tc_fun(X21183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21184,tc_HOL_Obool),tc_fun(tc_fun(X21184,tc_fun(X21183,tc_HOL_Obool)),tc_fun(X21183,tc_HOL_Obool)),X21182),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21184,tc_fun(X21183,tc_HOL_Obool))),X21180)),X21179)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(i_0_6556,plain,
    ! [X21173,X21174,X21175,X21176,X21177,X21178] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21178,tc_fun(X21177,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21176,tc_fun(X21178,tc_HOL_Obool)),X21175),X21174)),X21173) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21176,tc_fun(X21177,tc_HOL_Obool)),X21175),hAPP(hAPP(c_COMBC(X21176,tc_fun(X21178,tc_fun(X21177,tc_HOL_Obool)),tc_fun(X21177,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21178,tc_HOL_Obool),tc_fun(tc_fun(X21178,tc_fun(X21177,tc_HOL_Obool)),tc_fun(X21177,tc_HOL_Obool)),X21176),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21178,tc_fun(X21177,tc_HOL_Obool))),X21174)),X21173)),
    inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).

fof(i_0_6557,plain,
    ! [X17902,X17903,X17904,X17905,X17906,X17907,X17908] :
      ( hBOOL(hAPP(hAPP(c_member(X17908),X17907),X17906))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17908,X17905,X17904,X17903,X17906),X17902))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17908,X17905,X17904,X17903,hAPP(hAPP(c_Set_Oinsert(X17908),X17907),X17906)),hAPP(hAPP(X17904,X17907),X17902))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5403])]) ).

fof(i_0_6558,plain,
    ! [X33932,X33933,X33934,X33935] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33935,X33935)),hAPP(hAPP(c_Product__Type_OPair(X33935,X33935),esk565_4(X33932,X33933,X33934,X33935)),esk566_4(X33932,X33933,X33934,X33935))),X33934))
        | c_Equiv__Relations_Ocongruent(X33935,X33932,X33934,X33933) )
      & ( hAPP(X33933,esk565_4(X33932,X33933,X33934,X33935)) != hAPP(X33933,esk566_4(X33932,X33933,X33934,X33935))
        | c_Equiv__Relations_Ocongruent(X33935,X33932,X33934,X33933) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentI])])])]) ).

fof(i_0_6559,plain,
    ! [X29533,X29534] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk380_2(X29533,X29534)),hAPP(X29534,esk380_2(X29533,X29534))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X29534)),X29533)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])]) ).

fof(i_0_6560,plain,
    ! [X26431,X26432,X26433,X26434,X26435,X26436,X26437,X26438,X26439,X26440] :
      ( ~ c_Equiv__Relations_Ocongruent2(X26440,X26439,X26438,X26437,X26436,X26435)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26440,X26440)),hAPP(hAPP(c_Product__Type_OPair(X26440,X26440),X26434),X26433)),X26437))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26439,X26439)),hAPP(hAPP(c_Product__Type_OPair(X26439,X26439),X26432),X26431)),X26436))
      | hAPP(hAPP(X26435,X26434),X26432) = hAPP(hAPP(X26435,X26433),X26431) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).

fof(i_0_6561,plain,
    ! [X29468,X29469,X29470,X29471,X29472] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29472),esk371_5(X29468,X29469,X29470,X29471,X29472)),X29471))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29471),hAPP(c_Set_OCollect(X29472),X29469))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29470),hAPP(c_Set_OCollect(X29472),X29468))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),X29471),X29470)) )
      & ( hBOOL(hAPP(X29469,esk371_5(X29468,X29469,X29470,X29471,X29472)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29471),hAPP(c_Set_OCollect(X29472),X29469))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29470),hAPP(c_Set_OCollect(X29472),X29468))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),X29471),X29470)) )
      & ( ~ hBOOL(hAPP(X29468,esk371_5(X29468,X29469,X29470,X29471,X29472)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29471),hAPP(c_Set_OCollect(X29472),X29469))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29472,tc_HOL_Obool)),X29470),hAPP(c_Set_OCollect(X29472),X29468))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),X29471),X29470)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono])])])]) ).

fof(i_0_6562,plain,
    ! [X23268,X23269,X23270] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23270,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23270,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk152_3(X23268,X23269,X23270))),X23269)),X23268))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23270,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23270,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23269)),X23268)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).

fof(i_0_6563,plain,
    ! [X25346,X25347,X25348] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25348,tc_HOL_Obool)),X25347),X25346) = hAPP(c_Set_OCollect(X25348),hAPP(hAPP(c_COMBS(X25348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25348),c_fconj),hAPP(hAPP(c_COMBC(X25348,tc_fun(X25348,tc_HOL_Obool),tc_HOL_Obool),c_member(X25348)),X25347))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25348),c_fNot),hAPP(hAPP(c_COMBC(X25348,tc_fun(X25348,tc_HOL_Obool),tc_HOL_Obool),c_member(X25348)),X25346)))),
    inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).

fof(i_0_6564,plain,
    ! [X25270,X25271,X25272] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25272),hAPP(c_Set_OCollect(X25272),X25271)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25272),hAPP(c_Set_OCollect(X25272),hAPP(hAPP(c_COMBS(X25272,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25272),c_fconj),X25271)),X25270)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25272),hAPP(c_Set_OCollect(X25272),X25270)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25272),hAPP(c_Set_OCollect(X25272),hAPP(hAPP(c_COMBS(X25272,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25272),c_fconj),X25271)),X25270)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).

fof(i_0_6565,plain,
    ! [X23173,X23174] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23174,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X23174,tc_HOL_Obool)),tc_fun(X23174,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X23174,tc_HOL_Obool)),tc_fun(X23174,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23174,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X23173)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X23174,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X23173),
    inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq]) ).

cnf(i_0_6566,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk362_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5404]) ).

cnf(i_0_6567,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk361_4(X2,X3,X4,X1)),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5405]) ).

fof(i_0_6568,plain,
    ! [X28090,X28091,X28092,X28093,X28094,X28095,X28096,X28097] : hAPP(c_Product__Type_Omap__pair(X28097,X28096,X28095,X28094,X28093,X28092),hAPP(hAPP(c_Product__Type_OPair(X28097,X28095),X28091),X28090)) = hAPP(hAPP(c_Product__Type_OPair(X28096,X28094),hAPP(X28093,X28091)),hAPP(X28092,X28090)),
    inference(variable_rename,[status(thm)],[fact_map__pair__simp]) ).

cnf(i_0_6569,plain,
    hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_5406]) ).

cnf(i_0_6570,plain,
    hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),X5),hAPP(X4,X6)),
    inference(split_conjunct,[status(thm)],[i_0_5407]) ).

fof(i_0_6571,plain,
    ! [X31583,X31584,X31585,X31586,X31587] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31587,X31586)),esk425_5(X31583,X31584,X31585,X31586,X31587)),hAPP(c_List_Oset(tc_prod(X31587,X31586)),hAPP(hAPP(c_List_Ozip(X31587,X31586),X31585),X31584))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31587)),X31585) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31586)),X31584)
        | c_List_Olist__all2(X31587,X31586,X31583,X31585,X31584) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31587,X31586,tc_HOL_Obool),X31583),esk425_5(X31583,X31584,X31585,X31586,X31587)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31587)),X31585) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31586)),X31584)
        | c_List_Olist__all2(X31587,X31586,X31583,X31585,X31584) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2I])])])]) ).

fof(i_0_6572,plain,
    ! [X31428,X31429,X31430,X31431,X31432,X31433,X31434,X31435,X31436,X31437,X31438] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31432)),X31429) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31431)),X31428)
        | ~ c_List_Olist__all2(X31432,X31431,X31430,X31429,X31428) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31432,X31431)),X31433),hAPP(c_List_Oset(tc_prod(X31432,X31431)),hAPP(hAPP(c_List_Ozip(X31432,X31431),X31429),X31428))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31432,X31431,tc_HOL_Obool),X31430),X31433))
        | ~ c_List_Olist__all2(X31432,X31431,X31430,X31429,X31428) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31438,X31437)),esk423_5(X31434,X31435,X31436,X31437,X31438)),hAPP(c_List_Oset(tc_prod(X31438,X31437)),hAPP(hAPP(c_List_Ozip(X31438,X31437),X31435),X31434))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31438)),X31435) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31437)),X31434)
        | c_List_Olist__all2(X31438,X31437,X31436,X31435,X31434) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31438,X31437,tc_HOL_Obool),X31436),esk423_5(X31434,X31435,X31436,X31437,X31438)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31438)),X31435) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31437)),X31434)
        | c_List_Olist__all2(X31438,X31437,X31436,X31435,X31434) ) ),
    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_list__all2__def])])])])])]) ).

fof(i_0_6573,plain,
    ! [X28098,X28099,X28100] : hAPP(c_Product__Type_Omap__pair(X28100,X28100,X28099,X28099,c_COMBI(X28100),c_COMBI(X28099)),X28098) = X28098,
    inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).

fof(i_0_6574,plain,
    ! [X20984,X20985,X20986,X20987,X20988,X20989,X20990,X20991] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20991,X20990,X20989,X20988,X20987,X20986)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20990),X20985))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20990),X20984))
      | hAPP(hAPP(X20989,hAPP(X20986,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20990,tc_HOL_Obool)),X20985),X20984))),hAPP(X20986,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20990,tc_HOL_Obool)),X20985),X20984))) = hAPP(hAPP(X20989,hAPP(X20986,X20985)),hAPP(X20986,X20984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).

fof(i_0_6575,plain,
    ! [X21443,X21444,X21445,X21446,X21447] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21446),esk105_5(X21443,X21444,X21445,X21446,X21447)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21446,tc_HOL_Obool)),X21445),X21444)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21446,tc_HOL_Obool)),X21445),X21444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21447),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),X21445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),X21444))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21446),X21444))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21446),X21445))
        | ~ class_Groups_Ocomm__monoid__mult(X21447) )
      & ( hAPP(X21443,esk105_5(X21443,X21444,X21445,X21446,X21447)) != c_Groups_Oone__class_Oone(X21447)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21446,tc_HOL_Obool)),X21445),X21444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21447),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),X21445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21446,X21447),X21443),X21444))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21446),X21444))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21446),X21445))
        | ~ class_Groups_Ocomm__monoid__mult(X21447) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral])])])]) ).

fof(i_0_6576,plain,
    ! [X21437,X21438,X21439,X21440,X21441] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21440),esk104_5(X21437,X21438,X21439,X21440,X21441)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21440,tc_HOL_Obool)),X21439),X21438)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21440,tc_HOL_Obool)),X21439),X21438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),X21439)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),X21438))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21440),X21438))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21440),X21439))
        | ~ class_Groups_Ocomm__monoid__mult(X21441) )
      & ( hAPP(X21437,esk104_5(X21437,X21438,X21439,X21440,X21441)) != c_Groups_Oone__class_Oone(X21441)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21440,tc_HOL_Obool)),X21439),X21438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),X21439)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21440,X21441),X21437),X21438))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21440),X21438))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21440),X21439))
        | ~ class_Groups_Ocomm__monoid__mult(X21441) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__one])])])]) ).

fof(i_0_6577,plain,
    ! [X22797,X22798,X22799,X22800,X22801] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22800),esk135_5(X22797,X22798,X22799,X22800,X22801)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22800,tc_HOL_Obool)),X22799),X22798)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22800,tc_HOL_Obool)),X22799),X22798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22801),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),X22799)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),X22798))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22800),X22798))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22800),X22799))
        | ~ class_Groups_Ocomm__monoid__add(X22801) )
      & ( hAPP(X22797,esk135_5(X22797,X22798,X22799,X22800,X22801)) != c_Groups_Ozero__class_Ozero(X22801)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22800,tc_HOL_Obool)),X22799),X22798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22801),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),X22799)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22800,X22801),X22797),X22798))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22800),X22798))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22800),X22799))
        | ~ class_Groups_Ocomm__monoid__add(X22801) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral])])])]) ).

fof(i_0_6578,plain,
    ! [X22791,X22792,X22793,X22794,X22795] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22794),esk134_5(X22791,X22792,X22793,X22794,X22795)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22794,tc_HOL_Obool)),X22793),X22792)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22794,tc_HOL_Obool)),X22793),X22792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22795),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),X22793)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),X22792))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22794),X22792))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22794),X22793))
        | ~ class_Groups_Ocomm__monoid__add(X22795) )
      & ( hAPP(X22791,esk134_5(X22791,X22792,X22793,X22794,X22795)) != c_Groups_Ozero__class_Ozero(X22795)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22794,tc_HOL_Obool)),X22793),X22792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22795),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),X22793)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22794,X22795),X22791),X22792))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22794),X22792))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22794),X22793))
        | ~ class_Groups_Ocomm__monoid__add(X22795) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero])])])]) ).

fof(i_0_6579,plain,
    ! [X26536,X26537,X26538,X26539] : hAPP(c_Relation_OImage(X26539,X26538,X26537),hAPP(hAPP(c_Set_Oinsert(X26539),X26536),c_Orderings_Obot__class_Obot(tc_fun(X26539,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X26538),hAPP(hAPP(c_COMBC(X26538,tc_fun(tc_prod(X26539,X26538),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X26539,X26538),tc_fun(tc_fun(tc_prod(X26539,X26538),tc_HOL_Obool),tc_HOL_Obool),X26538),c_member(tc_prod(X26539,X26538))),hAPP(c_Product__Type_OPair(X26539,X26538),X26536))),X26537)),
    inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).

fof(i_0_6580,plain,
    ! [X32699,X32700,X32701,X32702] :
      ( ( ~ hBOOL(hAPP(X32701,X32700))
        | c_List_Olist__all(X32702,hAPP(hAPP(c_COMBS(X32702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32702),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32702),c_fNot),X32701))),hAPP(c_fequal,X32700)),X32699)
        | ~ c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) )
      & ( hBOOL(hAPP(X32701,X32700))
        | c_List_Olist__ex1(X32702,X32701,X32699)
        | ~ c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) )
      & ( ~ hBOOL(hAPP(X32701,X32700))
        | hBOOL(hAPP(X32701,X32700))
        | c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) )
      & ( ~ c_List_Olist__ex1(X32702,X32701,X32699)
        | hBOOL(hAPP(X32701,X32700))
        | c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) )
      & ( ~ hBOOL(hAPP(X32701,X32700))
        | ~ c_List_Olist__all(X32702,hAPP(hAPP(c_COMBS(X32702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32702),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32702),c_fNot),X32701))),hAPP(c_fequal,X32700)),X32699)
        | c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) )
      & ( ~ c_List_Olist__ex1(X32702,X32701,X32699)
        | ~ c_List_Olist__all(X32702,hAPP(hAPP(c_COMBS(X32702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32702),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32702),c_fNot),X32701))),hAPP(c_fequal,X32700)),X32699)
        | c_List_Olist__ex1(X32702,X32701,hAPP(hAPP(c_List_Olist_OCons(X32702),X32700),X32699)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5408])])]) ).

cnf(i_0_6581,plain,
    c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5409]) ).

fof(i_0_6582,plain,
    ! [X17374,X17375,X17376,X17377,X17378,X17379,X17380,X17381] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17381,X17380,X17379,X17378,X17377,X17376)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17380),X17375))
      | ~ hBOOL(hAPP(hAPP(c_member(X17380),X17374),X17375))
      | hAPP(X17376,X17375) = hAPP(hAPP(X17379,hAPP(X17377,X17374)),hAPP(X17376,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17380,tc_HOL_Obool)),X17375),hAPP(hAPP(c_Set_Oinsert(X17380),X17374),c_Orderings_Obot__class_Obot(tc_fun(X17380,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).

fof(i_0_6583,plain,
    ! [X17820,X17821,X17822,X17823,X17824,X17826,X17827,X17828,X17829,X17830,X17831] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17822,tc_HOL_Obool)),esk22_5(X17820,X17821,X17822,X17823,X17824)),X17820))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17824,tc_HOL_Obool)),X17823),hAPP(c_Set_Oimage(X17822,X17824,X17821),X17820))) )
      & ( X17823 = hAPP(c_Set_Oimage(X17822,X17824,X17821),esk22_5(X17820,X17821,X17822,X17823,X17824))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17824,tc_HOL_Obool)),X17823),hAPP(c_Set_Oimage(X17822,X17824,X17821),X17820))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17828,tc_HOL_Obool)),X17831),X17826))
        | X17829 != hAPP(c_Set_Oimage(X17828,X17830,X17827),X17831)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17830,tc_HOL_Obool)),X17829),hAPP(c_Set_Oimage(X17828,X17830,X17827),X17826))) ) ),
    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_subset__image__iff])])])])])]) ).

cnf(i_0_6584,plain,
    ( hAPP(hAPP(c_List_Onth(X2),c_List_OdropWhile(X2,X3,X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OdropWhile(X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5410]) ).

fof(i_0_6585,plain,
    ! [X21235,X21236,X21237,X21238,X21239,X21241,X21242,X21243,X21244,X21245,X21246] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21237),esk97_5(X21235,X21236,X21237,X21238,X21239)),X21236))
        | ~ hBOOL(hAPP(hAPP(c_member(X21239),X21238),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21237,tc_fun(X21239,tc_HOL_Obool)),X21236),X21235))) )
      & ( hBOOL(hAPP(hAPP(c_member(X21239),X21238),hAPP(X21235,esk97_5(X21235,X21236,X21237,X21238,X21239))))
        | ~ hBOOL(hAPP(hAPP(c_member(X21239),X21238),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21237,tc_fun(X21239,tc_HOL_Obool)),X21236),X21235))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21243),X21246),X21242))
        | ~ hBOOL(hAPP(hAPP(c_member(X21245),X21244),hAPP(X21241,X21246)))
        | hBOOL(hAPP(hAPP(c_member(X21245),X21244),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21243,tc_fun(X21245,tc_HOL_Obool)),X21242),X21241))) ) ),
    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_UN__iff])])])])])]) ).

fof(i_0_6586,plain,
    ! [X17337,X17338,X17339,X17340,X17341,X17342,X17343,X17344] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17344,X17343,X17342,X17341,X17340,X17339)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17343),X17338))
      | hAPP(X17339,hAPP(hAPP(c_Set_Oinsert(X17343),X17337),X17338)) = hAPP(hAPP(X17342,hAPP(X17340,X17337)),hAPP(X17339,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17343,tc_HOL_Obool)),X17338),hAPP(hAPP(c_Set_Oinsert(X17343),X17337),c_Orderings_Obot__class_Obot(tc_fun(X17343,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).

fof(i_0_6587,plain,
    ! [X33572,X33573,X33574,X33575,X33576,X33577,X33578] :
      ( ~ c_Fun_Oinj__on(X33578,X33577,X33576,hAPP(c_Set_Oimage(X33575,X33578,X33574),X33573))
      | ~ c_Fun_Oinj__on(X33575,X33578,X33574,X33573)
      | ~ hBOOL(hAPP(hAPP(c_member(X33577),X33572),hAPP(c_Set_Oimage(X33578,X33577,X33576),hAPP(c_Set_Oimage(X33575,X33578,X33574),X33573))))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33575,X33577,X33573,hAPP(c_Fun_Ocomp(X33578,X33577,X33575,X33576),X33574)),X33572) = hAPP(hAPP(c_Fun_Ocomp(X33578,X33575,X33577,c_Hilbert__Choice_Oinv__into(X33575,X33578,X33573,X33574)),c_Hilbert__Choice_Oinv__into(X33578,X33577,hAPP(c_Set_Oimage(X33575,X33578,X33574),X33573),X33576)),X33572) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__comp])]) ).

fof(i_0_6588,plain,
    ! [X28572,X28573,X28574,X28575,X28576,X28577,X28578] :
      ( ~ c_Fun_Oinj__on(X28578,X28577,X28576,hAPP(c_Set_Oimage(X28575,X28578,X28574),X28573))
      | ~ c_Fun_Oinj__on(X28575,X28578,X28574,X28573)
      | ~ hBOOL(hAPP(hAPP(c_member(X28577),X28572),hAPP(c_Set_Oimage(X28578,X28577,X28576),hAPP(c_Set_Oimage(X28575,X28578,X28574),X28573))))
      | hAPP(c_Fun_Othe__inv__into(X28575,X28577,X28573,hAPP(c_Fun_Ocomp(X28578,X28577,X28575,X28576),X28574)),X28572) = hAPP(hAPP(c_Fun_Ocomp(X28578,X28575,X28577,c_Fun_Othe__inv__into(X28575,X28578,X28573,X28574)),c_Fun_Othe__inv__into(X28578,X28577,hAPP(c_Set_Oimage(X28575,X28578,X28574),X28573),X28576)),X28572) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp])]) ).

cnf(i_0_6589,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_5411]) ).

fof(i_0_6590,plain,
    ! [X20446,X20447,X20448,X20449,X20450] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20449),esk87_5(X20446,X20447,X20448,X20449,X20450)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20449,tc_HOL_Obool)),X20448),X20447)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20449,X20450),X20446),X20447) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20449,X20450),X20446),X20448)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20449,tc_HOL_Obool)),X20447),X20448))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20449),X20448))
        | ~ class_Groups_Ocomm__monoid__mult(X20450) )
      & ( hAPP(X20446,esk87_5(X20446,X20447,X20448,X20449,X20450)) != c_Groups_Oone__class_Oone(X20450)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20449,X20450),X20446),X20447) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20449,X20450),X20446),X20448)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20449,tc_HOL_Obool)),X20447),X20448))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20449),X20448))
        | ~ class_Groups_Ocomm__monoid__mult(X20450) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left])])])]) ).

fof(i_0_6591,plain,
    ! [X20440,X20441,X20442,X20443,X20444] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20443),esk86_5(X20440,X20441,X20442,X20443,X20444)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20443,tc_HOL_Obool)),X20442),X20441)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20443,X20444),X20440),X20442) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20443,X20444),X20440),X20441)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20443,tc_HOL_Obool)),X20441),X20442))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20443),X20442))
        | ~ class_Groups_Ocomm__monoid__mult(X20444) )
      & ( hAPP(X20440,esk86_5(X20440,X20441,X20442,X20443,X20444)) != c_Groups_Oone__class_Oone(X20444)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20443,X20444),X20440),X20442) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20443,X20444),X20440),X20441)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20443,tc_HOL_Obool)),X20441),X20442))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20443),X20442))
        | ~ class_Groups_Ocomm__monoid__mult(X20444) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right])])])]) ).

fof(i_0_6592,plain,
    ! [X24484,X24485,X24486,X24487,X24488] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24487),esk207_5(X24484,X24485,X24486,X24487,X24488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24487,tc_HOL_Obool)),X24486),X24485)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24487,X24488),X24484),X24485) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24487,X24488),X24484),X24486)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24487,tc_HOL_Obool)),X24485),X24486))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24487),X24486))
        | ~ class_Groups_Ocomm__monoid__add(X24488) )
      & ( hAPP(X24484,esk207_5(X24484,X24485,X24486,X24487,X24488)) != c_Groups_Ozero__class_Ozero(X24488)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24487,X24488),X24484),X24485) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24487,X24488),X24484),X24486)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24487,tc_HOL_Obool)),X24485),X24486))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24487),X24486))
        | ~ class_Groups_Ocomm__monoid__add(X24488) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left])])])]) ).

fof(i_0_6593,plain,
    ! [X24478,X24479,X24480,X24481,X24482] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24481),esk206_5(X24478,X24479,X24480,X24481,X24482)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24481,tc_HOL_Obool)),X24480),X24479)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24481,X24482),X24478),X24480) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24481,X24482),X24478),X24479)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24481,tc_HOL_Obool)),X24479),X24480))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24481),X24480))
        | ~ class_Groups_Ocomm__monoid__add(X24482) )
      & ( hAPP(X24478,esk206_5(X24478,X24479,X24480,X24481,X24482)) != c_Groups_Ozero__class_Ozero(X24482)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24481,X24482),X24478),X24480) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24481,X24482),X24478),X24479)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24481,tc_HOL_Obool)),X24479),X24480))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24481),X24480))
        | ~ class_Groups_Ocomm__monoid__add(X24482) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right])])])]) ).

cnf(i_0_6594,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5394]) ).

cnf(i_0_6595,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5393]) ).

fof(i_0_6596,plain,
    ! [X21207,X21208,X21209,X21210,X21211,X21213,X21214,X21215,X21216,X21217,X21218] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21211),esk95_5(X21207,X21208,X21209,X21210,X21211)),X21209))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21211,tc_fun(X21210,tc_HOL_Obool)),X21209),X21208),X21207)) )
      & ( hBOOL(hAPP(hAPP(X21208,esk95_5(X21207,X21208,X21209,X21210,X21211)),X21207))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21211,tc_fun(X21210,tc_HOL_Obool)),X21209),X21208),X21207)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21217),X21218),X21215))
        | ~ hBOOL(hAPP(hAPP(X21214,X21218),X21213))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21217,tc_fun(X21216,tc_HOL_Obool)),X21215),X21214),X21213)) ) ),
    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_SUP1__iff])])])])])]) ).

fof(i_0_6597,plain,
    ! [X32558,X32559,X32560,X32561] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32560,X32561)),X32559),X32558))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32560),hAPP(hAPP(c_COMBS(X32560,X32561,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32561,tc_fun(X32561,tc_HOL_Obool),X32560),c_Orderings_Oord__class_Oless__eq(X32561)),X32559)),X32558)))
        | ~ class_Orderings_Oorder(X32561)
        | ~ class_Enum_Oenum(X32560) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32560),hAPP(hAPP(c_COMBS(X32560,X32561,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32561,tc_fun(X32561,tc_HOL_Obool),X32560),c_Orderings_Oord__class_Oless__eq(X32561)),X32559)),X32558)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32560,X32561)),X32559),X32558))
        | ~ class_Orderings_Oorder(X32561)
        | ~ class_Enum_Oenum(X32560) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])]) ).

fof(i_0_6598,plain,
    ! [X29281,X29282,X29283] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29283,X29283)),X29282),c_Transitive__Closure_Ortrancl(X29283,X29281)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29283,X29283)),X29282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X29283,X29283),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X29283,X29283),tc_HOL_Obool),tc_fun(tc_prod(X29283,X29283),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X29283,X29283),tc_HOL_Obool)),X29281)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).

fof(i_0_6599,plain,
    ! [X21520,X21521,X21522,X21523,X21524] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21524,tc_fun(X21523,tc_HOL_Obool)),X21522),hAPP(hAPP(c_COMBS(X21524,tc_fun(X21523,tc_HOL_Obool),tc_fun(X21523,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21523,tc_HOL_Obool),tc_fun(tc_fun(X21523,tc_HOL_Obool),tc_fun(X21523,tc_HOL_Obool)),X21524),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21523,tc_HOL_Obool))),X21521)),X21520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21523,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21523,tc_HOL_Obool),hAPP(c_Set_Oimage(X21524,tc_fun(X21523,tc_HOL_Obool),X21521),X21522))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21523,tc_HOL_Obool),hAPP(c_Set_Oimage(X21524,tc_fun(X21523,tc_HOL_Obool),X21520),X21522))),
    inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).

fof(i_0_6600,plain,
    ! [X25180,X25181,X25182,X25183,X25184] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25184,tc_fun(X25183,tc_HOL_Obool)),X25182),hAPP(hAPP(c_COMBS(X25184,tc_fun(X25183,tc_HOL_Obool),tc_fun(X25183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25183,tc_HOL_Obool),tc_fun(tc_fun(X25183,tc_HOL_Obool),tc_fun(X25183,tc_HOL_Obool)),X25184),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25183,tc_HOL_Obool))),X25181)),X25180)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25183,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25183,tc_HOL_Obool),hAPP(c_Set_Oimage(X25184,tc_fun(X25183,tc_HOL_Obool),X25181),X25182))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25183,tc_HOL_Obool),hAPP(c_Set_Oimage(X25184,tc_fun(X25183,tc_HOL_Obool),X25180),X25182))),
    inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).

fof(i_0_6601,plain,
    ! [X30543,X30544,X30545,X30546,X30547,X30548,X30549] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),X30546))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30549),tc_List_Olist(X30549))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30549),tc_List_Olist(X30549)),hAPP(hAPP(c_List_Oappend(X30549),X30545),hAPP(hAPP(c_List_Olist_OCons(X30549),X30548),X30544))),hAPP(hAPP(c_List_Oappend(X30549),X30545),hAPP(hAPP(c_List_Olist_OCons(X30549),X30547),X30543)))),c_List_Olexord(X30549,X30546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).

fof(i_0_6602,plain,
    ! [X27289,X27290,X27291,X27292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27292),X27291)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27290),X27289))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27292),X27289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27290),X27291) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27292),X27289) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27290),X27291)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27292),X27291)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27290),X27289))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).

fof(i_0_6603,plain,
    ! [X27119,X27120,X27121,X27122,X27123,X27124,X27125] :
      ( ~ hBOOL(hAPP(X27125,X27124))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27123,X27123)),hAPP(hAPP(c_Product__Type_OPair(X27123,X27123),X27122),X27121)),hAPP(X27120,X27124)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X27119,X27123),tc_prod(X27119,X27123))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X27119,X27123),tc_prod(X27119,X27123)),hAPP(hAPP(c_Product__Type_OPair(X27119,X27123),X27124),X27122)),hAPP(hAPP(c_Product__Type_OPair(X27119,X27123),X27124),X27121))),c_Recdef_Osame__fst(X27119,X27123,X27125,X27120))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_6604,plain,
    ! [X21409,X21410,X21411,X21412,X21413,X21415] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21411),esk102_5(X21409,X21410,X21411,X21412,X21413)),X21410))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21413),X21412),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21411,X21413),X21410),X21409)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21413)
        | ~ class_Orderings_Olinorder(X21413) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21413),X21412),hAPP(X21409,esk102_5(X21409,X21410,X21411,X21412,X21413))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21413),X21412),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21411,X21413),X21410),X21409)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21413)
        | ~ class_Orderings_Olinorder(X21413) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21411),X21415),X21410))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21413),X21412),hAPP(X21409,X21415)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21413),X21412),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21411,X21413),X21410),X21409)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21413)
        | ~ class_Orderings_Olinorder(X21413) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SUP__iff])])])])]) ).

fof(i_0_6605,plain,
    ! [X26729,X26730,X26731,X26732,X26733,X26734,X26735,X26736] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26736,X26735,X26734),X26733),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26732,X26731,tc_prod(X26736,X26735)),X26730),X26729)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26732,X26731,X26734),hAPP(hAPP(c_COMBB(tc_fun(X26731,tc_prod(X26736,X26735)),tc_fun(X26731,X26734),X26732),hAPP(c_COMBB(tc_prod(X26736,X26735),X26734,X26731),hAPP(c_Product__Type_Oprod_Oprod__case(X26736,X26735,X26734),X26733))),X26730)),X26729),
    inference(variable_rename,[status(thm)],[fact_split__twice]) ).

cnf(i_0_6606,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5412]) ).

cnf(i_0_6607,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5413]) ).

cnf(i_0_6608,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[i_0_5414]) ).

fof(i_0_6609,plain,
    ! [X18028,X18029,X18030,X18031] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),esk28_4(X18028,X18029,X18030,X18031)))
        | hBOOL(hAPP(X18028,X18030))
        | ~ hBOOL(hAPP(X18028,c_Orderings_Obot__class_Obot(tc_fun(X18031,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18031,tc_HOL_Obool)),X18030),X18029))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),X18030)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18031),esk27_4(X18028,X18029,X18030,X18031)),X18029))
        | hBOOL(hAPP(X18028,X18030))
        | ~ hBOOL(hAPP(X18028,c_Orderings_Obot__class_Obot(tc_fun(X18031,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18031,tc_HOL_Obool)),X18030),X18029))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),X18030)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18031),esk27_4(X18028,X18029,X18030,X18031)),esk28_4(X18028,X18029,X18030,X18031)))
        | hBOOL(hAPP(X18028,X18030))
        | ~ hBOOL(hAPP(X18028,c_Orderings_Obot__class_Obot(tc_fun(X18031,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18031,tc_HOL_Obool)),X18030),X18029))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),X18030)) )
      & ( hBOOL(hAPP(X18028,esk28_4(X18028,X18029,X18030,X18031)))
        | hBOOL(hAPP(X18028,X18030))
        | ~ hBOOL(hAPP(X18028,c_Orderings_Obot__class_Obot(tc_fun(X18031,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18031,tc_HOL_Obool)),X18030),X18029))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),X18030)) )
      & ( ~ hBOOL(hAPP(X18028,hAPP(hAPP(c_Set_Oinsert(X18031),esk27_4(X18028,X18029,X18030,X18031)),esk28_4(X18028,X18029,X18030,X18031))))
        | hBOOL(hAPP(X18028,X18030))
        | ~ hBOOL(hAPP(X18028,c_Orderings_Obot__class_Obot(tc_fun(X18031,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18031,tc_HOL_Obool)),X18030),X18029))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18031),X18030)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5415])])])]) ).

fof(i_0_6610,plain,
    ! [X30001,X30002,X30003,X30004] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30004),esk398_4(X30001,X30002,X30003,X30004)),hAPP(c_List_Oset(X30004),X30003)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X30004,X30002,X30003)),c_List_Olist_Olist__size(X30004,X30001,X30003))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X30002,esk398_4(X30001,X30002,X30003,X30004))),hAPP(X30001,esk398_4(X30001,X30002,X30003,X30004))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X30004,X30002,X30003)),c_List_Olist_Olist__size(X30004,X30001,X30003))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__pointwise])])])]) ).

fof(i_0_6611,plain,
    ! [X26382,X26383] : c_Fun_Oinj__on(tc_fun(X26383,X26382),tc_fun(tc_prod(X26383,X26382),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26383,X26382),tc_HOL_Obool),tc_fun(tc_prod(X26383,X26382),tc_HOL_Obool),tc_fun(X26383,X26382)),c_Set_OCollect(tc_prod(X26383,X26382))),hAPP(hAPP(c_COMBB(tc_fun(X26383,tc_fun(X26382,tc_HOL_Obool)),tc_fun(tc_prod(X26383,X26382),tc_HOL_Obool),tc_fun(X26383,X26382)),c_Product__Type_Oprod_Oprod__case(X26383,X26382,tc_HOL_Obool)),hAPP(c_COMBB(X26382,tc_fun(X26382,tc_HOL_Obool),X26383),hAPP(c_COMBC(X26382,X26382,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26383,X26382),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__graph]) ).

cnf(i_0_6612,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3]) ).

cnf(i_0_6613,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5416]) ).

cnf(i_0_6614,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).

fof(i_0_6615,plain,
    ! [X32372,X32373,X32374,X32375,X32376] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32375),esk443_5(X32372,X32373,X32374,X32375,X32376)),hAPP(c_List_Oset(X32375),X32374)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),hAPP(c_List_Ofilter(X32375,X32373),X32374))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),X32374))
        | ~ class_Groups_Omonoid__add(X32376) )
      & ( ~ hBOOL(hAPP(X32373,esk443_5(X32372,X32373,X32374,X32375,X32376)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),hAPP(c_List_Ofilter(X32375,X32373),X32374))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),X32374))
        | ~ class_Groups_Omonoid__add(X32376) )
      & ( hAPP(X32372,esk443_5(X32372,X32373,X32374,X32375,X32376)) != c_Groups_Ozero__class_Ozero(X32376)
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),hAPP(c_List_Ofilter(X32375,X32373),X32374))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32376),hAPP(hAPP(c_List_Omap(X32375,X32376),X32372),X32374))
        | ~ class_Groups_Omonoid__add(X32376) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5417])])])]) ).

cnf(i_0_6616,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5418]) ).

cnf(i_0_6617,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_5419]) ).

fof(i_0_6618,plain,
    ! [X33334,X33335,X33336,X33337,X33338,X33340,X33341,X33342,X33343,X33345] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33337),X33335))
        | ~ c_Wellfounded_Omax__extp(X33337,X33336,X33335,X33334) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33337),X33334))
        | ~ c_Wellfounded_Omax__extp(X33337,X33336,X33335,X33334) )
      & ( X33334 != c_Orderings_Obot__class_Obot(tc_fun(X33337,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X33337,X33336,X33335,X33334) )
      & ( hBOOL(hAPP(hAPP(c_member(X33337),esk516_5(X33334,X33335,X33336,X33337,X33338)),X33334))
        | ~ hBOOL(hAPP(hAPP(c_member(X33337),X33338),X33335))
        | ~ c_Wellfounded_Omax__extp(X33337,X33336,X33335,X33334) )
      & ( hBOOL(hAPP(hAPP(X33336,X33338),esk516_5(X33334,X33335,X33336,X33337,X33338)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33337),X33338),X33335))
        | ~ c_Wellfounded_Omax__extp(X33337,X33336,X33335,X33334) )
      & ( hBOOL(hAPP(hAPP(c_member(X33343),esk517_4(X33340,X33341,X33342,X33343)),X33341))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33343),X33341))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33343),X33340))
        | X33340 = c_Orderings_Obot__class_Obot(tc_fun(X33343,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X33343,X33342,X33341,X33340) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33343),X33345),X33340))
        | ~ hBOOL(hAPP(hAPP(X33342,esk517_4(X33340,X33341,X33342,X33343)),X33345))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33343),X33341))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33343),X33340))
        | X33340 = c_Orderings_Obot__class_Obot(tc_fun(X33343,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X33343,X33342,X33341,X33340) ) ),
    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_max__extp_Osimps])])])])])]) ).

fof(i_0_6619,plain,
    ! [X27479,X27480,X27481,X27482,X27483,X27485,X27486,X27487,X27488,X27490] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27482),X27480))
        | ~ c_Wellfounded_Omax__extp(X27482,X27481,X27480,X27479) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27482),X27479))
        | ~ c_Wellfounded_Omax__extp(X27482,X27481,X27480,X27479) )
      & ( X27479 != c_Orderings_Obot__class_Obot(tc_fun(X27482,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X27482,X27481,X27480,X27479) )
      & ( hBOOL(hAPP(hAPP(c_member(X27482),esk285_5(X27479,X27480,X27481,X27482,X27483)),X27479))
        | ~ hBOOL(hAPP(hAPP(c_member(X27482),X27483),X27480))
        | ~ c_Wellfounded_Omax__extp(X27482,X27481,X27480,X27479) )
      & ( hBOOL(hAPP(hAPP(X27481,X27483),esk285_5(X27479,X27480,X27481,X27482,X27483)))
        | ~ hBOOL(hAPP(hAPP(c_member(X27482),X27483),X27480))
        | ~ c_Wellfounded_Omax__extp(X27482,X27481,X27480,X27479) )
      & ( hBOOL(hAPP(hAPP(c_member(X27488),esk286_4(X27485,X27486,X27487,X27488)),X27486))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27486))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27485))
        | X27485 = c_Orderings_Obot__class_Obot(tc_fun(X27488,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X27488,X27487,X27486,X27485) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27488),X27490),X27485))
        | ~ hBOOL(hAPP(hAPP(X27487,esk286_4(X27485,X27486,X27487,X27488)),X27490))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27486))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27485))
        | X27485 = c_Orderings_Obot__class_Obot(tc_fun(X27488,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X27488,X27487,X27486,X27485) ) ),
    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_max__extp_Oequations])])])])])]) ).

fof(i_0_6620,plain,
    ! [X25329,X25330,X25331] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25331,tc_HOL_Obool)),X25330),X25329) = hAPP(c_Set_OCollect(X25331),hAPP(hAPP(c_COMBS(X25331,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25331),c_fconj),hAPP(hAPP(c_COMBC(X25331,tc_fun(X25331,tc_HOL_Obool),tc_HOL_Obool),c_member(X25331)),X25330))),hAPP(hAPP(c_COMBC(X25331,tc_fun(X25331,tc_HOL_Obool),tc_HOL_Obool),c_member(X25331)),X25329))),
    inference(variable_rename,[status(thm)],[fact_Int__def]) ).

fof(i_0_6621,plain,
    ! [X25326,X25327,X25328] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25328,tc_HOL_Obool)),X25327),X25326) = hAPP(c_Set_OCollect(X25328),hAPP(hAPP(c_COMBS(X25328,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25328),c_fdisj),hAPP(hAPP(c_COMBC(X25328,tc_fun(X25328,tc_HOL_Obool),tc_HOL_Obool),c_member(X25328)),X25327))),hAPP(hAPP(c_COMBC(X25328,tc_fun(X25328,tc_HOL_Obool),tc_HOL_Obool),c_member(X25328)),X25326))),
    inference(variable_rename,[status(thm)],[fact_Un__def]) ).

fof(i_0_6622,plain,
    ! [X21052,X21053,X21054,X21055,X21056,X21057,X21058,X21059] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X21059,X21058,X21057,X21056,X21055,X21054)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21058),X21053))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21058),X21052))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21058,tc_HOL_Obool)),X21053),X21052) != c_Orderings_Obot__class_Obot(tc_fun(X21058,tc_HOL_Obool))
      | hAPP(X21054,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21058,tc_HOL_Obool)),X21053),X21052)) = hAPP(hAPP(X21057,hAPP(X21054,X21053)),hAPP(X21054,X21052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).

cnf(i_0_6623,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OdropWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_5420]) ).

fof(i_0_6624,plain,
    ! [X18515,X18516,X18517,X18518,X18519,X18520] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),X18519),X18518)),X18517)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),X18516),X18518)),X18515)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18520),X18516),X18519)),X18518)),X18515)))
        | ~ class_Rings_Oordered__ring(X18520) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18520),X18516),X18519)),X18518)),X18515)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),X18519),X18518)),X18517)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18520),X18516),X18518)),X18515)))
        | ~ class_Rings_Oordered__ring(X18520) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).

fof(i_0_6625,plain,
    ! [X18527,X18528,X18529,X18530,X18531,X18532] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),X18531),X18530)),X18529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),X18528),X18530)),X18527)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18532),X18529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18532),X18528),X18531)),X18530)),X18527)))
        | ~ class_Rings_Oordered__ring(X18532) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18532),X18529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18532),X18528),X18531)),X18530)),X18527)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),X18531),X18530)),X18529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18532),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18532),X18528),X18530)),X18527)))
        | ~ class_Rings_Oordered__ring(X18532) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).

fof(i_0_6626,plain,
    ! [X25512,X25513,X25514,X25515,X25516,X25517] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25517,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25516,X25517,X25515),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25514,tc_fun(X25516,tc_HOL_Obool)),X25513),X25512))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25514,tc_fun(X25517,tc_HOL_Obool)),X25513),hAPP(hAPP(c_COMBB(tc_fun(X25516,tc_HOL_Obool),tc_fun(X25517,tc_HOL_Obool),X25514),c_Relation_OImage(X25516,X25517,X25515)),X25512)))),
    inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).

fof(i_0_6627,plain,
    ! [X17913,X17914,X17915,X17916,X17917,X17918,X17919,X17920] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17920,X17919,X17918,X17917,X17916,X17915)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17919),X17914))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17919,tc_HOL_Obool)),X17913),X17914))
      | hAPP(hAPP(X17918,hAPP(X17915,X17913)),hAPP(X17915,X17914)) = hAPP(X17915,X17914) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_6628,plain,
    ! [X17637,X17638,X17639,X17640,X17641] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17639,X17640)),X17638),X17637))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17640),hAPP(X17638,X17641)),hAPP(X17637,X17641)))
        | ~ class_Orderings_Oord(X17640) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17640),hAPP(X17638,esk19_4(X17637,X17638,X17639,X17640))),hAPP(X17637,esk19_4(X17637,X17638,X17639,X17640))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17639,X17640)),X17638),X17637))
        | ~ class_Orderings_Oord(X17640) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])]) ).

fof(i_0_6629,plain,
    ! [X19764,X19765,X19766,X19767,X19768,X19769,X19770] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X19770,X19769,X19768,X19767,X19766,X19765)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19769),X19764))
      | hAPP(X19765,X19764) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19770,X19769,X19768),X19766),X19767),X19764) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_6630,plain,
    ! [X31090,X31091,X31092,X31093,X31094,X31095,X31096,X31097,X31098,X31099,X31100] :
      ( ( hAPP(hAPP(c_List_Omap(X31094,X31093),X31092),X31091) != hAPP(hAPP(c_List_Omap(X31094,X31093),X31090),X31091)
        | ~ hBOOL(hAPP(hAPP(c_member(X31094),X31095),hAPP(c_List_Oset(X31094),X31091)))
        | hAPP(X31092,X31095) = hAPP(X31090,X31095) )
      & ( hBOOL(hAPP(hAPP(c_member(X31100),esk420_5(X31096,X31097,X31098,X31099,X31100)),hAPP(c_List_Oset(X31100),X31097)))
        | hAPP(hAPP(c_List_Omap(X31100,X31099),X31098),X31097) = hAPP(hAPP(c_List_Omap(X31100,X31099),X31096),X31097) )
      & ( hAPP(X31098,esk420_5(X31096,X31097,X31098,X31099,X31100)) != hAPP(X31096,esk420_5(X31096,X31097,X31098,X31099,X31100))
        | hAPP(hAPP(c_List_Omap(X31100,X31099),X31098),X31097) = hAPP(hAPP(c_List_Omap(X31100,X31099),X31096),X31097) ) ),
    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_map__eq__conv])])])])])]) ).

fof(i_0_6631,plain,
    ! [X27491,X27492,X27493,X27494,X27495,X27496,X27497,X27498] :
      ( ~ hBOOL(hAPP(hAPP(X27498,X27497),X27496))
      | ~ hBOOL(hAPP(hAPP(X27495,X27496),X27494))
      | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27493,X27492,X27491,X27498,X27495),X27497),X27494)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros])]) ).

fof(i_0_6632,plain,
    ! [X19756,X19757,X19758,X19759,X19760,X19761,X19762,X19763] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X19763,X19762,X19761,X19760,X19759,X19758)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19762),X19757))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19762),X19756))
      | hAPP(X19758,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19762,tc_HOL_Obool)),X19757),X19756)) = hAPP(hAPP(X19761,hAPP(X19758,X19757)),hAPP(X19758,X19756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).

fof(i_0_6633,plain,
    ! [X25876,X25877,X25878,X25879,X25880,X25881,X25882,X25883] :
      ( ~ c_Equiv__Relations_Oequiv(X25883,X25882,X25881)
      | ~ c_Equiv__Relations_Ocongruent2(X25883,X25880,X25879,X25881,X25878,X25877)
      | ~ hBOOL(hAPP(hAPP(c_member(X25883),X25876),X25882))
      | c_Equiv__Relations_Ocongruent(X25880,X25879,X25878,hAPP(X25877,X25876)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).

fof(i_0_6634,plain,
    ! [X30414,X30415,X30416,X30417,X30418,X30421,X30422,X30423,X30424,X30425,X30426,X30427] :
      ( ( hAPP(hAPP(c_List_Oappend(X30418),X30417),esk409_5(X30414,X30415,X30416,X30417,X30418)) = X30415
        | X30417 = hAPP(hAPP(c_List_Oappend(X30418),X30415),esk408_5(X30414,X30415,X30416,X30417,X30418))
        | hAPP(hAPP(c_List_Oappend(X30418),X30417),X30416) != hAPP(hAPP(c_List_Oappend(X30418),X30415),X30414) )
      & ( X30416 = hAPP(hAPP(c_List_Oappend(X30418),esk409_5(X30414,X30415,X30416,X30417,X30418)),X30414)
        | X30417 = hAPP(hAPP(c_List_Oappend(X30418),X30415),esk408_5(X30414,X30415,X30416,X30417,X30418))
        | hAPP(hAPP(c_List_Oappend(X30418),X30417),X30416) != hAPP(hAPP(c_List_Oappend(X30418),X30415),X30414) )
      & ( hAPP(hAPP(c_List_Oappend(X30418),X30417),esk409_5(X30414,X30415,X30416,X30417,X30418)) = X30415
        | hAPP(hAPP(c_List_Oappend(X30418),esk408_5(X30414,X30415,X30416,X30417,X30418)),X30416) = X30414
        | hAPP(hAPP(c_List_Oappend(X30418),X30417),X30416) != hAPP(hAPP(c_List_Oappend(X30418),X30415),X30414) )
      & ( X30416 = hAPP(hAPP(c_List_Oappend(X30418),esk409_5(X30414,X30415,X30416,X30417,X30418)),X30414)
        | hAPP(hAPP(c_List_Oappend(X30418),esk408_5(X30414,X30415,X30416,X30417,X30418)),X30416) = X30414
        | hAPP(hAPP(c_List_Oappend(X30418),X30417),X30416) != hAPP(hAPP(c_List_Oappend(X30418),X30415),X30414) )
      & ( X30424 != hAPP(hAPP(c_List_Oappend(X30425),X30422),X30426)
        | hAPP(hAPP(c_List_Oappend(X30425),X30426),X30423) != X30421
        | hAPP(hAPP(c_List_Oappend(X30425),X30424),X30423) = hAPP(hAPP(c_List_Oappend(X30425),X30422),X30421) )
      & ( hAPP(hAPP(c_List_Oappend(X30425),X30424),X30427) != X30422
        | X30423 != hAPP(hAPP(c_List_Oappend(X30425),X30427),X30421)
        | hAPP(hAPP(c_List_Oappend(X30425),X30424),X30423) = hAPP(hAPP(c_List_Oappend(X30425),X30422),X30421) ) ),
    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_append__eq__append__conv2])])])])])]) ).

fof(i_0_6635,plain,
    ! [X17259,X17260,X17261,X17262,X17263,X17264,X17265,X17266] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17266,X17265,X17264,X17263,X17262,X17261)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17265),X17260))
      | hBOOL(hAPP(hAPP(c_member(X17265),X17259),X17260))
      | hAPP(X17261,hAPP(hAPP(c_Set_Oinsert(X17265),X17259),X17260)) = hAPP(hAPP(X17264,hAPP(X17262,X17259)),hAPP(X17261,X17260)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5421])]) ).

fof(i_0_6636,plain,
    ! [X19861,X19862,X19863,X19864,X19865] :
      ( ( ~ c_Fun_Oinj__on(X19864,X19862,X19865,X19863)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19862,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19864,X19862,X19865),X19863)),X19861))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19864),X19863)),hAPP(c_Finite__Set_Ocard(X19862),X19861)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19862),X19861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19864),X19863)) )
      & ( c_Fun_Oinj__on(X19864,X19862,esk75_4(X19861,X19862,X19863,X19864),X19863)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19864),X19863)),hAPP(c_Finite__Set_Ocard(X19862),X19861)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19862),X19861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19864),X19863)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19862,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19864,X19862,esk75_4(X19861,X19862,X19863,X19864)),X19863)),X19861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19864),X19863)),hAPP(c_Finite__Set_Ocard(X19862),X19861)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19862),X19861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19864),X19863)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le])])])])]) ).

fof(i_0_6637,plain,
    ! [X17285,X17286,X17287,X17288,X17289,X17290,X17291,X17292] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17292,X17291,X17290,X17289,X17288,X17287)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17291),X17286))
      | ~ hBOOL(hAPP(hAPP(c_member(X17291),X17285),X17286))
      | hAPP(hAPP(X17290,hAPP(X17288,X17285)),hAPP(X17287,X17286)) = hAPP(X17287,X17286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).

fof(i_0_6638,plain,
    ! [X31559,X31560,X31561] : c_Enum_Osublists(X31561,hAPP(hAPP(c_List_Olist_OCons(X31561),X31560),X31559)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X31561)),tc_List_Olist(tc_List_Olist(X31561))),c_Enum_Osublists(X31561,X31559)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X31561)),tc_List_Olist(tc_List_Olist(X31561)),tc_List_Olist(tc_List_Olist(X31561))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X31561)),tc_fun(tc_List_Olist(tc_List_Olist(X31561)),tc_List_Olist(tc_List_Olist(X31561))),tc_List_Olist(tc_List_Olist(X31561))),c_List_Oappend(tc_List_Olist(X31561))),hAPP(c_List_Omap(tc_List_Olist(X31561),tc_List_Olist(X31561)),hAPP(c_List_Olist_OCons(X31561),X31560)))),c_COMBI(tc_List_Olist(tc_List_Olist(X31561))))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(i_0_6639,plain,
    ! [X17272,X17273,X17274,X17275,X17276,X17277,X17278,X17279] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17279,X17278,X17277,X17276,X17275,X17274)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17278),X17273))
      | hAPP(X17274,hAPP(hAPP(c_Set_Oinsert(X17278),X17272),X17273)) = hAPP(hAPP(X17277,hAPP(X17275,X17272)),hAPP(X17274,X17273)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).

fof(i_0_6640,plain,
    ! [X21713,X21714,X21715,X21716,X21717] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21717,tc_fun(X21716,tc_HOL_Obool)),X21715),hAPP(hAPP(c_COMBS(X21717,tc_fun(X21716,tc_HOL_Obool),tc_fun(X21716,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21716,tc_HOL_Obool),tc_fun(tc_fun(X21716,tc_HOL_Obool),tc_fun(X21716,tc_HOL_Obool)),X21717),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21716,tc_HOL_Obool))),X21714)),X21713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21717,tc_fun(X21716,tc_HOL_Obool)),X21715),X21714)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21717,tc_fun(X21716,tc_HOL_Obool)),X21715),X21713)),
    inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).

fof(i_0_6641,plain,
    ! [X21304,X21305,X21306,X21307,X21308] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21308,tc_fun(X21307,tc_HOL_Obool)),X21306),hAPP(hAPP(c_COMBS(X21308,tc_fun(X21307,tc_HOL_Obool),tc_fun(X21307,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21307,tc_HOL_Obool),tc_fun(tc_fun(X21307,tc_HOL_Obool),tc_fun(X21307,tc_HOL_Obool)),X21308),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21307,tc_HOL_Obool))),X21305)),X21304)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21307,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21308,tc_fun(X21307,tc_HOL_Obool)),X21306),X21305)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21308,tc_fun(X21307,tc_HOL_Obool)),X21306),X21304)),
    inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).

fof(i_0_6642,plain,
    ! [X17368,X17369,X17370,X17371,X17372,X17373] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17373,X17372,X17371,X17370,X17369,X17368)
      | hAPP(X17368,c_Orderings_Obot__class_Obot(tc_fun(X17372,tc_HOL_Obool))) = X17370 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).

fof(i_0_6643,plain,
    ! [X17309,X17310,X17311,X17312,X17313,X17314,X17315] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17315,X17314,X17313,X17312,X17311,X17310)
      | hAPP(hAPP(X17313,X17309),X17309) = X17309 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).

fof(i_0_6644,plain,
    ! [X27227] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27227))
      | X27227 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X27227)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).

fof(i_0_6645,plain,
    ! [X31835,X31836,X31837] : hAPP(c_List_Oset(X31837),hAPP(c_List_Ofilter(X31837,X31836),X31835)) = hAPP(c_Set_OCollect(X31837),hAPP(hAPP(c_COMBS(X31837,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31837),c_fconj),hAPP(hAPP(c_COMBC(X31837,tc_fun(X31837,tc_HOL_Obool),tc_HOL_Obool),c_member(X31837)),hAPP(c_List_Oset(X31837),X31835)))),X31836)),
    inference(variable_rename,[status(thm)],[fact_set__filter]) ).

fof(i_0_6646,plain,
    ! [X24115,X24116,X24117] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X24117,esk168_3(X24115,X24116,X24117))),hAPP(X24116,esk168_3(X24115,X24116,X24117))))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X24116),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24115))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X24117),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24115))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X24116)),X24117)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24115)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).

fof(i_0_6647,plain,
    ! [X17965,X17966,X17967,X17968,X17969,X17971] :
      ( ( ~ c_Fun_Oinj__on(X17967,X17966,X17969,X17968)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17966,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17967,X17966,X17969),X17968)),X17965))
        | hAPP(c_Set_Oimage(X17966,X17967,esk23_4(X17965,X17966,X17967,X17968)),X17965) = X17968
        | X17968 = c_Orderings_Obot__class_Obot(tc_fun(X17967,tc_HOL_Obool)) )
      & ( c_Fun_Oinj__on(X17967,X17966,esk24_4(X17965,X17966,X17967,X17968),X17968)
        | hAPP(c_Set_Oimage(X17966,X17967,X17971),X17965) != X17968
        | X17968 = c_Orderings_Obot__class_Obot(tc_fun(X17967,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17966,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17967,X17966,esk24_4(X17965,X17966,X17967,X17968)),X17968)),X17965))
        | hAPP(c_Set_Oimage(X17966,X17967,X17971),X17965) != X17968
        | X17968 = c_Orderings_Obot__class_Obot(tc_fun(X17967,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj])])])])]) ).

fof(i_0_6648,plain,
    ! [X27700,X27701,X27702,X27703] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27703),X27702),hAPP(c_Relation_ORange(X27701,X27703),X27700)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27701,X27703)),hAPP(hAPP(c_Product__Type_OPair(X27701,X27703),esk296_4(X27700,X27701,X27702,X27703)),X27702)),X27700)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5422])])]) ).

fof(i_0_6649,plain,
    ! [X27656,X27657,X27658,X27659,X27661,X27662,X27663,X27664,X27665] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27659),X27658),hAPP(c_Relation_ORange(X27657,X27659),X27656)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27657,X27659)),hAPP(hAPP(c_Product__Type_OPair(X27657,X27659),esk294_4(X27656,X27657,X27658,X27659)),X27658)),X27656)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27662,X27664)),hAPP(hAPP(c_Product__Type_OPair(X27662,X27664),X27665),X27663)),X27661))
        | hBOOL(hAPP(hAPP(c_member(X27664),X27663),hAPP(c_Relation_ORange(X27662,X27664),X27661))) ) ),
    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_Range__iff])])])])]) ).

fof(i_0_6650,plain,
    ! [X27255] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27255))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X27255)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).

fof(i_0_6651,plain,
    ! [X21914,X21915,X21916,X21917,X21918] :
      ( ( X21918 != c_Orderings_Obot__class_Obot(tc_fun(X21917,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21917,tc_fun(X21916,tc_HOL_Obool)),X21918),hAPP(hAPP(c_COMBC(X21917,tc_fun(X21916,tc_HOL_Obool),tc_fun(X21916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21916,tc_HOL_Obool),tc_fun(tc_fun(X21916,tc_HOL_Obool),tc_fun(X21916,tc_HOL_Obool)),X21917),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21916,tc_HOL_Obool))),X21915)),X21914)) = c_Orderings_Otop__class_Otop(tc_fun(X21916,tc_HOL_Obool)) )
      & ( X21918 = c_Orderings_Obot__class_Obot(tc_fun(X21917,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21917,tc_fun(X21916,tc_HOL_Obool)),X21918),hAPP(hAPP(c_COMBC(X21917,tc_fun(X21916,tc_HOL_Obool),tc_fun(X21916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21916,tc_HOL_Obool),tc_fun(tc_fun(X21916,tc_HOL_Obool),tc_fun(X21916,tc_HOL_Obool)),X21917),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21916,tc_HOL_Obool))),X21915)),X21914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21916,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21917,tc_fun(X21916,tc_HOL_Obool)),X21918),X21915)),X21914) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).

fof(i_0_6652,plain,
    ! [X21932,X21933,X21934,X21935,X21936] :
      ( ( X21936 != c_Orderings_Obot__class_Obot(tc_fun(X21935,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21935,tc_fun(X21934,tc_HOL_Obool)),X21936),hAPP(hAPP(c_COMBC(X21935,tc_fun(X21934,tc_HOL_Obool),tc_fun(X21934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21934,tc_HOL_Obool),tc_fun(tc_fun(X21934,tc_HOL_Obool),tc_fun(X21934,tc_HOL_Obool)),X21935),c_Groups_Ominus__class_Ominus(tc_fun(X21934,tc_HOL_Obool))),X21933)),X21932)) = c_Orderings_Otop__class_Otop(tc_fun(X21934,tc_HOL_Obool)) )
      & ( X21936 = c_Orderings_Obot__class_Obot(tc_fun(X21935,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21935,tc_fun(X21934,tc_HOL_Obool)),X21936),hAPP(hAPP(c_COMBC(X21935,tc_fun(X21934,tc_HOL_Obool),tc_fun(X21934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21934,tc_HOL_Obool),tc_fun(tc_fun(X21934,tc_HOL_Obool),tc_fun(X21934,tc_HOL_Obool)),X21935),c_Groups_Ominus__class_Ominus(tc_fun(X21934,tc_HOL_Obool))),X21933)),X21932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21934,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21935,tc_fun(X21934,tc_HOL_Obool)),X21936),X21933)),X21932) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).

fof(i_0_6653,plain,
    ! [X21426,X21427,X21428,X21429,X21430] :
      ( ( X21430 != c_Orderings_Obot__class_Obot(tc_fun(X21429,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21429,tc_fun(X21428,tc_HOL_Obool)),X21430),hAPP(hAPP(c_COMBC(X21429,tc_fun(X21428,tc_HOL_Obool),tc_fun(X21428,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21428,tc_HOL_Obool),tc_fun(tc_fun(X21428,tc_HOL_Obool),tc_fun(X21428,tc_HOL_Obool)),X21429),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21428,tc_HOL_Obool))),X21427)),X21426)) = c_Orderings_Obot__class_Obot(tc_fun(X21428,tc_HOL_Obool)) )
      & ( X21430 = c_Orderings_Obot__class_Obot(tc_fun(X21429,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21429,tc_fun(X21428,tc_HOL_Obool)),X21430),hAPP(hAPP(c_COMBC(X21429,tc_fun(X21428,tc_HOL_Obool),tc_fun(X21428,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21428,tc_HOL_Obool),tc_fun(tc_fun(X21428,tc_HOL_Obool),tc_fun(X21428,tc_HOL_Obool)),X21429),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21428,tc_HOL_Obool))),X21427)),X21426)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21428,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21429,tc_fun(X21428,tc_HOL_Obool)),X21430),X21427)),X21426) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).

fof(i_0_6654,plain,
    ! [X21854,X21855,X21856,X21857,X21858] :
      ( ( X21858 != c_Orderings_Obot__class_Obot(tc_fun(X21857,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21856,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21857,tc_fun(X21856,tc_HOL_Obool)),X21858),X21855)),X21854) = X21854 )
      & ( X21858 = c_Orderings_Obot__class_Obot(tc_fun(X21857,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21856,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21857,tc_fun(X21856,tc_HOL_Obool)),X21858),X21855)),X21854) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21857,tc_fun(X21856,tc_HOL_Obool)),X21858),hAPP(hAPP(c_COMBC(X21857,tc_fun(X21856,tc_HOL_Obool),tc_fun(X21856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21856,tc_HOL_Obool),tc_fun(tc_fun(X21856,tc_HOL_Obool),tc_fun(X21856,tc_HOL_Obool)),X21857),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21856,tc_HOL_Obool))),X21855)),X21854)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).

fof(i_0_6655,plain,
    ! [X21416,X21417,X21418,X21419,X21420] :
      ( ( X21420 != c_Orderings_Obot__class_Obot(tc_fun(X21419,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21418,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21419,tc_fun(X21418,tc_HOL_Obool)),X21420),X21417)),X21416) = X21416 )
      & ( X21420 = c_Orderings_Obot__class_Obot(tc_fun(X21419,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21418,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21419,tc_fun(X21418,tc_HOL_Obool)),X21420),X21417)),X21416) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21419,tc_fun(X21418,tc_HOL_Obool)),X21420),hAPP(hAPP(c_COMBC(X21419,tc_fun(X21418,tc_HOL_Obool),tc_fun(X21418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21418,tc_HOL_Obool),tc_fun(tc_fun(X21418,tc_HOL_Obool),tc_fun(X21418,tc_HOL_Obool)),X21419),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21418,tc_HOL_Obool))),X21417)),X21416)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).

fof(i_0_6656,plain,
    ! [X21927,X21928,X21929,X21930,X21931] :
      ( ( X21931 != c_Orderings_Obot__class_Obot(tc_fun(X21930,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21929,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21930,tc_fun(X21929,tc_HOL_Obool)),X21931),X21928)),X21927) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21929,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X21929,tc_HOL_Obool))),X21927) )
      & ( X21931 = c_Orderings_Obot__class_Obot(tc_fun(X21930,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21929,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21930,tc_fun(X21929,tc_HOL_Obool)),X21931),X21928)),X21927) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21930,tc_fun(X21929,tc_HOL_Obool)),X21931),hAPP(hAPP(c_COMBC(X21930,tc_fun(X21929,tc_HOL_Obool),tc_fun(X21929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21929,tc_HOL_Obool),tc_fun(tc_fun(X21929,tc_HOL_Obool),tc_fun(X21929,tc_HOL_Obool)),X21930),c_Groups_Ominus__class_Ominus(tc_fun(X21929,tc_HOL_Obool))),X21928)),X21927)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).

fof(i_0_6657,plain,
    ! [X21703,X21704,X21705,X21706,X21707] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21707,tc_fun(X21706,tc_HOL_Obool)),X21705),hAPP(hAPP(c_COMBC(X21707,tc_fun(X21706,tc_HOL_Obool),tc_fun(X21706,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21706,tc_HOL_Obool),tc_fun(tc_fun(X21706,tc_HOL_Obool),tc_fun(X21706,tc_HOL_Obool)),X21707),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21706,tc_HOL_Obool))),X21704)),X21703)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21706,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21707,tc_fun(X21706,tc_HOL_Obool)),X21705),X21704)),X21703),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(i_0_6658,plain,
    ! [X21319,X21320,X21321,X21322,X21323] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21323,tc_fun(X21322,tc_HOL_Obool)),X21321),hAPP(hAPP(c_COMBC(X21323,tc_fun(X21322,tc_HOL_Obool),tc_fun(X21322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21322,tc_HOL_Obool),tc_fun(tc_fun(X21322,tc_HOL_Obool),tc_fun(X21322,tc_HOL_Obool)),X21323),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21322,tc_HOL_Obool))),X21320)),X21319)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21322,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21323,tc_fun(X21322,tc_HOL_Obool)),X21321),X21320)),X21319),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(i_0_6659,plain,
    ! [X21358,X21359,X21360,X21361,X21362] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21362,tc_fun(X21361,tc_HOL_Obool)),X21360),hAPP(hAPP(c_COMBC(X21362,tc_fun(X21361,tc_HOL_Obool),tc_fun(X21361,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21361,tc_HOL_Obool),tc_fun(tc_fun(X21361,tc_HOL_Obool),tc_fun(X21361,tc_HOL_Obool)),X21362),c_Groups_Ominus__class_Ominus(tc_fun(X21361,tc_HOL_Obool))),X21359)),X21358)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21361,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21362,tc_fun(X21361,tc_HOL_Obool)),X21360),X21359)),X21358),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(i_0_6660,plain,
    ! [X21334,X21335,X21336,X21337,X21338] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21338,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21337,tc_fun(X21338,tc_HOL_Obool)),X21336),X21335)),X21334) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21337,tc_fun(X21338,tc_HOL_Obool)),X21336),hAPP(hAPP(c_COMBC(X21337,tc_fun(X21338,tc_HOL_Obool),tc_fun(X21338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21338,tc_HOL_Obool),tc_fun(tc_fun(X21338,tc_HOL_Obool),tc_fun(X21338,tc_HOL_Obool)),X21337),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21338,tc_HOL_Obool))),X21335)),X21334)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(i_0_6661,plain,
    ! [X21688,X21689,X21690,X21691,X21692] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21691,tc_fun(X21692,tc_HOL_Obool)),X21690),X21689)),X21688) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21691,tc_fun(X21692,tc_HOL_Obool)),X21690),hAPP(hAPP(c_COMBC(X21691,tc_fun(X21692,tc_HOL_Obool),tc_fun(X21692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21692,tc_HOL_Obool),tc_fun(tc_fun(X21692,tc_HOL_Obool),tc_fun(X21692,tc_HOL_Obool)),X21691),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21692,tc_HOL_Obool))),X21689)),X21688)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(i_0_6662,plain,
    ! [X21363,X21364,X21365,X21366,X21367] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21367,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21366,tc_fun(X21367,tc_HOL_Obool)),X21365),X21364)),X21363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21366,tc_fun(X21367,tc_HOL_Obool)),X21365),hAPP(hAPP(c_COMBC(X21366,tc_fun(X21367,tc_HOL_Obool),tc_fun(X21367,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21367,tc_HOL_Obool),tc_fun(tc_fun(X21367,tc_HOL_Obool),tc_fun(X21367,tc_HOL_Obool)),X21366),c_Groups_Ominus__class_Ominus(tc_fun(X21367,tc_HOL_Obool))),X21364)),X21363)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(i_0_6663,plain,
    ! [X27848,X27849,X27850,X27851,X27852,X27853,X27854,X27855] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27855,X27854),tc_HOL_Obool)),X27853),hAPP(hAPP(c_Product__Type_OSigma(X27855,X27854),X27852),hAPP(c_COMBK(tc_fun(X27854,tc_HOL_Obool),X27855),X27851))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27854,X27850),tc_HOL_Obool)),X27849),hAPP(hAPP(c_Product__Type_OSigma(X27854,X27850),X27851),hAPP(c_COMBK(tc_fun(X27850,tc_HOL_Obool),X27854),X27848))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27855,X27850),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27855,X27854,X27850),X27853),X27849)),hAPP(hAPP(c_Product__Type_OSigma(X27855,X27850),X27852),hAPP(c_COMBK(tc_fun(X27850,tc_HOL_Obool),X27855),X27848)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).

fof(i_0_6664,plain,
    ! [X29646,X29647,X29648,X29649,X29650,X29651] :
      ( ( X29650 = X29648
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29651,X29651)),hAPP(hAPP(c_Product__Type_OPair(X29651,X29651),X29650),X29648)),X29646))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),X29649),X29647)),c_List_Olistrel1(X29651,X29646)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29651,X29651)),hAPP(hAPP(c_Product__Type_OPair(X29651,X29651),X29650),X29648)),X29646))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) )
      & ( X29650 = X29648
        | X29649 = X29647
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),X29649),X29647)),c_List_Olistrel1(X29651,X29646)))
        | X29649 = X29647
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29651,X29651)),hAPP(hAPP(c_Product__Type_OPair(X29651,X29651),X29650),X29648)),X29646))
        | X29649 != X29647
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) )
      & ( X29650 != X29648
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),X29649),X29647)),c_List_Olistrel1(X29651,X29646)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29651),tc_List_Olist(X29651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29651),tc_List_Olist(X29651)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29650),X29649)),hAPP(hAPP(c_List_Olist_OCons(X29651),X29648),X29647))),c_List_Olistrel1(X29651,X29646))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).

fof(i_0_6665,plain,
    ! [X29588,X29589,X29590,X29591,X29592,X29593] :
      ( ( X29592 = X29590
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29593,X29593)),hAPP(hAPP(c_Product__Type_OPair(X29593,X29593),X29592),X29590)),X29588))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29592),X29591)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29590),X29589))),c_List_Olexord(X29593,X29588))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),X29591),X29589)),c_List_Olexord(X29593,X29588)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29593,X29593)),hAPP(hAPP(c_Product__Type_OPair(X29593,X29593),X29592),X29590)),X29588))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29592),X29591)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29590),X29589))),c_List_Olexord(X29593,X29588))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29593,X29593)),hAPP(hAPP(c_Product__Type_OPair(X29593,X29593),X29592),X29590)),X29588))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29592),X29591)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29590),X29589))),c_List_Olexord(X29593,X29588))) )
      & ( X29592 != X29590
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),X29591),X29589)),c_List_Olexord(X29593,X29588)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29593),tc_List_Olist(X29593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29593),tc_List_Olist(X29593)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29592),X29591)),hAPP(hAPP(c_List_Olist_OCons(X29593),X29590),X29589))),c_List_Olexord(X29593,X29588))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).

fof(i_0_6666,plain,
    ! [X29572,X29573,X29574,X29575,X29576,X29577] :
      ( ( X29576 = X29574
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29577,X29577)),hAPP(hAPP(c_Product__Type_OPair(X29577,X29577),X29576),X29574)),X29572))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),X29575),X29573)),c_List_Olex(X29577,X29572)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29577,X29577)),hAPP(hAPP(c_Product__Type_OPair(X29577,X29577),X29576),X29574)),X29572))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) )
      & ( X29576 = X29574
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29575) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29573)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),X29575),X29573)),c_List_Olex(X29577,X29572)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29575) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29573)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29577,X29577)),hAPP(hAPP(c_Product__Type_OPair(X29577,X29577),X29576),X29574)),X29572))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29575) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29577)),X29573)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) )
      & ( X29576 != X29574
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),X29575),X29573)),c_List_Olex(X29577,X29572)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29577),tc_List_Olist(X29577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29577),tc_List_Olist(X29577)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29576),X29575)),hAPP(hAPP(c_List_Olist_OCons(X29577),X29574),X29573))),c_List_Olex(X29577,X29572))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).

fof(i_0_6667,plain,
    ! [X27877,X27878,X27879,X27880,X27881] : hAPP(hAPP(c_Product__Type_OSigma(X27881,X27880),X27879),hAPP(hAPP(c_COMBS(X27881,tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_HOL_Obool),tc_fun(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool)),X27881),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27880,tc_HOL_Obool))),X27878)),X27877)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27881,X27880),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27881,X27880),X27879),X27878)),hAPP(hAPP(c_Product__Type_OSigma(X27881,X27880),X27879),X27877)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(i_0_6668,plain,
    ! [X27833,X27834,X27835,X27836,X27837] : hAPP(hAPP(c_Product__Type_OSigma(X27837,X27836),X27835),hAPP(hAPP(c_COMBS(X27837,tc_fun(X27836,tc_HOL_Obool),tc_fun(X27836,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27836,tc_HOL_Obool),tc_fun(tc_fun(X27836,tc_HOL_Obool),tc_fun(X27836,tc_HOL_Obool)),X27837),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27836,tc_HOL_Obool))),X27834)),X27833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27837,X27836),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27837,X27836),X27835),X27834)),hAPP(hAPP(c_Product__Type_OSigma(X27837,X27836),X27835),X27833)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(i_0_6669,plain,
    ! [X27894,X27895,X27896,X27897,X27898] : hAPP(hAPP(c_Product__Type_OSigma(X27898,X27897),X27896),hAPP(hAPP(c_COMBS(X27898,tc_fun(X27897,tc_HOL_Obool),tc_fun(X27897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27897,tc_HOL_Obool),tc_fun(tc_fun(X27897,tc_HOL_Obool),tc_fun(X27897,tc_HOL_Obool)),X27898),c_Groups_Ominus__class_Ominus(tc_fun(X27897,tc_HOL_Obool))),X27895)),X27894)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27898,X27897),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27898,X27897),X27896),X27895)),hAPP(hAPP(c_Product__Type_OSigma(X27898,X27897),X27896),X27894)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(i_0_6670,plain,
    ! [X25131,X25132,X25133,X25134,X25135] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25135)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25135),hAPP(c_Groups_Oabs__class_Oabs(X25135),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25135),X25134),X25133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25135),X25132),X25131)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25135),hAPP(c_Groups_Oabs__class_Oabs(X25135),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25135),X25134),X25132))),hAPP(c_Groups_Oabs__class_Oabs(X25135),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25135),X25133),X25131))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).

fof(i_0_6671,plain,
    ! [X20205,X20206,X20207,X20208,X20209] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20209),X20207)),X20206)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20208),X20207)),X20205)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20208),X20209)),X20207)),X20205)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20209),X20208)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20208),X20209)),X20207)),X20205)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20209),X20207)),X20206)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20208),X20207)),X20205)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20209),X20208)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).

fof(i_0_6672,plain,
    ! [X20230,X20231,X20232,X20233,X20234] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20234),X20232)),X20231)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20233),X20232)),X20230)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20233),X20234)),X20232)),X20230)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20234),X20233)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20233),X20234)),X20232)),X20230)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20234),X20232)),X20231)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20233),X20232)),X20230)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20234),X20233)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).

fof(i_0_6673,plain,
    ! [X28649,X28650,X28651,X28652,X28653,X28654,X28655,X28656] :
      ( ~ c_Finite__Set_Ofolding__image(X28656,X28655,X28654,X28653,X28652)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28655),X28651))
      | hAPP(hAPP(X28652,hAPP(hAPP(c_COMBS(X28655,X28656,X28656),hAPP(hAPP(c_COMBB(X28656,tc_fun(X28656,X28656),X28655),X28654),X28650)),X28649)),X28651) = hAPP(hAPP(X28654,hAPP(hAPP(X28652,X28650),X28651)),hAPP(hAPP(X28652,X28649),X28651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib])]) ).

cnf(i_0_6674,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5423]) ).

fof(i_0_6675,plain,
    ! [X21093,X21094,X21095,X21096,X21097] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21097)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21096),X21095))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21096),X21094))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21097),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21097,X21096,c_Groups_Otimes__class_Otimes(X21097)),X21093),c_Groups_Oone__class_Oone(X21097)),X21095)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21097,X21096,c_Groups_Otimes__class_Otimes(X21097)),X21093),c_Groups_Oone__class_Oone(X21097)),X21094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21097),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21097,X21096,c_Groups_Otimes__class_Otimes(X21097)),X21093),c_Groups_Oone__class_Oone(X21097)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21096,tc_HOL_Obool)),X21095),X21094))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21097,X21096,c_Groups_Otimes__class_Otimes(X21097)),X21093),c_Groups_Oone__class_Oone(X21097)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21096,tc_HOL_Obool)),X21095),X21094))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).

fof(i_0_6676,plain,
    ! [X22755,X22756,X22757] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22757)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X22756))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22755))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22755),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22756)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).

fof(i_0_6677,plain,
    ! [X20794,X20795,X20796,X20797] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20797,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20797,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20797,tc_HOL_Obool)),X20796),X20795)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20797,tc_HOL_Obool)),X20795),X20794))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20797,tc_HOL_Obool)),X20794),X20796)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20797,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20797,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20797,tc_HOL_Obool)),X20796),X20795)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20797,tc_HOL_Obool)),X20795),X20794))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20797,tc_HOL_Obool)),X20794),X20796)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).

fof(i_0_6678,plain,
    ! [X29598,X29599,X29600,X29601,X29602,X29603] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29603,X29603)),hAPP(hAPP(c_Product__Type_OPair(X29603,X29603),X29602),X29601)),c_Transitive__Closure_Ortrancl(X29603,X29600)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29603),tc_List_Olist(X29603))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29603),tc_List_Olist(X29603)),X29599),X29598)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29603),c_List_Olistrel1(X29603,X29600))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29603),tc_List_Olist(X29603))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29603),tc_List_Olist(X29603)),hAPP(hAPP(c_List_Olist_OCons(X29603),X29602),X29599)),hAPP(hAPP(c_List_Olist_OCons(X29603),X29601),X29598))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29603),c_List_Olistrel1(X29603,X29600)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).

fof(i_0_6679,plain,
    ! [X17897,X17898,X17899,X17900,X17901] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17901,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17901,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17900,X17901,X17899),X17898)),hAPP(c_Set_Oimage(X17900,X17901,X17899),X17897))),hAPP(c_Set_Oimage(X17900,X17901,X17899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17900,tc_HOL_Obool)),X17898),X17897)))),
    inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).

cnf(i_0_6680,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5424]) ).

cnf(i_0_6681,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5425]) ).

fof(i_0_6682,plain,
    ! [X25433] : hAPP(c_Set_OCollect(tc_Nat_Onat),X25433) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X25433),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(i_0_6683,plain,
    ! [X29536,X29537] : c_List_Olenlex(X29537,X29536) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X29537)),tc_List_Olist(X29537)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X29537),c_Wellfounded_Oless__than,c_List_Olex(X29537,X29536))),hAPP(hAPP(c_COMBS(tc_List_Olist(X29537),tc_List_Olist(X29537),tc_prod(tc_Nat_Onat,tc_List_Olist(X29537))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X29537),tc_prod(tc_Nat_Onat,tc_List_Olist(X29537))),tc_List_Olist(X29537)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X29537))),c_Nat_Osize__class_Osize(tc_List_Olist(X29537)))),c_COMBI(tc_List_Olist(X29537)))),
    inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).

fof(i_0_6684,plain,
    ! [X33665,X33666,X33667,X33668,X33669,X33670,X33671,X33672] :
      ( ( ~ c_Fun_Obij__betw(X33667,X33672,X33666,X33665,X33669)
        | c_Fun_Obij__betw(X33667,X33671,hAPP(c_Fun_Ocomp(X33672,X33671,X33667,X33670),X33666),X33665,X33668)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33672,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33667,X33672,X33666),X33665)),X33669))
        | ~ c_Fun_Obij__betw(X33672,X33671,X33670,X33669,X33668) )
      & ( ~ c_Fun_Obij__betw(X33667,X33671,hAPP(c_Fun_Ocomp(X33672,X33671,X33667,X33670),X33666),X33665,X33668)
        | c_Fun_Obij__betw(X33667,X33672,X33666,X33665,X33669)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33672,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33667,X33672,X33666),X33665)),X33669))
        | ~ c_Fun_Obij__betw(X33672,X33671,X33670,X33669,X33668) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff2])])]) ).

fof(i_0_6685,plain,
    ! [X28221,X28222,X28223] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28223),esk312_3(X28221,X28222,X28223)),X28221))
        | c_Relation_Orefl__on(X28223,X28221,X28222)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28223,X28223),tc_HOL_Obool)),X28222),hAPP(hAPP(c_Product__Type_OSigma(X28223,X28223),X28221),hAPP(c_COMBK(tc_fun(X28223,tc_HOL_Obool),X28223),X28221)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28223,X28223)),hAPP(hAPP(c_Product__Type_OPair(X28223,X28223),esk312_3(X28221,X28222,X28223)),esk312_3(X28221,X28222,X28223))),X28222))
        | c_Relation_Orefl__on(X28223,X28221,X28222)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28223,X28223),tc_HOL_Obool)),X28222),hAPP(hAPP(c_Product__Type_OSigma(X28223,X28223),X28221),hAPP(c_COMBK(tc_fun(X28223,tc_HOL_Obool),X28223),X28221)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).

fof(i_0_6686,plain,
    ! [X28165,X28166,X28167,X28168,X28169,X28170,X28171] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28167,X28167),tc_HOL_Obool)),X28165),hAPP(hAPP(c_Product__Type_OSigma(X28167,X28167),X28166),hAPP(c_COMBK(tc_fun(X28167,tc_HOL_Obool),X28167),X28166))))
        | ~ c_Relation_Orefl__on(X28167,X28166,X28165) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28167),X28168),X28166))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28167,X28167)),hAPP(hAPP(c_Product__Type_OPair(X28167,X28167),X28168),X28168)),X28165))
        | ~ c_Relation_Orefl__on(X28167,X28166,X28165) )
      & ( hBOOL(hAPP(hAPP(c_member(X28171),esk310_3(X28169,X28170,X28171)),X28170))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28171,X28171),tc_HOL_Obool)),X28169),hAPP(hAPP(c_Product__Type_OSigma(X28171,X28171),X28170),hAPP(c_COMBK(tc_fun(X28171,tc_HOL_Obool),X28171),X28170))))
        | c_Relation_Orefl__on(X28171,X28170,X28169) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28171,X28171)),hAPP(hAPP(c_Product__Type_OPair(X28171,X28171),esk310_3(X28169,X28170,X28171)),esk310_3(X28169,X28170,X28171))),X28169))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28171,X28171),tc_HOL_Obool)),X28169),hAPP(hAPP(c_Product__Type_OSigma(X28171,X28171),X28170),hAPP(c_COMBK(tc_fun(X28171,tc_HOL_Obool),X28171),X28170))))
        | c_Relation_Orefl__on(X28171,X28170,X28169) ) ),
    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_refl__on__def])])])])])]) ).

fof(i_0_6687,plain,
    ! [X25323,X25324,X25325] : hAPP(hAPP(c_Set_Oinsert(X25325),X25324),X25323) = hAPP(c_Set_OCollect(X25325),hAPP(hAPP(c_COMBS(X25325,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25325),c_fdisj),hAPP(hAPP(c_COMBC(X25325,X25325,tc_HOL_Obool),c_fequal),X25324))),hAPP(hAPP(c_COMBC(X25325,tc_fun(X25325,tc_HOL_Obool),tc_HOL_Obool),c_member(X25325)),X25323))),
    inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).

fof(i_0_6688,plain,
    ! [X25320,X25321,X25322] : hAPP(hAPP(c_Set_Oinsert(X25322),X25321),X25320) = hAPP(c_Set_OCollect(X25322),hAPP(hAPP(c_COMBS(X25322,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25322),c_fdisj),hAPP(hAPP(c_COMBC(X25322,X25322,tc_HOL_Obool),c_fequal),X25321))),hAPP(hAPP(c_COMBC(X25322,tc_fun(X25322,tc_HOL_Obool),tc_HOL_Obool),c_member(X25322)),X25320))),
    inference(variable_rename,[status(thm)],[fact_insert__compr]) ).

cnf(i_0_6689,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk361_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5405]) ).

fof(i_0_6690,plain,
    ! [X29690,X29691,X29692,X29693,X29694,X29695] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29695,X29695)),hAPP(hAPP(c_Product__Type_OPair(X29695,X29695),X29694),X29693)),X29692))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29695),tc_List_Olist(X29695))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29695),tc_List_Olist(X29695)),X29691),X29690)),c_List_Olistrel(X29695,X29692)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29695),tc_List_Olist(X29695))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29695),tc_List_Olist(X29695)),hAPP(hAPP(c_List_Olist_OCons(X29695),X29694),X29691)),hAPP(hAPP(c_List_Olist_OCons(X29695),X29693),X29690))),c_List_Olistrel(X29695,X29692))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).

cnf(i_0_6691,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk362_4(X3,X4,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5404]) ).

fof(i_0_6692,plain,
    ! [X17979,X17980,X17981,X17982,X17983] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17983,X17983,X17982,X17981,X17980),X17979))
      | hBOOL(hAPP(hAPP(c_member(X17983),X17981),X17980))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X17983,X17982,hAPP(hAPP(c_Set_Oinsert(X17983),X17981),X17980)),X17979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5426])]) ).

cnf(i_0_6693,plain,
    ( c_List_OdropWhile(X1,X2,X3) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),c_List_OdropWhile(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5427]) ).

cnf(i_0_6694,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5428]) ).

cnf(i_0_6695,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5429]) ).

fof(i_0_6696,plain,
    ! [X27226] :
      ( X27226 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27226),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__emptyI])]) ).

fof(i_0_6697,plain,
    ! [X27305,X27306] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27306),X27305)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27305),X27306)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_minus]) ).

fof(i_0_6698,plain,
    ! [X27256] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27256),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(variable_rename,[status(thm)],[fact_wmin__emptyI]) ).

fof(i_0_6699,plain,
    ! [X18144,X18145,X18146,X18147,X18148,X18149] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18149,X18148,X18147)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18149,X18148,X18147,X18146,X18145),X18144))
      | hAPP(hAPP(c_Finite__Set_Ofold(X18149,X18148,X18147),X18146),X18145) = X18144 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).

fof(i_0_6700,plain,
    ! [X17855,X17856,X17857,X17858,X17859] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17859,X17858,X17857,X17856,c_Orderings_Obot__class_Obot(tc_fun(X17859,tc_HOL_Obool))),X17855))
      | X17855 = X17856 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).

fof(i_0_6701,plain,
    ! [X26576,X26577,X26578,X26579,X26580] :
      ( ~ c_Equiv__Relations_Oequiv(X26580,X26579,X26578)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26580,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26580,X26580,X26578),hAPP(hAPP(c_Set_Oinsert(X26580),X26577),c_Orderings_Obot__class_Obot(tc_fun(X26580,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26580,X26580,X26578),hAPP(hAPP(c_Set_Oinsert(X26580),X26576),c_Orderings_Obot__class_Obot(tc_fun(X26580,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(X26580),X26577),X26579))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X26580,X26580)),hAPP(hAPP(c_Product__Type_OPair(X26580,X26580),X26576),X26577)),X26578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).

fof(i_0_6702,plain,
    ! [X20286,X20287,X20288,X20289,X20290,X20291] :
      ( ( hBOOL(hAPP(hAPP(X20288,X20287),X20290))
        | ~ hBOOL(hAPP(hAPP(c_member(X20291),X20290),c_SetInterval_Oord_OgreaterThanAtMost(X20291,X20289,X20288,X20287,X20286))) )
      & ( hBOOL(hAPP(hAPP(X20289,X20290),X20286))
        | ~ hBOOL(hAPP(hAPP(c_member(X20291),X20290),c_SetInterval_Oord_OgreaterThanAtMost(X20291,X20289,X20288,X20287,X20286))) )
      & ( ~ hBOOL(hAPP(hAPP(X20288,X20287),X20290))
        | ~ hBOOL(hAPP(hAPP(X20289,X20290),X20286))
        | hBOOL(hAPP(hAPP(c_member(X20291),X20290),c_SetInterval_Oord_OgreaterThanAtMost(X20291,X20289,X20288,X20287,X20286))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).

fof(i_0_6703,plain,
    ! [X20280,X20281,X20282,X20283,X20284,X20285] :
      ( ( hBOOL(hAPP(hAPP(X20283,X20281),X20284))
        | ~ hBOOL(hAPP(hAPP(c_member(X20285),X20284),c_SetInterval_Oord_OatLeastLessThan(X20285,X20283,X20282,X20281,X20280))) )
      & ( hBOOL(hAPP(hAPP(X20282,X20284),X20280))
        | ~ hBOOL(hAPP(hAPP(c_member(X20285),X20284),c_SetInterval_Oord_OatLeastLessThan(X20285,X20283,X20282,X20281,X20280))) )
      & ( ~ hBOOL(hAPP(hAPP(X20283,X20281),X20284))
        | ~ hBOOL(hAPP(hAPP(X20282,X20284),X20280))
        | hBOOL(hAPP(hAPP(c_member(X20285),X20284),c_SetInterval_Oord_OatLeastLessThan(X20285,X20283,X20282,X20281,X20280))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).

fof(i_0_6704,plain,
    ! [X24568,X24569,X24570,X24571,X24572] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk209_5(X24568,X24569,X24570,X24571,X24572)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24572),X24569),X24571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24572),X24568),X24570)
        | ~ c_Nat__Transfer_Onat__set(X24570)
        | X24571 != X24570
        | ~ class_Groups_Ocomm__monoid__add(X24572)
        | ~ class_Groups_Ocomm__monoid__mult(X24572) )
      & ( hAPP(X24569,esk209_5(X24568,X24569,X24570,X24571,X24572)) != hAPP(X24568,esk209_5(X24568,X24569,X24570,X24571,X24572))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24572),X24569),X24571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24572),X24568),X24570)
        | ~ c_Nat__Transfer_Onat__set(X24570)
        | X24571 != X24570
        | ~ class_Groups_Ocomm__monoid__add(X24572)
        | ~ class_Groups_Ocomm__monoid__mult(X24572) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J])])])]) ).

fof(i_0_6705,plain,
    ! [X24941,X24942,X24943,X24944,X24945] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk218_5(X24941,X24942,X24943,X24944,X24945)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24945),X24942),X24944) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24945),X24941),X24943)
        | ~ c_Nat__Transfer_Onat__set(X24943)
        | X24944 != X24943
        | ~ class_Groups_Ocomm__monoid__add(X24945)
        | ~ class_Groups_Ocomm__monoid__mult(X24945) )
      & ( hAPP(X24942,esk218_5(X24941,X24942,X24943,X24944,X24945)) != hAPP(X24941,esk218_5(X24941,X24942,X24943,X24944,X24945))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24945),X24942),X24944) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24945),X24941),X24943)
        | ~ c_Nat__Transfer_Onat__set(X24943)
        | X24944 != X24943
        | ~ class_Groups_Ocomm__monoid__add(X24945)
        | ~ class_Groups_Ocomm__monoid__mult(X24945) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J])])])]) ).

fof(i_0_6706,plain,
    ! [X31877,X31878] : c_Random_Oselect__weight(X31878,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31878),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31878,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31878,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31878)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31877)) = c_Random_Oselect__weight(X31878,X31877),
    inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(i_0_6707,plain,
    ! [X31879,X31880] : c_Random_Opick(X31880,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31880),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31880,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31880,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31880)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31879)) = c_Random_Opick(X31880,X31879),
    inference(variable_rename,[status(thm)],[fact_pick__drop__zero]) ).

cnf(i_0_6708,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).

cnf(i_0_6709,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).

fof(i_0_6710,plain,
    ! [X33654,X33655,X33656,X33657,X33658] :
      ( ~ c_Fun_Obij__betw(X33658,X33657,X33656,c_Orderings_Otop__class_Otop(tc_fun(X33658,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33657,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(X33655,X33658,X33654,c_Orderings_Otop__class_Otop(tc_fun(X33655,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33658,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X33655,X33657,c_Orderings_Otop__class_Otop(tc_fun(X33655,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X33658,X33657,X33655,X33656),X33654)) = hAPP(c_Fun_Ocomp(X33658,X33655,X33657,c_Hilbert__Choice_Oinv__into(X33655,X33658,c_Orderings_Otop__class_Otop(tc_fun(X33655,tc_HOL_Obool)),X33654)),c_Hilbert__Choice_Oinv__into(X33658,X33657,c_Orderings_Otop__class_Otop(tc_fun(X33658,tc_HOL_Obool)),X33656)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__distrib])]) ).

cnf(i_0_6711,plain,
    hAPP(c_List_OremoveAll(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_OremoveAll(X1,X2),X3)),hAPP(c_List_OremoveAll(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_5430]) ).

cnf(i_0_6712,plain,
    c_List_OremoveAll(X1,X2) = c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5431]) ).

fof(i_0_6713,plain,
    ! [X27749,X27750,X27751,X27752] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27752,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27752,X27751),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27752,X27751),tc_HOL_Obool)),X27750),X27749))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27752,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27752,X27751),X27750)),hAPP(c_Relation_ODomain(X27752,X27751),X27749)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).

fof(i_0_6714,plain,
    ! [X27671,X27672,X27673,X27674] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27674,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27673,X27674),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27673,X27674),tc_HOL_Obool)),X27672),X27671))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27674,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27673,X27674),X27672)),hAPP(c_Relation_ORange(X27673,X27674),X27671)))),
    inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).

fof(i_0_6715,plain,
    ! [X23662,X23663,X23664,X23665,X23666] :
      ( ~ class_Fields_Ofield__inverse__zero(X23666)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23665),X23664))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23665,X23666),hAPP(hAPP(c_COMBS(X23665,X23666,X23666),hAPP(hAPP(c_COMBB(X23666,tc_fun(X23666,X23666),X23665),c_Rings_Oinverse__class_Odivide(X23666)),X23663)),X23662)),X23664) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23666),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23665,X23666),X23663),X23664)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23665,X23666),X23662),X23664)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).

fof(i_0_6716,plain,
    ! [X19078,X19079,X19080,X19081,X19082] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19082)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19081),X19080))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19081,X19082),hAPP(hAPP(c_COMBS(X19081,X19082,X19082),hAPP(hAPP(c_COMBB(X19082,tc_fun(X19082,X19082),X19081),c_Groups_Otimes__class_Otimes(X19082)),X19079)),X19078)),X19080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19082),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19081,X19082),X19079),X19080)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19081,X19082),X19078),X19080)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).

fof(i_0_6717,plain,
    ! [X18128,X18129,X18130,X18131,X18132] :
      ( ~ class_Groups_Ocomm__monoid__add(X18132)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18131),X18130))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18131,X18132),hAPP(hAPP(c_COMBS(X18131,X18132,X18132),hAPP(hAPP(c_COMBB(X18132,tc_fun(X18132,X18132),X18131),c_Groups_Oplus__class_Oplus(X18132)),X18129)),X18128)),X18130) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18132),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18131,X18132),X18129),X18130)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18131,X18132),X18128),X18130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).

fof(i_0_6718,plain,
    ! [X17868,X17869,X17870,X17871,X17872,X17873] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17873,X17872,X17871,X17870,X17869),X17868))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17873),X17869)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).

fof(i_0_6719,plain,
    ! [X30573,X30574] : hAPP(c_List_Orotate1(X30574),X30573) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X30574),X30574,c_List_Olist_ONil(X30574),hAPP(hAPP(c_COMBB(tc_List_Olist(X30574),tc_fun(tc_List_Olist(X30574),tc_List_Olist(X30574)),X30574),hAPP(c_COMBC(tc_List_Olist(X30574),tc_List_Olist(X30574),tc_List_Olist(X30574)),c_List_Oappend(X30574))),hAPP(hAPP(c_COMBC(X30574,tc_List_Olist(X30574),tc_List_Olist(X30574)),c_List_Olist_OCons(X30574)),c_List_Olist_ONil(X30574)))),X30573),
    inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).

fof(i_0_6720,plain,
    ! [X19027,X19028,X19029,X19030,X19031] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19031)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19030,X19031),hAPP(hAPP(c_COMBS(X19030,X19031,X19031),hAPP(hAPP(c_COMBB(X19031,tc_fun(X19031,X19031),X19030),c_Groups_Otimes__class_Otimes(X19031)),X19029)),X19028)),X19027) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19031),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19030,X19031),X19029),X19027)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19030,X19031),X19028),X19027)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).

fof(i_0_6721,plain,
    ! [X18109,X18110,X18111,X18112,X18113] :
      ( ~ class_Groups_Ocomm__monoid__add(X18113)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18112,X18113),hAPP(hAPP(c_COMBS(X18112,X18113,X18113),hAPP(hAPP(c_COMBB(X18113,tc_fun(X18113,X18113),X18112),c_Groups_Oplus__class_Oplus(X18113)),X18111)),X18110)),X18109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18113),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18112,X18113),X18111),X18109)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18112,X18113),X18110),X18109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).

fof(i_0_6722,plain,
    ! [X17715,X17716,X17717,X17718,X17719] :
      ( ~ class_Groups_Oab__group__add(X17719)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17718,X17719),hAPP(hAPP(c_COMBS(X17718,X17719,X17719),hAPP(hAPP(c_COMBB(X17719,tc_fun(X17719,X17719),X17718),c_Groups_Ominus__class_Ominus(X17719)),X17717)),X17716)),X17715) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17719),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17718,X17719),X17717),X17715)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17718,X17719),X17716),X17715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).

fof(i_0_6723,plain,
    ! [X26847,X26848,X26849,X26850,X26851] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26851,X26850),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26849),X26848)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26847))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26851,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26850),X26847)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26849),X26847)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26850),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26849,X26847))),X26848)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).

fof(i_0_6724,plain,
    ! [X31420,X31421,X31422] : c_List_Olistsp(X31422,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31422,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X31422,tc_fun(X31422,tc_HOL_Obool),tc_HOL_Obool),c_member(X31422)),X31421)),hAPP(hAPP(c_COMBC(X31422,tc_fun(X31422,tc_HOL_Obool),tc_HOL_Obool),c_member(X31422)),X31420))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X31422),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31422),tc_fun(tc_List_Olist(X31422),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X31422))),c_List_Olists(X31422,X31421))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31422),tc_fun(tc_List_Olist(X31422),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X31422))),c_List_Olists(X31422,X31420))),
    inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).

fof(i_0_6725,plain,
    ! [X31316,X31317] : c_Random_Oselect__weight(X31317,X31316) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X31317,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X31317),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X31317)),X31316)))),hAPP(hAPP(c_COMBB(X31317,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X31317,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X31317,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X31317,X31316))),
    inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).

fof(i_0_6726,plain,
    ! [X27975,X27976,X27977,X27978,X27979,X27980] : hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),hAPP(hAPP(c_Set_Oinsert(X27980),X27978),X27977)),hAPP(c_COMBK(tc_fun(X27979,tc_HOL_Obool),X27980),hAPP(hAPP(c_Set_Oinsert(X27979),X27976),X27975))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X27980,X27979)),hAPP(hAPP(c_Product__Type_OPair(X27980,X27979),X27978),X27976)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27980,X27979),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),X27977),hAPP(c_COMBK(tc_fun(X27979,tc_HOL_Obool),X27980),hAPP(hAPP(c_Set_Oinsert(X27979),X27976),X27975)))),hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),hAPP(hAPP(c_Set_Oinsert(X27980),X27978),X27977)),hAPP(c_COMBK(tc_fun(X27979,tc_HOL_Obool),X27980),X27975)))),
    inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).

fof(i_0_6727,plain,
    ! [X23602,X23603,X23604,X23605,X23606] :
      ( ~ class_Fields_Ofield(X23606)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23606),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23605,X23606),X23604),X23603)),X23602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23605,X23606),hAPP(hAPP(c_COMBC(X23605,X23606,X23606),hAPP(hAPP(c_COMBB(X23606,tc_fun(X23606,X23606),X23605),c_Rings_Oinverse__class_Odivide(X23606)),X23604)),X23602)),X23603) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).

fof(i_0_6728,plain,
    ! [X18469,X18470,X18471,X18472,X18473] :
      ( ~ class_Rings_Osemiring__0(X18473)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18473),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18472,X18473),X18471),X18470)),X18469) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18472,X18473),hAPP(hAPP(c_COMBC(X18472,X18473,X18473),hAPP(hAPP(c_COMBB(X18473,tc_fun(X18473,X18473),X18472),c_Groups_Otimes__class_Otimes(X18473)),X18471)),X18469)),X18470) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).

fof(i_0_6729,plain,
    ! [X26394,X26395,X26396,X26397,X26398] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26398,X26397),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26396),X26395)))
      | X26397 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26394))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26397),X26394)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26396),X26394)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26397),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26396,X26394))),X26395)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).

fof(i_0_6730,plain,
    ! [X29672,X29673,X29674,X29675,X29676] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29676),tc_List_Olist(X29676))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29676),tc_List_Olist(X29676)),X29675),X29674)),c_List_Olistrel(X29676,c_Transitive__Closure_Ortrancl(X29676,X29673))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29676),tc_List_Olist(X29676))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29676),tc_List_Olist(X29676)),X29674),X29672)),c_List_Olistrel(X29676,c_Transitive__Closure_Ortrancl(X29676,X29673))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29676),tc_List_Olist(X29676))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29676),tc_List_Olist(X29676)),X29675),X29672)),c_List_Olistrel(X29676,c_Transitive__Closure_Ortrancl(X29676,X29673)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).

cnf(i_0_6731,plain,
    hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orev(X1),X3)) = hAPP(c_List_Orev(X1),hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_5432]) ).

cnf(i_0_6732,plain,
    c_List_Orotate(X1,X2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5433]) ).

fof(i_0_6733,plain,
    ! [X17874,X17875,X17876] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17876,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17876,tc_fun(X17876,tc_HOL_Obool),tc_HOL_Obool),c_member(X17876)),X17875)),hAPP(hAPP(c_COMBC(X17876,tc_fun(X17876,tc_HOL_Obool),tc_HOL_Obool),c_member(X17876)),X17874)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17876,tc_HOL_Obool)),X17875),X17874)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17876,tc_HOL_Obool)),X17875),X17874))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17876,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17876,tc_fun(X17876,tc_HOL_Obool),tc_HOL_Obool),c_member(X17876)),X17875)),hAPP(hAPP(c_COMBC(X17876,tc_fun(X17876,tc_HOL_Obool),tc_HOL_Obool),c_member(X17876)),X17874))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

cnf(i_0_6734,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5434]) ).

cnf(i_0_6735,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5435]) ).

fof(i_0_6736,plain,
    ! [X27592,X27593,X27594,X27595] :
      ( ~ c_FunDef_Oreduction__pair(X27595,X27594)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool)),X27593),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool),tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool)),X27594)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool)),X27592),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool),tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool)),X27594)))
      | ~ c_Wellfounded_Owf(X27595,X27592)
      | c_Wellfounded_Owf(X27595,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27595,X27595),tc_HOL_Obool)),X27593),X27592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).

fof(i_0_6737,plain,
    ! [X25185,X25186,X25187] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25187,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25187,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X25187,tc_HOL_Obool),tc_HOL_Obool)),X25186),X25185))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25187,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25187,tc_HOL_Obool),X25186)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25187,tc_HOL_Obool),X25185)))),
    inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).

fof(i_0_6738,plain,
    ! [X17459,X17460,X17461,X17462,X17463,X17464,X17465] :
      ( X17465 = X17464
      | c_Fun_Ofun__upd(X17463,X17462,c_Fun_Ofun__upd(X17463,X17462,X17461,X17465,X17460),X17464,X17459) = c_Fun_Ofun__upd(X17463,X17462,c_Fun_Ofun__upd(X17463,X17462,X17461,X17464,X17459),X17465,X17460) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).

fof(i_0_6739,plain,
    ! [X29174,X29175,X29176,X29177,X29178] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29178,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29177,X29178,X29176),X29175)),X29174))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29177,tc_HOL_Obool)),X29175),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29177,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29178,X29177,hAPP(c_Relation_Oconverse(X29177,X29178),X29176)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29178,tc_HOL_Obool)),X29174))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29177,tc_HOL_Obool)),X29175),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29177,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29178,X29177,hAPP(c_Relation_Oconverse(X29177,X29178),X29176)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29178,tc_HOL_Obool)),X29174)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29178,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29177,X29178,X29176),X29175)),X29174)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])]) ).

cnf(i_0_6740,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5436]) ).

cnf(i_0_6741,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5437]) ).

fof(i_0_6742,plain,
    ! [X21139,X21140,X21141,X21142] : hAPP(c_Set_Oimage(X21142,X21141,X21140),X21139) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21142,tc_fun(X21141,tc_HOL_Obool)),X21139),hAPP(hAPP(c_COMBC(X21142,tc_fun(X21141,tc_HOL_Obool),tc_fun(X21141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X21141,tc_fun(tc_fun(X21141,tc_HOL_Obool),tc_fun(X21141,tc_HOL_Obool)),X21142),c_Set_Oinsert(X21141)),X21140)),c_Orderings_Obot__class_Obot(tc_fun(X21141,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).

fof(i_0_6743,plain,
    ! [X25343,X25344,X25345] :
      ( ( ~ hBOOL(hAPP(X25345,X25344))
        | hAPP(c_Set_OCollect(X25343),hAPP(hAPP(c_COMBS(X25343,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25343),c_fconj),hAPP(hAPP(c_COMBC(X25343,X25343,tc_HOL_Obool),c_fequal),X25344))),X25345)) = hAPP(hAPP(c_Set_Oinsert(X25343),X25344),c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X25345,X25344))
        | hAPP(c_Set_OCollect(X25343),hAPP(hAPP(c_COMBS(X25343,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25343),c_fconj),hAPP(hAPP(c_COMBC(X25343,X25343,tc_HOL_Obool),c_fequal),X25344))),X25345)) = c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5438])]) ).

fof(i_0_6744,plain,
    ! [X29619,X29620,X29621,X29622,X29623] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29623),tc_List_Olist(X29623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29623),tc_List_Olist(X29623)),X29622),X29621)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29623),c_List_Olistrel1(X29623,X29620))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29623),tc_List_Olist(X29623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29623),tc_List_Olist(X29623)),hAPP(hAPP(c_List_Olist_OCons(X29623),X29619),X29622)),hAPP(hAPP(c_List_Olist_OCons(X29623),X29619),X29621))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29623),c_List_Olistrel1(X29623,X29620)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).

fof(i_0_6745,plain,
    ! [X27214,X27215,X27216,X27217] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27217),X27216))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27215),X27214))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27217),X27215)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27216),X27214))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).

fof(i_0_6746,plain,
    ! [X27194,X27195,X27196,X27197] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27197),X27196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27195),X27194))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27197),X27195)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27196),X27194))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).

fof(i_0_6747,plain,
    ! [X28982,X28983,X28984] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28984,X28984),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28984,X28984),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28984,X28983)),c_Transitive__Closure_Ortrancl(X28984,X28982))),c_Transitive__Closure_Ortrancl(X28984,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28984,X28984),tc_HOL_Obool)),X28983),X28982)))),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(i_0_6748,plain,
    ! [X33200,X33201,X33202,X33203,X33204] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33204),tc_List_Olist(X33204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33204),tc_List_Olist(X33204)),X33203),X33202)),c_List_Olexord(X33204,X33201)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33204),tc_List_Olist(X33204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33204),tc_List_Olist(X33204)),X33202),X33200)),c_List_Olexord(X33204,X33201)))
      | ~ c_Relation_Otrans(X33204,X33201)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33204),tc_List_Olist(X33204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33204),tc_List_Olist(X33204)),X33203),X33200)),c_List_Olexord(X33204,X33201))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).

fof(i_0_6749,plain,
    ! [X25518,X25519,X25520,X25521,X25522] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25522,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25521,X25522,X25520),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25521,tc_HOL_Obool)),X25519),X25518))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25522,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25521,X25522,X25520),X25519)),hAPP(c_Relation_OImage(X25521,X25522,X25520),X25518)))),
    inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).

fof(i_0_6750,plain,
    ! [X20886,X20887,X20888,X20889,X20890] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20890,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20889,X20890,X20888),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20889,tc_HOL_Obool)),X20887),X20886))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20890,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20889,X20890,X20888),X20887)),hAPP(c_Set_Oimage(X20889,X20890,X20888),X20886)))),
    inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).

fof(i_0_6751,plain,
    ! [X29465,X29466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk370_2(X29465,X29466)))
        | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29466)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29465)) )
      & ( ~ hBOOL(hAPP(X29466,esk370_2(X29465,X29466)))
        | ~ hBOOL(hAPP(X29465,esk370_2(X29465,X29466)))
        | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29466)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29465)) )
      & ( hBOOL(hAPP(X29466,esk370_2(X29465,X29466)))
        | hBOOL(hAPP(X29465,esk370_2(X29465,X29466)))
        | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29466)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29465)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong])])])]) ).

cnf(i_0_6752,plain,
    c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7) = c_List_Ofoldr(X4,X2,hAPP(c_Fun_Ocomp(X1,tc_fun(X2,X2),X4,X3),X5),X6,X7),
    inference(split_conjunct,[status(thm)],[i_0_5439]) ).

fof(i_0_6753,plain,
    ! [X27228,X27229,X27230,X27231] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27231),X27230))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27231),X27229)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27230),X27228))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).

fof(i_0_6754,plain,
    ! [X27210,X27211,X27212,X27213] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27213),X27212))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27213),X27211)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27212),X27210))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).

fof(i_0_6755,plain,
    ! [X29905,X29906] : c_List_Olists(X29906,X29905) = hAPP(c_Set_OCollect(tc_List_Olist(X29906)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29906),tc_fun(X29906,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29906,tc_HOL_Obool),tc_fun(tc_fun(X29906,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29906)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29906,tc_HOL_Obool))),c_List_Oset(X29906))),X29905)),
    inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).

fof(i_0_6756,plain,
    ! [X17419,X17420,X17421,X17422,X17423,X17424] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17424),X17423),X17422))
        | hAPP(c_Set_Oimage(X17424,X17421,c_Fun_Ofun__upd(X17424,X17421,X17420,X17423,X17419)),X17422) = hAPP(hAPP(c_Set_Oinsert(X17421),X17419),hAPP(c_Set_Oimage(X17424,X17421,X17420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17424,tc_HOL_Obool)),X17422),hAPP(hAPP(c_Set_Oinsert(X17424),X17423),c_Orderings_Obot__class_Obot(tc_fun(X17424,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17424),X17423),X17422))
        | hAPP(c_Set_Oimage(X17424,X17421,c_Fun_Ofun__upd(X17424,X17421,X17420,X17423,X17419)),X17422) = hAPP(c_Set_Oimage(X17424,X17421,X17420),X17422) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5440])]) ).

fof(i_0_6757,plain,
    ! [X30508,X30509,X30510,X30511,X30512,X30513] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30513),tc_List_Olist(X30513))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30513),tc_List_Olist(X30513)),X30512),X30511)),c_List_Olistrel1(X30513,X30510)))
        | X30509 != X30508
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30513),tc_List_Olist(X30513))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30513),tc_List_Olist(X30513)),hAPP(hAPP(c_List_Oappend(X30513),X30512),X30509)),hAPP(hAPP(c_List_Oappend(X30513),X30511),X30508))),c_List_Olistrel1(X30513,X30510))) )
      & ( X30512 != X30511
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30513),tc_List_Olist(X30513))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30513),tc_List_Olist(X30513)),X30509),X30508)),c_List_Olistrel1(X30513,X30510)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30513),tc_List_Olist(X30513))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30513),tc_List_Olist(X30513)),hAPP(hAPP(c_List_Oappend(X30513),X30512),X30509)),hAPP(hAPP(c_List_Oappend(X30513),X30511),X30508))),c_List_Olistrel1(X30513,X30510))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).

fof(i_0_6758,plain,
    ! [X30514,X30515,X30516,X30517,X30518] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30518),tc_List_Olist(X30518))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30518),tc_List_Olist(X30518)),X30517),X30516)),c_List_Olexord(X30518,X30515)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30518),tc_List_Olist(X30518))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30518),tc_List_Olist(X30518)),hAPP(hAPP(c_List_Oappend(X30518),X30514),X30517)),hAPP(hAPP(c_List_Oappend(X30518),X30514),X30516))),c_List_Olexord(X30518,X30515))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).

fof(i_0_6759,plain,
    ! [X29624,X29625,X29626,X29627,X29628] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29628),tc_List_Olist(X29628))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29628),tc_List_Olist(X29628)),X29627),X29626)),c_List_Olistrel1(X29628,X29625)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29628),tc_List_Olist(X29628))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29628),tc_List_Olist(X29628)),hAPP(hAPP(c_List_Olist_OCons(X29628),X29624),X29627)),hAPP(hAPP(c_List_Olist_OCons(X29628),X29624),X29626))),c_List_Olistrel1(X29628,X29625))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).

cnf(i_0_6760,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5441]) ).

fof(i_0_6761,plain,
    ! [X25431] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X25431))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(i_0_6762,plain,
    ! [X33681,X33682,X33683,X33684,X33685,X33686,X33687,X33688] :
      ( ( ~ c_Fun_Obij__betw(X33687,X33683,X33682,X33684,X33681)
        | c_Fun_Obij__betw(X33688,X33683,hAPP(c_Fun_Ocomp(X33687,X33683,X33688,X33682),X33686),X33685,X33681)
        | ~ c_Fun_Obij__betw(X33688,X33687,X33686,X33685,X33684) )
      & ( ~ c_Fun_Obij__betw(X33688,X33683,hAPP(c_Fun_Ocomp(X33687,X33683,X33688,X33682),X33686),X33685,X33681)
        | c_Fun_Obij__betw(X33687,X33683,X33682,X33684,X33681)
        | ~ c_Fun_Obij__betw(X33688,X33687,X33686,X33685,X33684) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff])])]) ).

fof(i_0_6763,plain,
    ! [X31057,X31058,X31059,X31060,X31061,X31062] : hAPP(hAPP(c_List_Ozip(X31062,X31061),hAPP(hAPP(c_List_Omap(X31060,X31062),X31059),X31058)),X31057) = hAPP(hAPP(c_List_Omap(tc_prod(X31060,X31061),tc_prod(X31062,X31061)),hAPP(c_Product__Type_Oprod_Oprod__case(X31060,X31061,tc_prod(X31062,X31061)),hAPP(hAPP(c_COMBB(X31062,tc_fun(X31061,tc_prod(X31062,X31061)),X31060),c_Product__Type_OPair(X31062,X31061)),X31059))),hAPP(hAPP(c_List_Ozip(X31060,X31061),X31058),X31057)),
    inference(variable_rename,[status(thm)],[fact_zip__map1]) ).

fof(i_0_6764,plain,
    ! [X27204,X27205,X27206] : c_Wellfounded_Omlex__prod(X27206,X27205,X27204) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X27206),X27206),c_Wellfounded_Olex__prod(tc_Nat_Onat,X27206,c_Wellfounded_Oless__than,X27204)),hAPP(hAPP(c_COMBS(X27206,X27206,tc_prod(tc_Nat_Onat,X27206)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X27206,tc_prod(tc_Nat_Onat,X27206)),X27206),c_Product__Type_OPair(tc_Nat_Onat,X27206)),X27205)),c_COMBI(X27206))),
    inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).

fof(i_0_6765,plain,
    ! [X17425,X17426,X17427] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17427),esk18_3(X17425,X17426,X17427)))
        | hBOOL(hAPP(X17425,c_Orderings_Obot__class_Obot(tc_fun(X17427,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17425,X17426))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17427),X17426)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17427),esk17_3(X17425,X17426,X17427)),esk18_3(X17425,X17426,X17427)))
        | hBOOL(hAPP(X17425,c_Orderings_Obot__class_Obot(tc_fun(X17427,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17425,X17426))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17427),X17426)) )
      & ( hBOOL(hAPP(X17425,esk18_3(X17425,X17426,X17427)))
        | hBOOL(hAPP(X17425,c_Orderings_Obot__class_Obot(tc_fun(X17427,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17425,X17426))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17427),X17426)) )
      & ( ~ hBOOL(hAPP(X17425,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17427,tc_HOL_Obool)),esk18_3(X17425,X17426,X17427)),hAPP(hAPP(c_Set_Oinsert(X17427),esk17_3(X17425,X17426,X17427)),c_Orderings_Obot__class_Obot(tc_fun(X17427,tc_HOL_Obool))))))
        | hBOOL(hAPP(X17425,c_Orderings_Obot__class_Obot(tc_fun(X17427,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17425,X17426))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17427),X17426)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__empty__induct])])])]) ).

fof(i_0_6766,plain,
    ! [X27939,X27940,X27941,X27942,X27943,X27944] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27941,X27944),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27941,X27944),X27940),hAPP(c_COMBK(tc_fun(X27944,tc_HOL_Obool),X27941),X27942))),hAPP(hAPP(c_Product__Type_OSigma(X27941,X27944),X27939),hAPP(c_COMBK(tc_fun(X27944,tc_HOL_Obool),X27941),X27942))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27941,tc_HOL_Obool)),X27940),X27939))
        | ~ hBOOL(hAPP(hAPP(c_member(X27944),X27943),X27942)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27941,tc_HOL_Obool)),X27940),X27939))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27941,X27944),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27941,X27944),X27940),hAPP(c_COMBK(tc_fun(X27944,tc_HOL_Obool),X27941),X27942))),hAPP(hAPP(c_Product__Type_OSigma(X27941,X27944),X27939),hAPP(c_COMBK(tc_fun(X27944,tc_HOL_Obool),X27941),X27942))))
        | ~ hBOOL(hAPP(hAPP(c_member(X27944),X27943),X27942)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).

cnf(i_0_6767,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)))),c_COMBI(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5442]) ).

fof(i_0_6768,plain,
    ! [X29340,X29341,X29342,X29343,X29344,X29345] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29345,X29345)),hAPP(hAPP(c_Product__Type_OPair(X29345,X29345),X29344),X29343)),X29342))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29345,X29345)),hAPP(hAPP(c_Product__Type_OPair(X29345,X29345),X29343),X29341)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29345,X29345),tc_HOL_Obool),X29340),X29342)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29345,X29345)),hAPP(hAPP(c_Product__Type_OPair(X29345,X29345),X29344),X29341)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29345,X29345),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29340)),X29342))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).

fof(i_0_6769,plain,
    ! [X29346,X29347,X29348,X29349,X29350,X29351] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29351,X29351)),hAPP(hAPP(c_Product__Type_OPair(X29351,X29351),X29350),X29349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29351,X29351),tc_HOL_Obool),X29348),X29347)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29351,X29351)),hAPP(hAPP(c_Product__Type_OPair(X29351,X29351),X29349),X29346)),X29347))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29351,X29351)),hAPP(hAPP(c_Product__Type_OPair(X29351,X29351),X29350),X29346)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29351,X29351),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29348)),X29347))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).

fof(i_0_6770,plain,
    ! [X33689,X33690,X33691,X33692,X33693] :
      ( ~ c_Fun_Obij__betw(X33693,X33692,X33691,c_Orderings_Otop__class_Otop(tc_fun(X33693,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33692,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(X33692,X33690,X33689,c_Orderings_Otop__class_Otop(tc_fun(X33692,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33690,tc_HOL_Obool)))
      | c_Fun_Obij__betw(X33693,X33690,hAPP(c_Fun_Ocomp(X33692,X33690,X33693,X33689),X33691),c_Orderings_Otop__class_Otop(tc_fun(X33693,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33690,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__comp])]) ).

fof(i_0_6771,plain,
    ! [X24546,X24547,X24548,X24549,X24550] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24550,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24549,X24550,X24548),X24547)),X24546))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X24550,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X24549,tc_HOL_Obool),tc_fun(X24550,tc_HOL_Obool),c_Set_Oimage(X24549,X24550,X24548)),hAPP(c_Set_OPow(X24549),X24547))),hAPP(c_Set_OPow(X24550),X24546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).

fof(i_0_6772,plain,
    ! [X26919,X26920] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26919),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X26920,X26919) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26920),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26919))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26920),X26919))) )
      & ( X26920 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26920,X26919) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26919),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26920),X26919))) )
      & ( X26919 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26920,X26919) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26919),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26920),X26919))) )
      & ( X26920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X26919 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26920,X26919) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X26920),X26919)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26920))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26919)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26919),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26920),X26919))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5443])])]) ).

cnf(i_0_6773,plain,
    c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),X6) = c_List_Ofoldr(X1,X2,X3,X4,c_List_Ofoldr(X1,X2,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_5444]) ).

fof(i_0_6774,plain,
    ! [X31313,X31314,X31315] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X31315),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X31315)),X31314))))
      | hBOOL(hAPP(hAPP(c_member(X31315),hAPP(c_Product__Type_Ofst(X31315,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X31315,X31314),X31313))),hAPP(c_List_Oset(X31315),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X31315),X31315),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X31315)),X31314)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).

fof(i_0_6775,plain,
    ! [X24953,X24954,X24955,X24956] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24956)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24956),hAPP(c_Groups_Oabs__class_Oabs(X24956),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24955,X24956),X24954),X24953))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24955,X24956),hAPP(hAPP(c_COMBB(X24956,X24956,X24955),c_Groups_Oabs__class_Oabs(X24956)),X24954)),X24953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).

fof(i_0_6776,plain,
    ! [X31850,X31851,X31852] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31852,tc_HOL_Obool)),hAPP(c_List_Oset(X31852),X31851)),hAPP(hAPP(c_Set_Oinsert(X31852),X31850),c_Orderings_Obot__class_Obot(tc_fun(X31852,tc_HOL_Obool)))) = hAPP(c_List_Oset(X31852),hAPP(c_List_Ofilter(X31852,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31852),c_fNot),hAPP(hAPP(c_COMBC(X31852,X31852,tc_HOL_Obool),c_fequal),X31850))),X31851)),
    inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).

fof(i_0_6777,plain,
    ! [X31772,X31773,X31774,X31775] : hAPP(c_List_Ofilter(X31775,X31774),hAPP(c_List_Ofilter(X31775,X31773),X31772)) = hAPP(c_List_Ofilter(X31775,hAPP(hAPP(c_COMBS(X31775,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31775),c_fconj),X31773)),X31774)),X31772),
    inference(variable_rename,[status(thm)],[fact_filter__filter]) ).

fof(i_0_6778,plain,
    ! [X27753,X27754,X27755,X27756] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27756,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27756,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27756,X27755),X27754)),hAPP(c_Relation_ODomain(X27756,X27755),X27753))),hAPP(c_Relation_ODomain(X27756,X27755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27756,X27755),tc_HOL_Obool)),X27754),X27753)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(i_0_6779,plain,
    ! [X27634,X27635,X27636,X27637] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27637,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27637,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27636,X27637),X27635)),hAPP(c_Relation_ORange(X27636,X27637),X27634))),hAPP(c_Relation_ORange(X27636,X27637),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27636,X27637),tc_HOL_Obool)),X27635),X27634)))),
    inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).

fof(i_0_6780,plain,
    ! [X18230,X18231,X18232,X18233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),c_Orderings_Obot__class_Obot(tc_fun(X18233,tc_HOL_Obool))))),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),c_Orderings_Obot__class_Obot(tc_fun(X18233,tc_HOL_Obool))))),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),c_Orderings_Obot__class_Obot(tc_fun(X18233,tc_HOL_Obool))))),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18233),X18231),X18232))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),c_Orderings_Obot__class_Obot(tc_fun(X18233,tc_HOL_Obool))))),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),c_Orderings_Obot__class_Obot(tc_fun(X18233,tc_HOL_Obool))))),X18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18233,tc_HOL_Obool)),X18232),hAPP(hAPP(c_Set_Oinsert(X18233),X18231),X18230))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5445])])]) ).

fof(i_0_6781,plain,
    ! [X29656,X29657,X29658] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29658,X29658)),hAPP(hAPP(c_Product__Type_OPair(X29658,X29658),esk381_3(X29656,X29657,X29658)),esk381_3(X29656,X29657,X29658))),X29657))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29658),tc_List_Olist(X29658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29658),tc_List_Olist(X29658)),X29656),X29656)),c_List_Olexord(X29658,X29657))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5446])])]) ).

fof(i_0_6782,hypothesis,
    ! [X34276] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X34276)),hAPP(v_c0,X34276)),hAPP(v_Q_H,X34276))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X34276)),hAPP(v_c0,X34276)),hAPP(v_Q,X34276))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])]) ).

fof(i_0_6783,plain,
    ! [X17430] : c_Finite__Set_Ofun__left__comm__idem(X17430,tc_fun(X17430,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17430,tc_HOL_Obool),tc_fun(tc_fun(X17430,tc_HOL_Obool),tc_fun(X17430,tc_HOL_Obool)),X17430),hAPP(c_COMBC(tc_fun(X17430,tc_HOL_Obool),tc_fun(X17430,tc_HOL_Obool),tc_fun(X17430,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X17430,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X17430,tc_fun(X17430,tc_HOL_Obool),tc_fun(X17430,tc_HOL_Obool)),c_Set_Oinsert(X17430)),c_Orderings_Obot__class_Obot(tc_fun(X17430,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

cnf(i_0_6784,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5447]) ).

fof(i_0_6785,plain,
    ! [X19312,X19313,X19314] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19314),X19313))
      | ~ hBOOL(hAPP(hAPP(c_member(X19314),X19312),X19313))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19314),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19314,tc_HOL_Obool)),X19313),hAPP(hAPP(c_Set_Oinsert(X19314),X19312),c_Orderings_Obot__class_Obot(tc_fun(X19314,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X19314),X19313))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).

fof(i_0_6786,plain,
    ! [X27021,X27022,X27023,X27024,X27025,X27026] : hAPP(hAPP(c_COMBS(tc_prod(X27026,X27025),X27025,X27024),hAPP(hAPP(c_COMBB(X27023,tc_fun(X27025,X27024),tc_prod(X27026,X27025)),X27022),hAPP(hAPP(c_COMBB(X27026,X27023,tc_prod(X27026,X27025)),X27021),c_Product__Type_Ofst(X27026,X27025)))),c_Product__Type_Osnd(X27026,X27025)) = hAPP(c_Product__Type_Oprod_Oprod__case(X27026,X27025,X27024),hAPP(hAPP(c_COMBB(X27023,tc_fun(X27025,X27024),X27026),X27022),X27021)),
    inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).

fof(i_0_6787,plain,
    ! [X32002,X32003,X32004,X32005,X32006] :
      ( ~ class_Orderings_Olinorder(X32006)
      | ~ hBOOL(hAPP(hAPP(c_member(X32005),X32004),hAPP(c_List_Oset(X32005),X32003)))
      | ~ c_List_Olinorder__class_Osorted(X32006,hAPP(hAPP(c_List_Omap(X32005,X32006),X32002),X32003))
      | hAPP(c_List_Ohd(X32005),hAPP(c_List_Ofilter(X32005,hAPP(hAPP(c_COMBB(X32006,tc_HOL_Obool,X32005),hAPP(c_fequal,hAPP(X32002,X32004))),X32002)),X32003)) != X32004
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32005,X32006,X32002),X32004),c_List_Oremove1(X32005,X32004,X32003)) = X32003 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).

fof(i_0_6788,plain,
    ! [X33797,X33798,X33799,X33800,X33801,X33802,X33803] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33803,tc_HOL_Obool)),X33802),X33801) != c_Orderings_Obot__class_Obot(tc_fun(X33803,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33800,tc_HOL_Obool)),X33799),X33798) != c_Orderings_Obot__class_Obot(tc_fun(X33800,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(X33803,X33800,X33797,X33802,X33799)
      | ~ c_Fun_Obij__betw(X33803,X33800,X33797,X33801,X33798)
      | c_Fun_Obij__betw(X33803,X33800,X33797,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33803,tc_HOL_Obool)),X33802),X33801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33800,tc_HOL_Obool)),X33799),X33798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__Disj__Un])]) ).

fof(i_0_6789,plain,
    ! [X27287,X27288] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27288),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27287),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27288),X27287)),c_Int_Ointrel)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27288),X27287)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27288),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27287),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff])]) ).

fof(i_0_6790,plain,
    ! [X33108,X33109,X33110,X33111] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk498_4(X33108,X33109,X33110,X33111)),X33109))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk499_4(X33108,X33109,X33110,X33111)),X33109))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( esk498_4(X33108,X33109,X33110,X33111) != esk499_4(X33108,X33109,X33110,X33111)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(X33110),esk500_4(X33108,X33109,X33110,X33111)),esk498_4(X33108,X33109,X33110,X33111)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(X33110),esk500_4(X33108,X33109,X33110,X33111)),esk499_4(X33108,X33109,X33110,X33111)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hAPP(X33108,esk500_4(X33108,X33109,X33110,X33111)) != c_Groups_Ozero__class_Ozero(X33111)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk497_4(X33108,X33109,X33110,X33111)),X33109))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk498_4(X33108,X33109,X33110,X33111)),X33109))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33110,tc_HOL_Obool)),esk499_4(X33108,X33109,X33110,X33111)),X33109))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( esk498_4(X33108,X33109,X33110,X33111) != esk499_4(X33108,X33109,X33110,X33111)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(X33110),esk500_4(X33108,X33109,X33110,X33111)),esk498_4(X33108,X33109,X33110,X33111)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hBOOL(hAPP(hAPP(c_member(X33110),esk500_4(X33108,X33109,X33110,X33111)),esk499_4(X33108,X33109,X33110,X33111)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) )
      & ( hAPP(X33108,esk500_4(X33108,X33109,X33110,X33111)) != c_Groups_Ozero__class_Ozero(X33111)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33110,tc_HOL_Obool),X33109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33110,tc_HOL_Obool),X33111),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33110,X33111),X33108)),X33109)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33110),esk497_4(X33108,X33109,X33110,X33111)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33110,tc_HOL_Obool)),X33109))
        | ~ class_Groups_Ocomm__monoid__add(X33111) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__UNION__zero])])])]) ).

fof(i_0_6791,plain,
    ! [X17769,X17770,X17771,X17772] : c_Nitpick_Ofold__graph_H(X17772,X17771,X17770,X17769,c_Orderings_Obot__class_Obot(tc_fun(X17772,tc_HOL_Obool)),X17769),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(i_0_6792,plain,
    ! [X17765,X17766,X17767,X17768] : c_Nitpick_Ofold__graph_H(X17768,X17767,X17766,X17765,c_Orderings_Obot__class_Obot(tc_fun(X17768,tc_HOL_Obool)),X17765),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(i_0_6793,plain,
    ! [X17518,X17519,X17520,X17521,X17522] :
      ( ( c_Fun_Oinj__on(X17522,X17521,X17520,X17518)
        | ~ c_Fun_Oinj__on(X17522,X17521,X17520,hAPP(hAPP(c_Set_Oinsert(X17522),X17519),X17518)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17521),hAPP(X17520,X17519)),hAPP(c_Set_Oimage(X17522,X17521,X17520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17522,tc_HOL_Obool)),X17518),hAPP(hAPP(c_Set_Oinsert(X17522),X17519),c_Orderings_Obot__class_Obot(tc_fun(X17522,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(X17522,X17521,X17520,hAPP(hAPP(c_Set_Oinsert(X17522),X17519),X17518)) )
      & ( ~ c_Fun_Oinj__on(X17522,X17521,X17520,X17518)
        | hBOOL(hAPP(hAPP(c_member(X17521),hAPP(X17520,X17519)),hAPP(c_Set_Oimage(X17522,X17521,X17520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17522,tc_HOL_Obool)),X17518),hAPP(hAPP(c_Set_Oinsert(X17522),X17519),c_Orderings_Obot__class_Obot(tc_fun(X17522,tc_HOL_Obool)))))))
        | c_Fun_Oinj__on(X17522,X17521,X17520,hAPP(hAPP(c_Set_Oinsert(X17522),X17519),X17518)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5448])])]) ).

fof(i_0_6794,plain,
    ! [X28125,X28126] : c_Product__Type_Omap__pair(X28126,X28126,X28125,X28125,c_Fun_Oid(X28126),c_Fun_Oid(X28125)) = c_Fun_Oid(tc_prod(X28126,X28125)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oid]) ).

cnf(i_0_6795,plain,
    c_Product__Type_Oapfst(X1,X1,X2,c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5449]) ).

fof(i_0_6796,plain,
    ! [X28115,X28116] : c_Product__Type_Omap__pair(X28116,X28116,X28115,X28115,c_COMBI(X28116),c_COMBI(X28115)) = c_Fun_Oid(tc_prod(X28116,X28115)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity]) ).

cnf(i_0_6797,plain,
    c_Product__Type_Oapsnd(X1,X1,X2,c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X2,X1)),
    inference(split_conjunct,[status(thm)],[i_0_5450]) ).

fof(i_0_6798,plain,
    ! [X18169,X18170,X18171,X18172,X18173] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18173,X18172,X18171)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18173),X18170))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18173,X18172,X18171,X18169,X18170),hAPP(hAPP(c_Finite__Set_Ofold(X18173,X18172,X18171),X18169),X18170))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])]) ).

fof(i_0_6799,plain,
    ! [X33673,X33674,X33675,X33676,X33677,X33678,X33679,X33680] :
      ( ~ c_Fun_Obij__betw(X33680,X33679,X33678,X33677,X33676)
      | ~ c_Fun_Obij__betw(X33679,X33675,X33674,X33676,X33673)
      | c_Fun_Obij__betw(X33680,X33675,hAPP(c_Fun_Ocomp(X33679,X33675,X33680,X33674),X33678),X33677,X33673) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__trans])]) ).

cnf(i_0_6800,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_negateSnd__def]) ).

fof(i_0_6801,plain,
    ! [X19834,X19835,X19836] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19836),X19835))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19836,tc_HOL_Obool)),X19835),hAPP(hAPP(c_Set_Oinsert(X19836),X19834),c_Orderings_Obot__class_Obot(tc_fun(X19836,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X19836),X19835))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).

fof(i_0_6802,plain,
    ! [X27384,X27385,X27386,X27387,X27388,X27389,X27390] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27390,X27389),tc_HOL_Obool)),X27388),X27387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27389,X27386),tc_HOL_Obool)),X27385),X27384))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27390,X27386),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27390,X27389,X27386),X27388),X27385)),hAPP(hAPP(c_Relation_Orel__comp(X27390,X27389,X27386),X27387),X27384))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).

fof(i_0_6803,plain,
    ! [X26555,X26556,X26557,X26558,X26559] :
      ( ~ c_Equiv__Relations_Oequiv(X26559,X26558,X26557)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26559,X26559)),hAPP(hAPP(c_Product__Type_OPair(X26559,X26559),X26556),X26555)),X26557))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26559,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26559,X26559,X26557),hAPP(hAPP(c_Set_Oinsert(X26559),X26556),c_Orderings_Obot__class_Obot(tc_fun(X26559,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26559,X26559,X26557),hAPP(hAPP(c_Set_Oinsert(X26559),X26555),c_Orderings_Obot__class_Obot(tc_fun(X26559,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).

fof(i_0_6804,plain,
    ! [X17705,X17706,X17707,X17708,X17709,X17710] :
      ( ~ c_Fun_Oinj__on(X17710,X17709,X17708,X17707)
      | ~ hBOOL(hAPP(hAPP(c_member(X17709),X17706),hAPP(c_Set_Oimage(X17710,X17709,X17708),X17707)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17710,tc_HOL_Obool)),X17707),X17705))
      | hBOOL(hAPP(hAPP(c_member(X17710),hAPP(c_Fun_Othe__inv__into(X17710,X17709,X17707,X17708),X17706)),X17705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).

fof(i_0_6805,plain,
    ! [X19747,X19748,X19749,X19750,X19751] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19751),hAPP(c_Set_Oimage(X19750,X19751,X19749),c_Orderings_Otop__class_Otop(tc_fun(X19750,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X19748),hAPP(c_Set_Oimage(X19750,X19748,hAPP(hAPP(c_COMBB(X19751,X19748,X19750),X19747),X19749)),c_Orderings_Otop__class_Otop(tc_fun(X19750,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_6806,plain,
    ! [X21885,X21886,X21887] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21887,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21887,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21887,tc_HOL_Obool),X21886)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21887,tc_HOL_Obool),X21885))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21887,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X21887,tc_HOL_Obool),tc_HOL_Obool)),X21886),X21885)))),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).

fof(i_0_6807,plain,
    ! [X29726,X29727,X29728] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29728,X29728),tc_HOL_Obool)),X29727),hAPP(hAPP(c_Product__Type_OSigma(X29728,X29728),X29726),hAPP(c_COMBK(tc_fun(X29728,tc_HOL_Obool),X29728),X29726))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29728),tc_List_Olist(X29728)),tc_HOL_Obool)),c_List_Olistrel(X29728,X29727)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X29728),tc_List_Olist(X29728)),c_List_Olists(X29728,X29726)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X29728),tc_HOL_Obool),tc_List_Olist(X29728)),c_List_Olists(X29728,X29726))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).

fof(i_0_6808,plain,
    ! [X28579,X28580,X28581,X28582,X28583,X28584,X28585] :
      ( ~ class_Groups_Oab__semigroup__mult(X28585)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28584),X28583))
      | ~ c_Fun_Oinj__on(X28584,X28582,X28581,X28583)
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28585,X28582,c_Groups_Otimes__class_Otimes(X28585)),X28580),X28579),hAPP(c_Set_Oimage(X28584,X28582,X28581),X28583)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28585,X28584,c_Groups_Otimes__class_Otimes(X28585)),hAPP(c_Fun_Ocomp(X28582,X28585,X28584,X28580),X28581)),X28579),X28583) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).

fof(i_0_6809,plain,
    ! [X24814,X24815,X24816,X24817] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24817))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24816),X24815))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24815),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24814,X24817))),X24816)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24815),X24817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).

fof(i_0_6810,plain,
    ! [X25639,X25640,X25641,X25642] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25642),esk256_4(X25639,X25640,X25641,X25642)),X25641))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25642),hAPP(hAPP(c_Finite__Set_Ofold(X25642,X25642,c_Lattices_Osemilattice__sup__class_Osup(X25642)),X25639),X25641)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25642),X25640),X25639)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25642),X25641))
        | ~ class_Lattices_Osemilattice__sup(X25642) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25642),esk256_4(X25639,X25640,X25641,X25642)),X25640))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25642),hAPP(hAPP(c_Finite__Set_Ofold(X25642,X25642,c_Lattices_Osemilattice__sup__class_Osup(X25642)),X25639),X25641)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25642),X25640),X25639)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25642),X25641))
        | ~ class_Lattices_Osemilattice__sup(X25642) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup])])])]) ).

fof(i_0_6811,plain,
    ! [X19298,X19299,X19300,X19301] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19301),esk64_4(X19298,X19299,X19300,X19301)),X19300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19301),hAPP(hAPP(c_Finite__Set_Ofold(X19301,X19301,c_Orderings_Oord__class_Omax(X19301)),X19298),X19300)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19301),X19299),X19298)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19301),X19300))
        | ~ class_Orderings_Olinorder(X19301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19301),esk64_4(X19298,X19299,X19300,X19301)),X19299))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19301),hAPP(hAPP(c_Finite__Set_Ofold(X19301,X19301,c_Orderings_Oord__class_Omax(X19301)),X19298),X19300)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19301),X19299),X19298)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19301),X19300))
        | ~ class_Orderings_Olinorder(X19301) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup])])])]) ).

fof(i_0_6812,plain,
    ! [X33790,X33791,X33792,X33793,X33794,X33795,X33796] :
      ( ~ c_Fun_Obij__betw(X33796,X33795,X33794,X33793,X33792)
      | ~ c_Fun_Obij__betw(X33796,X33795,X33794,X33791,X33790)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33795,tc_HOL_Obool)),X33792),X33790) != c_Orderings_Obot__class_Obot(tc_fun(X33795,tc_HOL_Obool))
      | c_Fun_Obij__betw(X33796,X33795,X33794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33796,tc_HOL_Obool)),X33793),X33791),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33795,tc_HOL_Obool)),X33792),X33790)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__combine])]) ).

cnf(i_0_6813,plain,
    c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5451]) ).

fof(i_0_6814,plain,
    ! [X17536,X17537,X17538,X17539] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),c_Orderings_Obot__class_Obot(tc_fun(X17539,tc_HOL_Obool))))),X17536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),X17536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),X17536))
        | hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17539),X17537),X17538))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),c_Orderings_Obot__class_Obot(tc_fun(X17539,tc_HOL_Obool))))),X17536))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),X17536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),c_Orderings_Obot__class_Obot(tc_fun(X17539,tc_HOL_Obool))))),X17536))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17539,tc_HOL_Obool)),X17538),hAPP(hAPP(c_Set_Oinsert(X17539),X17537),X17536))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5452])])]) ).

fof(i_0_6815,plain,
    ! [X29641,X29642,X29643,X29644,X29645] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29645,X29645)),hAPP(hAPP(c_Product__Type_OPair(X29645,X29645),X29644),X29643)),X29642))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29645),tc_List_Olist(X29645))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29645),tc_List_Olist(X29645)),hAPP(hAPP(c_List_Olist_OCons(X29645),X29644),X29641)),hAPP(hAPP(c_List_Olist_OCons(X29645),X29643),X29641))),c_List_Olistrel1(X29645,X29642))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).

cnf(i_0_6816,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5453]) ).

cnf(i_0_6817,plain,
    ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5454]) ).

fof(i_0_6818,plain,
    ! [X32124,X32125,X32126] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32126),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32126))),X32125)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32124),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32126))),X32125)))
      | hAPP(hAPP(c_List_Omap(tc_List_Olist(X32126),X32126),hAPP(hAPP(c_COMBC(tc_List_Olist(X32126),tc_Nat_Onat,X32126),c_List_Onth(X32126)),X32124)),hAPP(c_List_Ofilter(tc_List_Olist(X32126),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32126)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32124)),c_Nat_Osize__class_Osize(tc_List_Olist(X32126)))),c_List_Otranspose(X32126,X32125))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X32126)),X32125),X32124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).

fof(i_0_6819,plain,
    ! [X28559,X28560,X28561] : c_Hilbert__Choice_OEps(tc_prod(X28561,X28560),X28559) = c_Hilbert__Choice_OEps(tc_prod(X28561,X28560),hAPP(c_Product__Type_Oprod_Oprod__case(X28561,X28560,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28560,tc_prod(X28561,X28560)),tc_fun(X28560,tc_HOL_Obool),X28561),hAPP(c_COMBB(tc_prod(X28561,X28560),tc_HOL_Obool,X28560),X28559)),c_Product__Type_OPair(X28561,X28560)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).

fof(i_0_6820,plain,
    ! [X26762,X26763,X26764] : c_HOL_OThe(tc_prod(X26764,X26763),X26762) = c_HOL_OThe(tc_prod(X26764,X26763),hAPP(c_Product__Type_Oprod_Oprod__case(X26764,X26763,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X26763,tc_prod(X26764,X26763)),tc_fun(X26763,tc_HOL_Obool),X26764),hAPP(c_COMBB(tc_prod(X26764,X26763),tc_HOL_Obool,X26763),X26762)),c_Product__Type_OPair(X26764,X26763)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).

fof(i_0_6821,plain,
    ! [X17238,X17239,X17240,X17241,X17242,X17243,X17244] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17244,X17243,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17244)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17244),X17242),X17241),X17240)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17244),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17244,X17243,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17244)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17244),X17240),X17239),X17238)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17244),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17244,X17243,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17244)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17244),X17242),c_Com_Ocom_OSemi(X17241,X17239)),X17238)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17244),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Comp])]) ).

fof(i_0_6822,plain,
    ! [X29369,X29370,X29371,X29372,X29373,X29374,X29375,X29376] :
      ( ( ~ c_Relation_Ototal__on(X29371,X29370,X29369)
        | ~ hBOOL(hAPP(hAPP(c_member(X29371),X29372),X29370))
        | ~ hBOOL(hAPP(hAPP(c_member(X29371),X29373),X29370))
        | X29372 = X29373
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29371,X29371)),hAPP(hAPP(c_Product__Type_OPair(X29371,X29371),X29372),X29373)),X29369))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29371,X29371)),hAPP(hAPP(c_Product__Type_OPair(X29371,X29371),X29373),X29372)),X29369)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29376),esk347_3(X29374,X29375,X29376)),X29375))
        | c_Relation_Ototal__on(X29376,X29375,X29374) )
      & ( hBOOL(hAPP(hAPP(c_member(X29376),esk348_3(X29374,X29375,X29376)),X29375))
        | c_Relation_Ototal__on(X29376,X29375,X29374) )
      & ( esk347_3(X29374,X29375,X29376) != esk348_3(X29374,X29375,X29376)
        | c_Relation_Ototal__on(X29376,X29375,X29374) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29376,X29376)),hAPP(hAPP(c_Product__Type_OPair(X29376,X29376),esk347_3(X29374,X29375,X29376)),esk348_3(X29374,X29375,X29376))),X29374))
        | c_Relation_Ototal__on(X29376,X29375,X29374) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29376,X29376)),hAPP(hAPP(c_Product__Type_OPair(X29376,X29376),esk348_3(X29374,X29375,X29376)),esk347_3(X29374,X29375,X29376))),X29374))
        | c_Relation_Ototal__on(X29376,X29375,X29374) ) ),
    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_total__on__def])])])])])]) ).

fof(i_0_6823,plain,
    ! [X24920,X24921,X24922,X24923] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24923))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24922),X24921))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24921),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24920,X24923))),X24922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24921),X24923))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).

fof(i_0_6824,plain,
    ! [X29265,X29266,X29267,X29268,X29269] :
      ( ~ c_Relation_Osingle__valued(X29269,X29269,X29268)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29269,X29269)),hAPP(hAPP(c_Product__Type_OPair(X29269,X29269),X29267),X29266)),c_Transitive__Closure_Ortrancl(X29269,X29268)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29269,X29269)),hAPP(hAPP(c_Product__Type_OPair(X29269,X29269),X29267),X29265)),c_Transitive__Closure_Ortrancl(X29269,X29268)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29269,X29269)),hAPP(hAPP(c_Product__Type_OPair(X29269,X29269),X29266),X29265)),c_Transitive__Closure_Ortrancl(X29269,X29268)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29269,X29269)),hAPP(hAPP(c_Product__Type_OPair(X29269,X29269),X29265),X29266)),c_Transitive__Closure_Ortrancl(X29269,X29268))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).

fof(i_0_6825,plain,
    ! [X27476,X27477,X27478] :
      ( ~ c_Wellfounded_Owf(X27478,X27477)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27478,X27478),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27478,X27478,X27478),X27477),X27476)),X27477))
      | c_FunDef_Oreduction__pair(X27478,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X27478,X27478),tc_HOL_Obool),tc_fun(tc_prod(X27478,X27478),tc_HOL_Obool)),X27477),X27476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).

fof(i_0_6826,plain,
    ! [X24806,X24807,X24808,X24809] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24808),X24807))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24807),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24808),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24806,X24809))),X24807)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2])]) ).

fof(i_0_6827,plain,
    ! [X31318,X31319] : c_Random_Oselect(X31319,X31318) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X31319,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31319)),X31318)))),hAPP(hAPP(c_COMBB(X31319,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X31319,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X31319,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X31319,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X31319),X31318)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[fact_select__def]) ).

fof(i_0_6828,plain,
    ! [X26603,X26604] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26604),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X26603,X26604) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26603),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26604)) )
      & ( X26603 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26603,X26604) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26604),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X26604 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26603,X26604) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26604),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X26603 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X26604 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X26603,X26604) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X26603),X26604)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26603))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26604)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26604),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5455])])]) ).

fof(i_0_6829,plain,
    ! [X27297,X27298,X27299] :
      ( ~ class_Rings_Oring__1(X27299)
      | hAPP(c_Int_Oring__1__class_Oof__int(X27299),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27298),X27297)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27299),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27299),X27298)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27299),X27297)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).

cnf(i_0_6830,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk446_3(X2,X3,X1)),hAPP(c_List_Oset(X1),c_List_OdropWhile(X1,X3,X2))))
    | c_List_OtakeWhile(X1,X3,X2) = hAPP(c_List_Ofilter(X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5456]) ).

cnf(i_0_6831,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5457]) ).

cnf(i_0_6832,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5458]) ).

fof(i_0_6833,plain,
    ! [X17540,X17541,X17542,X17543] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17543,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17543,tc_HOL_Obool)),X17542),hAPP(hAPP(c_Set_Oinsert(X17543),X17541),c_Orderings_Obot__class_Obot(tc_fun(X17543,tc_HOL_Obool))))),X17540))
      | ~ hBOOL(hAPP(hAPP(c_member(X17543),X17541),X17542))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17543,tc_HOL_Obool)),X17542),hAPP(hAPP(c_Set_Oinsert(X17543),X17541),X17540))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).

fof(i_0_6834,plain,
    ! [X27312,X27313] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27313),X27312)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27313),X27312),
    inference(variable_rename,[status(thm)],[fact_nat]) ).

cnf(i_0_6835,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5459]) ).

cnf(i_0_6836,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Groups_Omonoid__mult(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5460]) ).

cnf(i_0_6837,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5461]) ).

fof(i_0_6838,plain,
    ! [X21088,X21089,X21090,X21091,X21092] :
      ( ( c_Fun_Oinj__on(X21092,X21091,X21090,X21089)
        | ~ c_Fun_Oinj__on(X21092,X21091,X21090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088)) )
      & ( c_Fun_Oinj__on(X21092,X21091,X21090,X21088)
        | ~ c_Fun_Oinj__on(X21092,X21091,X21090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21091,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21092,X21091,X21090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088))),hAPP(c_Set_Oimage(X21092,X21091,X21090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21092,tc_HOL_Obool)),X21088),X21089))) = c_Orderings_Obot__class_Obot(tc_fun(X21091,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(X21092,X21091,X21090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088)) )
      & ( ~ c_Fun_Oinj__on(X21092,X21091,X21090,X21089)
        | ~ c_Fun_Oinj__on(X21092,X21091,X21090,X21088)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21091,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21092,X21091,X21090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088))),hAPP(c_Set_Oimage(X21092,X21091,X21090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21092,tc_HOL_Obool)),X21088),X21089))) != c_Orderings_Obot__class_Obot(tc_fun(X21091,tc_HOL_Obool))
        | c_Fun_Oinj__on(X21092,X21091,X21090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21092,tc_HOL_Obool)),X21089),X21088)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).

fof(i_0_6839,plain,
    ! [X27100,X27101,X27102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X27102,tc_HOL_Obool)),X27101),X27100))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool)),X27101),X27100)),c_Wellfounded_Ofinite__psubset(X27102))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27102),X27100))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool)),X27101),X27100)),c_Wellfounded_Ofinite__psubset(X27102))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X27102,tc_HOL_Obool)),X27101),X27100))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27102),X27100))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27102,tc_HOL_Obool),tc_fun(X27102,tc_HOL_Obool)),X27101),X27100)),c_Wellfounded_Ofinite__psubset(X27102))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

fof(i_0_6840,plain,
    ! [X27769,X27770,X27771,X27772] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27772),X27771),hAPP(c_Relation_ODomain(X27772,X27770),X27769)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27772,X27770)),hAPP(hAPP(c_Product__Type_OPair(X27772,X27770),X27771),esk298_4(X27769,X27770,X27771,X27772))),X27769)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5462])])]) ).

fof(i_0_6841,plain,
    ! [X27734,X27735,X27736,X27737,X27739,X27740,X27741,X27742,X27743] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27737),X27736),hAPP(c_Relation_ODomain(X27737,X27735),X27734)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27737,X27735)),hAPP(hAPP(c_Product__Type_OPair(X27737,X27735),X27736),esk297_4(X27734,X27735,X27736,X27737))),X27734)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27742,X27740)),hAPP(hAPP(c_Product__Type_OPair(X27742,X27740),X27741),X27743)),X27739))
        | hBOOL(hAPP(hAPP(c_member(X27742),X27741),hAPP(c_Relation_ODomain(X27742,X27740),X27739))) ) ),
    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_Domain__iff])])])])]) ).

fof(i_0_6842,plain,
    ! [X24556,X24557,X24558] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X24558,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X24558,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X24558),X24557)),hAPP(c_Set_OPow(X24558),X24556))),hAPP(c_Set_OPow(X24558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24558,tc_HOL_Obool)),X24557),X24556)))),
    inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).

fof(i_0_6843,plain,
    ! [X33543,X33544,X33545,X33546,X33547] :
      ( ~ c_Fun_Oinj__on(X33547,X33546,X33545,c_Orderings_Otop__class_Otop(tc_fun(X33547,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33546,X33544,X33547,hAPP(c_Fun_Ocomp(X33547,X33544,X33546,X33543),c_Hilbert__Choice_Oinv__into(X33547,X33546,c_Orderings_Otop__class_Otop(tc_fun(X33547,tc_HOL_Obool)),X33545))),X33545) = X33543 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__o__cancel])]) ).

fof(i_0_6844,plain,
    ! [X20220,X20221,X20222,X20223,X20224] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20224),X20223))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20223),X20222)),X20221)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20224),X20222)),X20220)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20223),X20224)),X20222)),X20221)),X20220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).

cnf(i_0_6845,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
    inference(split_conjunct,[status(thm)],[i_0_5463]) ).

fof(i_0_6846,plain,
    ! [X31293,X31294,X31295] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X31295),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X31294),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X31294)),X31293))))
      | hBOOL(hAPP(hAPP(c_member(X31294),hAPP(c_Random_Opick(X31294,X31293),X31295)),hAPP(c_List_Oset(X31294),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X31294),X31294),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X31294)),X31293)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).

fof(i_0_6847,plain,
    ! [X27342,X27343,X27344,X27345,X27346,X27347,X27348,X27349] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27349,X27348)),hAPP(hAPP(c_Product__Type_OPair(X27349,X27348),X27347),X27346)),X27345))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27348,X27344)),hAPP(hAPP(c_Product__Type_OPair(X27348,X27344),X27346),X27343)),X27342))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27349,X27344)),hAPP(hAPP(c_Product__Type_OPair(X27349,X27344),X27347),X27343)),hAPP(hAPP(c_Relation_Orel__comp(X27349,X27348,X27344),X27345),X27342))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).

fof(i_0_6848,plain,
    ! [X32053,X32054,X32055,X32056,X32057] :
      ( ~ class_Orderings_Olinorder(X32057)
      | ~ c_List_Olinorder__class_Osorted(X32057,hAPP(hAPP(c_List_Omap(X32056,X32057),X32055),X32054))
      | c_List_Olinorder__class_Osorted(X32057,hAPP(hAPP(c_List_Omap(X32056,X32057),X32055),c_List_Olinorder__class_Oinsort__insert__key(X32056,X32057,X32055,X32053,X32054))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).

fof(i_0_6849,plain,
    ! [X31467,X31468,X31469,X31470,X31471,X31472,X31473] :
      ( ( c_List_Olist__all2(X31473,X31471,X31469,X31472,X31470)
        | ~ c_List_Olist__all2(X31473,X31471,X31469,hAPP(hAPP(c_List_Oappend(X31473),X31472),X31468),hAPP(hAPP(c_List_Oappend(X31471),X31470),X31467))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31473)),X31472) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31471)),X31470) )
      & ( c_List_Olist__all2(X31473,X31471,X31469,X31468,X31467)
        | ~ c_List_Olist__all2(X31473,X31471,X31469,hAPP(hAPP(c_List_Oappend(X31473),X31472),X31468),hAPP(hAPP(c_List_Oappend(X31471),X31470),X31467))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31473)),X31472) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31471)),X31470) )
      & ( ~ c_List_Olist__all2(X31473,X31471,X31469,X31472,X31470)
        | ~ c_List_Olist__all2(X31473,X31471,X31469,X31468,X31467)
        | c_List_Olist__all2(X31473,X31471,X31469,hAPP(hAPP(c_List_Oappend(X31473),X31472),X31468),hAPP(hAPP(c_List_Oappend(X31471),X31470),X31467))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31473)),X31472) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31471)),X31470) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__append])])]) ).

fof(i_0_6850,plain,
    ! [X19390,X19391,X19392,X19393,X19394,X19397,X19398,X19399,X19400,X19401,X19402] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19393),esk68_4(X19390,X19391,X19392,X19393)),X19391))
        | hBOOL(hAPP(hAPP(c_member(X19393),esk67_4(X19390,X19391,X19392,X19393)),X19392))
        | ~ hBOOL(hAPP(hAPP(c_member(X19393),X19394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19393,tc_HOL_Obool)),X19392),X19391)))
        | ~ hBOOL(hAPP(X19390,X19394)) )
      & ( hBOOL(hAPP(X19390,esk68_4(X19390,X19391,X19392,X19393)))
        | hBOOL(hAPP(hAPP(c_member(X19393),esk67_4(X19390,X19391,X19392,X19393)),X19392))
        | ~ hBOOL(hAPP(hAPP(c_member(X19393),X19394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19393,tc_HOL_Obool)),X19392),X19391)))
        | ~ hBOOL(hAPP(X19390,X19394)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19393),esk68_4(X19390,X19391,X19392,X19393)),X19391))
        | hBOOL(hAPP(X19390,esk67_4(X19390,X19391,X19392,X19393)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19393),X19394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19393,tc_HOL_Obool)),X19392),X19391)))
        | ~ hBOOL(hAPP(X19390,X19394)) )
      & ( hBOOL(hAPP(X19390,esk68_4(X19390,X19391,X19392,X19393)))
        | hBOOL(hAPP(X19390,esk67_4(X19390,X19391,X19392,X19393)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19393),X19394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19393,tc_HOL_Obool)),X19392),X19391)))
        | ~ hBOOL(hAPP(X19390,X19394)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19400),esk69_4(X19397,X19398,X19399,X19400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19400,tc_HOL_Obool)),X19399),X19398)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19400),X19401),X19399))
        | ~ hBOOL(hAPP(X19397,X19401)) )
      & ( hBOOL(hAPP(X19397,esk69_4(X19397,X19398,X19399,X19400)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19400),X19401),X19399))
        | ~ hBOOL(hAPP(X19397,X19401)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19400),esk69_4(X19397,X19398,X19399,X19400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19400,tc_HOL_Obool)),X19399),X19398)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19400),X19402),X19398))
        | ~ hBOOL(hAPP(X19397,X19402)) )
      & ( hBOOL(hAPP(X19397,esk69_4(X19397,X19398,X19399,X19400)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19400),X19402),X19398))
        | ~ hBOOL(hAPP(X19397,X19402)) ) ),
    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_bex__Un])])])])])]) ).

cnf(i_0_6851,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5464]) ).

fof(i_0_6852,plain,
    ! [X19404,X19405,X19406,X19407,X19409,X19410,X19411,X19412,X19413,X19414,X19417] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19407),X19409),X19406))
        | hBOOL(hAPP(X19404,X19409))
        | hBOOL(hAPP(hAPP(c_member(X19407),esk70_4(X19404,X19405,X19406,X19407)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19407,tc_HOL_Obool)),X19406),X19405))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19407),X19410),X19405))
        | hBOOL(hAPP(X19404,X19410))
        | hBOOL(hAPP(hAPP(c_member(X19407),esk70_4(X19404,X19405,X19406,X19407)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19407,tc_HOL_Obool)),X19406),X19405))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19407),X19409),X19406))
        | hBOOL(hAPP(X19404,X19409))
        | ~ hBOOL(hAPP(X19404,esk70_4(X19404,X19405,X19406,X19407))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19407),X19410),X19405))
        | hBOOL(hAPP(X19404,X19410))
        | ~ hBOOL(hAPP(X19404,esk70_4(X19404,X19405,X19406,X19407))) )
      & ( hBOOL(hAPP(hAPP(c_member(X19414),esk72_4(X19411,X19412,X19413,X19414)),X19412))
        | hBOOL(hAPP(hAPP(c_member(X19414),esk71_4(X19411,X19412,X19413,X19414)),X19413))
        | ~ hBOOL(hAPP(hAPP(c_member(X19414),X19417),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19414,tc_HOL_Obool)),X19413),X19412)))
        | hBOOL(hAPP(X19411,X19417)) )
      & ( ~ hBOOL(hAPP(X19411,esk72_4(X19411,X19412,X19413,X19414)))
        | hBOOL(hAPP(hAPP(c_member(X19414),esk71_4(X19411,X19412,X19413,X19414)),X19413))
        | ~ hBOOL(hAPP(hAPP(c_member(X19414),X19417),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19414,tc_HOL_Obool)),X19413),X19412)))
        | hBOOL(hAPP(X19411,X19417)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19414),esk72_4(X19411,X19412,X19413,X19414)),X19412))
        | ~ hBOOL(hAPP(X19411,esk71_4(X19411,X19412,X19413,X19414)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19414),X19417),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19414,tc_HOL_Obool)),X19413),X19412)))
        | hBOOL(hAPP(X19411,X19417)) )
      & ( ~ hBOOL(hAPP(X19411,esk72_4(X19411,X19412,X19413,X19414)))
        | ~ hBOOL(hAPP(X19411,esk71_4(X19411,X19412,X19413,X19414)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19414),X19417),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19414,tc_HOL_Obool)),X19413),X19412)))
        | hBOOL(hAPP(X19411,X19417)) ) ),
    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_ball__Un])])])])])]) ).

cnf(i_0_6853,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5465]) ).

cnf(i_0_6854,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5466]) ).

cnf(i_0_6855,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X2)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5428]) ).

fof(i_0_6856,plain,
    ! [X21504,X21505,X21506,X21507,X21508,X21509,X21510,X21511] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21511,tc_fun(X21510,tc_fun(X21509,tc_HOL_Obool))),X21508),X21507),X21506),X21505))
      | hBOOL(hAPP(hAPP(hAPP(X21507,X21504),X21506),X21505))
      | ~ hBOOL(hAPP(hAPP(c_member(X21511),X21504),X21508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5467])]) ).

fof(i_0_6857,plain,
    ! [X21496,X21497,X21498,X21499,X21500,X21501,X21502,X21503] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21503,tc_fun(X21502,tc_fun(X21501,tc_HOL_Obool))),X21500),X21499),X21498),X21497))
      | ~ hBOOL(hAPP(hAPP(c_member(X21503),X21496),X21500))
      | hBOOL(hAPP(hAPP(hAPP(X21499,X21496),X21498),X21497)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).

cnf(i_0_6858,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5468]) ).

cnf(i_0_6859,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_5469]) ).

cnf(i_0_6860,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5470]) ).

cnf(i_0_6861,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5471]) ).

cnf(i_0_6862,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5429]) ).

cnf(i_0_6863,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5428]) ).

fof(i_0_6864,plain,
    ! [X31460,X31461,X31462,X31463,X31464,X31465,X31466] :
      ( ~ c_List_Olist__all2(X31466,X31465,X31464,X31463,X31462)
      | ~ c_List_Olist__all2(X31466,X31465,X31464,X31461,X31460)
      | c_List_Olist__all2(X31466,X31465,X31464,hAPP(hAPP(c_List_Oappend(X31466),X31463),X31461),hAPP(hAPP(c_List_Oappend(X31465),X31462),X31460)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])]) ).

cnf(i_0_6865,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[fact_nat__2]) ).

fof(i_0_6866,plain,
    ! [X31224,X31225,X31226,X31227,X31228,X31229] :
      ( hBOOL(hAPP(hAPP(c_member(X31229),X31228),hAPP(c_List_Oset(X31229),X31227)))
      | hAPP(hAPP(c_List_Omap(X31229,X31226),c_Fun_Ofun__upd(X31229,X31226,X31225,X31228,X31224)),X31227) = hAPP(hAPP(c_List_Omap(X31229,X31226),X31225),X31227) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5472])]) ).

fof(i_0_6867,plain,
    ! [X28348,X28349,X28350,X28351,X28352,X28353,X28354] : hAPP(c_Fun_Ocomp(X28354,X28353,X28352,X28351),c_Fun_Ofun__upd(X28352,X28354,X28350,X28349,X28348)) = c_Fun_Ofun__upd(X28352,X28353,hAPP(c_Fun_Ocomp(X28354,X28353,X28352,X28351),X28350),X28349,hAPP(X28351,X28348)),
    inference(variable_rename,[status(thm)],[fact_fun__upd__comp]) ).

cnf(i_0_6868,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J]) ).

fof(i_0_6869,plain,
    ! [X25356,X25357,X25358,X25359] : hAPP(c_Set_Ovimage(X25359,X25358,X25357),X25356) = hAPP(c_Set_OCollect(X25359),hAPP(hAPP(c_COMBC(X25359,tc_fun(X25358,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X25358,tc_fun(tc_fun(X25358,tc_HOL_Obool),tc_HOL_Obool),X25359),c_member(X25358)),X25357)),X25356)),
    inference(variable_rename,[status(thm)],[fact_vimage__def]) ).

fof(i_0_6870,plain,
    ! [X30694,X30695,X30696,X30697,X30698] : hAPP(hAPP(c_List_Ozip(X30698,X30697),X30696),hAPP(hAPP(c_List_Oappend(X30697),X30695),X30694)) = hAPP(hAPP(c_List_Oappend(tc_prod(X30698,X30697)),hAPP(hAPP(c_List_Ozip(X30698,X30697),hAPP(hAPP(c_List_Otake(X30698),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30697)),X30695)),X30696)),X30695)),hAPP(hAPP(c_List_Ozip(X30698,X30697),hAPP(hAPP(c_List_Odrop(X30698),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30697)),X30695)),X30696)),X30694)),
    inference(variable_rename,[status(thm)],[fact_zip__append2]) ).

fof(i_0_6871,plain,
    ! [X29637,X29638,X29639,X29640] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29640),tc_List_Olist(X29640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29640),tc_List_Olist(X29640)),X29639),X29638)),c_List_Olistrel1(X29640,hAPP(c_Relation_Oconverse(X29640,X29640),X29637))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29640),tc_List_Olist(X29640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29640),tc_List_Olist(X29640)),X29639),X29638)),hAPP(c_Relation_Oconverse(tc_List_Olist(X29640),tc_List_Olist(X29640)),c_List_Olistrel1(X29640,X29637)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29640),tc_List_Olist(X29640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29640),tc_List_Olist(X29640)),X29639),X29638)),hAPP(c_Relation_Oconverse(tc_List_Olist(X29640),tc_List_Olist(X29640)),c_List_Olistrel1(X29640,X29637))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29640),tc_List_Olist(X29640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29640),tc_List_Olist(X29640)),X29639),X29638)),c_List_Olistrel1(X29640,hAPP(c_Relation_Oconverse(X29640,X29640),X29637)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).

fof(i_0_6872,plain,
    ! [X30369,X30370,X30371,X30372,X30373,X30375,X30376,X30377,X30378,X30379,X30380] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),esk407_5(X30369,X30370,X30371,X30372,X30373)) = X30370
        | X30370 = c_List_Olist_ONil(X30373)
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) != hAPP(hAPP(c_List_Oappend(X30373),X30370),X30369) )
      & ( X30371 = hAPP(hAPP(c_List_Oappend(X30373),esk407_5(X30369,X30370,X30371,X30372,X30373)),X30369)
        | X30370 = c_List_Olist_ONil(X30373)
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) != hAPP(hAPP(c_List_Oappend(X30373),X30370),X30369) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),esk407_5(X30369,X30370,X30371,X30372,X30373)) = X30370
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) = X30369
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) != hAPP(hAPP(c_List_Oappend(X30373),X30370),X30369) )
      & ( X30371 = hAPP(hAPP(c_List_Oappend(X30373),esk407_5(X30369,X30370,X30371,X30372,X30373)),X30369)
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) = X30369
        | hAPP(hAPP(c_List_Olist_OCons(X30373),X30372),X30371) != hAPP(hAPP(c_List_Oappend(X30373),X30370),X30369) )
      & ( X30376 != c_List_Olist_ONil(X30379)
        | hAPP(hAPP(c_List_Olist_OCons(X30379),X30378),X30377) != X30375
        | hAPP(hAPP(c_List_Olist_OCons(X30379),X30378),X30377) = hAPP(hAPP(c_List_Oappend(X30379),X30376),X30375) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X30379),X30378),X30380) != X30376
        | X30377 != hAPP(hAPP(c_List_Oappend(X30379),X30380),X30375)
        | hAPP(hAPP(c_List_Olist_OCons(X30379),X30378),X30377) = hAPP(hAPP(c_List_Oappend(X30379),X30376),X30375) ) ),
    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_Cons__eq__append__conv])])])])])]) ).

fof(i_0_6873,plain,
    ! [X30357,X30358,X30359,X30360,X30361,X30363,X30364,X30365,X30366,X30367,X30368] :
      ( ( X30360 = hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),esk406_5(X30357,X30358,X30359,X30360,X30361))
        | X30360 = c_List_Olist_ONil(X30361)
        | hAPP(hAPP(c_List_Oappend(X30361),X30360),X30359) != hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357) )
      & ( hAPP(hAPP(c_List_Oappend(X30361),esk406_5(X30357,X30358,X30359,X30360,X30361)),X30359) = X30357
        | X30360 = c_List_Olist_ONil(X30361)
        | hAPP(hAPP(c_List_Oappend(X30361),X30360),X30359) != hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357) )
      & ( X30360 = hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),esk406_5(X30357,X30358,X30359,X30360,X30361))
        | X30359 = hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357)
        | hAPP(hAPP(c_List_Oappend(X30361),X30360),X30359) != hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357) )
      & ( hAPP(hAPP(c_List_Oappend(X30361),esk406_5(X30357,X30358,X30359,X30360,X30361)),X30359) = X30357
        | X30359 = hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357)
        | hAPP(hAPP(c_List_Oappend(X30361),X30360),X30359) != hAPP(hAPP(c_List_Olist_OCons(X30361),X30358),X30357) )
      & ( X30366 != c_List_Olist_ONil(X30367)
        | X30365 != hAPP(hAPP(c_List_Olist_OCons(X30367),X30364),X30363)
        | hAPP(hAPP(c_List_Oappend(X30367),X30366),X30365) = hAPP(hAPP(c_List_Olist_OCons(X30367),X30364),X30363) )
      & ( X30366 != hAPP(hAPP(c_List_Olist_OCons(X30367),X30364),X30368)
        | hAPP(hAPP(c_List_Oappend(X30367),X30368),X30365) != X30363
        | hAPP(hAPP(c_List_Oappend(X30367),X30366),X30365) = hAPP(hAPP(c_List_Olist_OCons(X30367),X30364),X30363) ) ),
    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_append__eq__Cons__conv])])])])])]) ).

fof(i_0_6874,plain,
    ! [X33505,X33506,X33507,X33508,X33509] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33509),X33508),hAPP(c_Set_Oimage(X33507,X33509,X33506),X33505)))
      | hBOOL(hAPP(hAPP(c_member(X33507),hAPP(c_Hilbert__Choice_Oinv__into(X33507,X33509,X33505,X33506),X33508)),X33505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_6875,plain,
    ! [X19269,X19270] :
      ( ~ class_Orderings_Olinorder(X19270)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19270),X19269))
      | X19269 = c_Orderings_Obot__class_Obot(tc_fun(X19270,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19270),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19270),esk52_2(X19269,X19270)),esk53_2(X19269,X19270))),hAPP(hAPP(c_Set_Oinsert(X19270),esk52_2(X19269,X19270)),hAPP(hAPP(c_Set_Oinsert(X19270),esk53_2(X19269,X19270)),c_Orderings_Obot__class_Obot(tc_fun(X19270,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19270),c_Big__Operators_Olattice_OInf__fin(X19270,c_Orderings_Oord__class_Omin(X19270),X19269)),X19269)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])]) ).

fof(i_0_6876,plain,
    ! [X19265,X19266] :
      ( ~ class_Orderings_Olinorder(X19266)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19266),X19265))
      | X19265 = c_Orderings_Obot__class_Obot(tc_fun(X19266,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19266),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19266),esk50_2(X19265,X19266)),esk51_2(X19265,X19266))),hAPP(hAPP(c_Set_Oinsert(X19266),esk50_2(X19265,X19266)),hAPP(hAPP(c_Set_Oinsert(X19266),esk51_2(X19265,X19266)),c_Orderings_Obot__class_Obot(tc_fun(X19266,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19266),c_Big__Operators_Olattice_OSup__fin(X19266,c_Orderings_Oord__class_Omax(X19266),X19265)),X19265)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])]) ).

fof(i_0_6877,plain,
    ! [X28058,X28059,X28060,X28061] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28061),esk304_4(X28058,X28059,X28060,X28061)),X28060))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X28061,X28059)),hAPP(hAPP(c_Product__Type_OSigma(X28061,X28059),X28060),X28058)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28061,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28059,tc_HOL_Obool),tc_Nat_Onat,X28061),c_Finite__Set_Ocard(X28059)),X28058)),X28060)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28061),X28060)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28059),hAPP(X28058,esk304_4(X28058,X28059,X28060,X28061))))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X28061,X28059)),hAPP(hAPP(c_Product__Type_OSigma(X28061,X28059),X28060),X28058)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28061,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28059,tc_HOL_Obool),tc_Nat_Onat,X28061),c_Finite__Set_Ocard(X28059)),X28058)),X28060)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28061),X28060)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])]) ).

fof(i_0_6878,plain,
    ! [X17864,X17865,X17866,X17867] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17867,X17866,X17865,X17864,c_Orderings_Obot__class_Obot(tc_fun(X17867,tc_HOL_Obool))),X17864)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(i_0_6879,plain,
    ! [X17860,X17861,X17862,X17863] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17863,X17862,X17861,X17860,c_Orderings_Obot__class_Obot(tc_fun(X17863,tc_HOL_Obool))),X17860)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(i_0_6880,plain,
    ! [X27586,X27587,X27588] :
      ( ~ c_Wellfounded_Owf(X27588,X27587)
      | ~ c_Wellfounded_Owf(X27588,X27586)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27588,X27588),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27588,X27588,X27588),X27587),X27586)),X27587))
      | c_Wellfounded_Owf(X27588,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27588,X27588),tc_HOL_Obool)),X27587),X27586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).

fof(i_0_6881,plain,
    ! [X19192,X19193] :
      ( ~ class_Groups_Oab__semigroup__mult(X19193)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19193),X19192))
      | X19192 = c_Orderings_Obot__class_Obot(tc_fun(X19193,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19193),esk48_2(X19192,X19193)),esk49_2(X19192,X19193))),hAPP(hAPP(c_Set_Oinsert(X19193),esk48_2(X19192,X19193)),hAPP(hAPP(c_Set_Oinsert(X19193),esk49_2(X19192,X19193)),c_Orderings_Obot__class_Obot(tc_fun(X19193,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19193),hAPP(c_Finite__Set_Ofold1(X19193,c_Groups_Otimes__class_Otimes(X19193)),X19192)),X19192)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__in])])]) ).

cnf(i_0_6882,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5473]) ).

fof(i_0_6883,plain,
    ! [X23215,X23216,X23217,X23218,X23219] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23219),X23218)),X23217)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23219),X23216)),X23215)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23217))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23217),X23219))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23215),X23219))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23218),X23216)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).

fof(i_0_6884,plain,
    ! [X23237,X23238,X23239,X23240,X23241] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23241),X23240)),X23239)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23241),X23238)),X23237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23237),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23241),X23237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23241),X23239))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23238),X23240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).

fof(i_0_6885,plain,
    ! [X30946,X30947,X30948,X30949,X30950] :
      ( ~ class_Orderings_Olinorder(X30950)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30949),X30948))
      | hBOOL(hAPP(c_List_Odistinct(X30949),c_List_Olinorder__class_Oinsort__insert__key(X30949,X30950,X30947,X30946,X30948))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).

fof(i_0_6886,plain,
    ! [X31828,X31829,X31830] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31830),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31829))),c_List_Otranspose(X31829,X31828))))
      | hAPP(hAPP(c_List_Onth(tc_List_Olist(X31829)),c_List_Otranspose(X31829,X31828)),X31830) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31829),X31829),hAPP(hAPP(c_COMBC(tc_List_Olist(X31829),tc_Nat_Onat,X31829),c_List_Onth(X31829)),X31830)),hAPP(c_List_Ofilter(tc_List_Olist(X31829),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31829)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31830)),c_Nat_Osize__class_Osize(tc_List_Olist(X31829)))),X31828)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).

fof(i_0_6887,plain,
    ! [X24559,X24560,X24561] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X24561,hAPP(hAPP(c_COMBC(X24561,tc_fun(X24561,tc_HOL_Obool),tc_HOL_Obool),c_member(X24561)),X24560)),X24559))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24561,tc_HOL_Obool)),X24559),hAPP(c_Set_OPow(X24561),X24560))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24561,tc_HOL_Obool)),X24559),hAPP(c_Set_OPow(X24561),X24560)))
        | hBOOL(hAPP(c_Predicate_OPowp(X24561,hAPP(hAPP(c_COMBC(X24561,tc_fun(X24561,tc_HOL_Obool),tc_HOL_Obool),c_member(X24561)),X24560)),X24559)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).

fof(i_0_6888,plain,
    ! [X19846,X19847,X19848,X19849,X19850,X19851] :
      ( ~ c_Fun_Oinj__on(X19851,X19850,X19849,X19848)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19850,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19851,X19850,X19849),X19848)),X19847))
      | ~ c_Fun_Oinj__on(X19850,X19851,X19846,X19847)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19851,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19850,X19851,X19846),X19847)),X19848))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19851),X19848))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19850),X19847))
      | hAPP(c_Finite__Set_Ocard(X19851),X19848) = hAPP(c_Finite__Set_Ocard(X19850),X19847) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_6889,plain,
    ! [X28325,X28326,X28327] : c_Hilbert__Choice_OEps(tc_prod(X28327,X28326),hAPP(c_Product__Type_Oprod_Oprod__case(X28327,X28326,tc_HOL_Obool),X28325)) = c_Hilbert__Choice_OEps(tc_prod(X28327,X28326),hAPP(hAPP(c_COMBS(tc_prod(X28327,X28326),X28326,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28327,tc_fun(X28326,tc_HOL_Obool),tc_prod(X28327,X28326)),X28325),c_Product__Type_Ofst(X28327,X28326))),c_Product__Type_Osnd(X28327,X28326))),
    inference(variable_rename,[status(thm)],[fact_Eps__split]) ).

fof(i_0_6890,plain,
    ! [X27037,X27038,X27039] : c_HOL_OThe(tc_prod(X27039,X27038),hAPP(c_Product__Type_Oprod_Oprod__case(X27039,X27038,tc_HOL_Obool),X27037)) = c_HOL_OThe(tc_prod(X27039,X27038),hAPP(hAPP(c_COMBS(tc_prod(X27039,X27038),X27038,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27039,tc_fun(X27038,tc_HOL_Obool),tc_prod(X27039,X27038)),X27037),c_Product__Type_Ofst(X27039,X27038))),c_Product__Type_Osnd(X27039,X27038))),
    inference(variable_rename,[status(thm)],[fact_The__split]) ).

fof(i_0_6891,plain,
    ! [X32457,X32458,X32459,X32460,X32461] :
      ( ( hAPP(X32458,X32460) = hAPP(X32458,X32459)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32458,X32460)),hAPP(X32458,X32459)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32461,tc_Nat_Onat)),X32458),X32457)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,X32457)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32458,X32460)),hAPP(X32458,X32459)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32461,tc_Nat_Onat)),X32458),X32457)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32458,X32460)),hAPP(X32458,X32459)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32461,tc_Nat_Onat)),X32458),X32457)))) )
      & ( hAPP(X32458,X32460) != hAPP(X32458,X32459)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,X32457)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32461,X32461)),hAPP(hAPP(c_Product__Type_OPair(X32461,X32461),X32460),X32459)),c_List_Omeasures(X32461,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32461,tc_Nat_Onat)),X32458),X32457)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).

fof(i_0_6892,plain,
    ! [X34008,X34009,X34010,X34011,X34012,X34013] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34011),X34012),X34008)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X34011),X34012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34011),X34013),X34009))),X34008)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),X34009))
        | ~ class_Rings_Ocomm__ring(X34011)
        | ~ class_Rings_Odvd(X34011) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X34011),X34012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34011),X34013),X34009))),X34008)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34011),X34012),X34008)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34011),X34010),X34009))
        | ~ class_Rings_Ocomm__ring(X34011)
        | ~ class_Rings_Odvd(X34011) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).

fof(i_0_6893,plain,
    ! [X34002,X34003,X34004,X34005,X34006,X34007] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34005),X34006),X34002)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X34005),X34006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34005),X34007),X34003))),X34002)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),X34003))
        | ~ class_Rings_Ocomm__ring(X34005)
        | ~ class_Rings_Odvd(X34005) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X34005),X34006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34005),X34007),X34003))),X34002)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34005),X34006),X34002)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34005),X34004),X34003))
        | ~ class_Rings_Ocomm__ring(X34005)
        | ~ class_Rings_Odvd(X34005) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).

fof(i_0_6894,plain,
    ! [X24765,X24766,X24767,X24768] :
      ( ~ class_Divides_Osemiring__div(X24768)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24768),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24768),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24768),X24767),X24766)),X24766)),c_Divides_Odiv__class_Omod(X24768,X24767,X24766))),X24765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24768),X24767),X24765) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).

fof(i_0_6895,plain,
    ! [X17442,X17443,X17444,X17445,X17446,X17447] : c_Fun_Ofun__upd(X17447,X17446,c_Fun_Ofun__upd(X17447,X17446,X17445,X17444,X17443),X17444,X17442) = c_Fun_Ofun__upd(X17447,X17446,X17445,X17444,X17442),
    inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).

fof(i_0_6896,plain,
    ! [X20452,X20453,X20454,X20455,X20456] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20456)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20455),X20454))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20455),X20453))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20455,tc_HOL_Obool)),X20454),X20453) != c_Orderings_Obot__class_Obot(tc_fun(X20455,tc_HOL_Obool))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20456,X20455,c_Groups_Otimes__class_Otimes(X20456)),X20452),c_Groups_Oone__class_Oone(X20456)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20455,tc_HOL_Obool)),X20454),X20453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20456),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20456,X20455,c_Groups_Otimes__class_Otimes(X20456)),X20452),c_Groups_Oone__class_Oone(X20456)),X20454)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20456,X20455,c_Groups_Otimes__class_Otimes(X20456)),X20452),c_Groups_Oone__class_Oone(X20456)),X20453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint])]) ).

fof(i_0_6897,plain,
    ! [X33810,X33811,X33812,X33813,X33814] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33814,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X33814,X33813,X33812),X33811)),X33810))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33813,tc_HOL_Obool)),X33811),hAPP(c_Set_Oimage(X33814,X33813,X33812),X33810)))
        | ~ c_Fun_Obij__betw(X33814,X33813,X33812,c_Orderings_Otop__class_Otop(tc_fun(X33814,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33813,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33813,tc_HOL_Obool)),X33811),hAPP(c_Set_Oimage(X33814,X33813,X33812),X33810)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33814,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X33814,X33813,X33812),X33811)),X33810))
        | ~ c_Fun_Obij__betw(X33814,X33813,X33812,c_Orderings_Otop__class_Otop(tc_fun(X33814,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33813,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subset__eq])])]) ).

cnf(i_0_6898,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5474]) ).

fof(i_0_6899,plain,
    ! [X31236,X31237,X31238,X31239] :
      ( ~ class_Groups_Oab__group__add(X31239)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X31239),hAPP(c_List_Omonoid__add__class_Olistsum(X31239),hAPP(hAPP(c_List_Omap(X31238,X31239),X31237),X31236))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31239),hAPP(hAPP(c_List_Omap(X31238,X31239),hAPP(c_Fun_Ocomp(X31239,X31239,X31238,c_Groups_Ouminus__class_Ouminus(X31239)),X31237)),X31236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).

fof(i_0_6900,plain,
    ! [X32762,X32763,X32764,X32765] : c_New__Random__Sequence_Oneg__map(X32765,X32764,X32763,X32762) = c_New__Random__Sequence_Oneg__bind(X32765,X32764,X32762,hAPP(c_Fun_Ocomp(X32764,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32764)))))),X32765,c_New__Random__Sequence_Oneg__single(X32764)),X32763)),
    inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).

fof(i_0_6901,plain,
    ! [X31413,X31414,X31415] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X31415,hAPP(hAPP(c_COMBC(X31415,tc_fun(X31415,tc_HOL_Obool),tc_HOL_Obool),c_member(X31415)),X31414)),X31413))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31415)),X31413),c_List_Olists(X31415,X31414))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31415)),X31413),c_List_Olists(X31415,X31414)))
        | hBOOL(hAPP(c_List_Olistsp(X31415,hAPP(hAPP(c_COMBC(X31415,tc_fun(X31415,tc_HOL_Obool),tc_HOL_Obool),c_member(X31415)),X31414)),X31413)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).

fof(i_0_6902,plain,
    ! [X24957,X24958,X24959,X24960] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24960)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24960),c_Groups_Ozero__class_Ozero(X24960)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24959,X24960),hAPP(hAPP(c_COMBB(X24960,X24960,X24959),c_Groups_Oabs__class_Oabs(X24960)),X24958)),X24957))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).

fof(i_0_6903,plain,
    ! [X25415,X25416] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25416),X25415))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25416,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X25416,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X25416,tc_HOL_Obool),tc_fun(X25416,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X25416,tc_HOL_Obool))),X25415)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).

fof(i_0_6904,plain,
    ! [X22204,X22205,X22206] :
      ( ( X22205 = c_Groups_Ozero__class_Ozero(X22206)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22205),X22205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22204),X22204))),c_Groups_Ozero__class_Ozero(X22206)))
        | ~ class_Rings_Olinordered__ring__strict(X22206) )
      & ( X22204 = c_Groups_Ozero__class_Ozero(X22206)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22205),X22205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22204),X22204))),c_Groups_Ozero__class_Ozero(X22206)))
        | ~ class_Rings_Olinordered__ring__strict(X22206) )
      & ( X22205 != c_Groups_Ozero__class_Ozero(X22206)
        | X22204 != c_Groups_Ozero__class_Ozero(X22206)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22205),X22205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22206),X22204),X22204))),c_Groups_Ozero__class_Ozero(X22206)))
        | ~ class_Rings_Olinordered__ring__strict(X22206) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).

fof(i_0_6905,plain,
    ! [X22019,X22020] :
      ( ~ class_Lattices_Olattice(X22020)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22020),X22019))
      | X22019 = c_Orderings_Obot__class_Obot(tc_fun(X22020,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X22020),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22020),esk115_2(X22019,X22020)),esk116_2(X22019,X22020))),hAPP(hAPP(c_Set_Oinsert(X22020),esk115_2(X22019,X22020)),hAPP(hAPP(c_Set_Oinsert(X22020),esk116_2(X22019,X22020)),c_Orderings_Obot__class_Obot(tc_fun(X22020,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X22020),c_Big__Operators_Olattice__class_OInf__fin(X22020,X22019)),X22019)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).

fof(i_0_6906,plain,
    ! [X20423,X20424] :
      ( ~ class_Lattices_Olattice(X20424)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20424),X20423))
      | X20423 = c_Orderings_Obot__class_Obot(tc_fun(X20424,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X20424),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20424),esk82_2(X20423,X20424)),esk83_2(X20423,X20424))),hAPP(hAPP(c_Set_Oinsert(X20424),esk82_2(X20423,X20424)),hAPP(hAPP(c_Set_Oinsert(X20424),esk83_2(X20423,X20424)),c_Orderings_Obot__class_Obot(tc_fun(X20424,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X20424),c_Big__Operators_Olattice__class_OSup__fin(X20424,X20423)),X20423)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).

fof(i_0_6907,plain,
    ! [X19188,X19189] :
      ( ~ class_Orderings_Olinorder(X19189)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19189),X19188))
      | X19188 = c_Orderings_Obot__class_Obot(tc_fun(X19189,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19189),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19189),esk46_2(X19188,X19189)),esk47_2(X19188,X19189))),hAPP(hAPP(c_Set_Oinsert(X19189),esk46_2(X19188,X19189)),hAPP(hAPP(c_Set_Oinsert(X19189),esk47_2(X19188,X19189)),c_Orderings_Obot__class_Obot(tc_fun(X19189,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19189),c_Big__Operators_Olinorder__class_OMin(X19189,X19188)),X19188)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).

fof(i_0_6908,plain,
    ! [X19184,X19185] :
      ( ~ class_Orderings_Olinorder(X19185)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19185),X19184))
      | X19184 = c_Orderings_Obot__class_Obot(tc_fun(X19185,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19185),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19185),esk44_2(X19184,X19185)),esk45_2(X19184,X19185))),hAPP(hAPP(c_Set_Oinsert(X19185),esk44_2(X19184,X19185)),hAPP(hAPP(c_Set_Oinsert(X19185),esk45_2(X19184,X19185)),c_Orderings_Obot__class_Obot(tc_fun(X19185,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19185),c_Big__Operators_Olinorder__class_OMax(X19185,X19184)),X19184)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).

fof(i_0_6909,plain,
    ! [X22213,X22214,X22215] :
      ( ~ class_Rings_Olinordered__ring(X22215)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22215),X22214),X22214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22215),X22213),X22213))),c_Groups_Ozero__class_Ozero(X22215))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5475])]) ).

fof(i_0_6910,plain,
    ! [X28592,X28593,X28594,X28595,X28596,X28597,X28598,X28599] :
      ( ~ c_Finite__Set_Ofolding__image(X28599,X28598,X28597,X28596,X28595)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28598),X28594))
      | ~ c_Fun_Oinj__on(X28598,X28598,X28593,X28594)
      | hAPP(hAPP(X28595,X28592),hAPP(c_Set_Oimage(X28598,X28598,X28593),X28594)) = hAPP(hAPP(X28595,hAPP(c_Fun_Ocomp(X28598,X28599,X28598,X28592),X28593)),X28594) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).

fof(i_0_6911,plain,
    ! [X32236,X32237,X32238] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32238),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32238))),X32237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32236),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32238))),X32237)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32238))),hAPP(c_List_Ofilter(tc_List_Olist(X32238),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32238)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32236)),c_Nat_Osize__class_Osize(tc_List_Olist(X32238)))),c_List_Otranspose(X32238,X32237))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32238)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32238)),X32237),X32236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).

fof(i_0_6912,plain,
    ! [X26596,X26597,X26598,X26599,X26600,X26601,X26602] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26602,X26601)),hAPP(hAPP(c_Product__Type_OPair(X26602,X26601),X26600),X26599)),X26598))
      | hBOOL(hAPP(hAPP(c_member(X26597),hAPP(hAPP(X26596,X26600),X26599)),hAPP(c_Set_Oimage(tc_prod(X26602,X26601),X26597,hAPP(c_Product__Type_Oprod_Oprod__case(X26602,X26601,X26597),X26596)),X26598))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).

fof(i_0_6913,plain,
    ! [X31838,X31839,X31840,X31841,X31842] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31842)),hAPP(c_List_Ofilter(X31842,X31841),hAPP(hAPP(c_List_Omap(X31840,X31842),X31839),X31838))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31840)),hAPP(c_List_Ofilter(X31840,hAPP(c_Fun_Ocomp(X31842,tc_HOL_Obool,X31840,X31841),X31839)),X31838)),
    inference(variable_rename,[status(thm)],[fact_length__filter__map]) ).

cnf(i_0_6914,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_5476]) ).

fof(i_0_6915,plain,
    ! [X29060,X29061,X29062,X29063,X29064] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29064,X29064)),hAPP(hAPP(c_Product__Type_OPair(X29064,X29064),X29063),X29062)),c_Transitive__Closure_Ortrancl(X29064,X29061)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29064,X29064),tc_HOL_Obool)),X29061),hAPP(hAPP(c_Product__Type_OSigma(X29064,X29064),X29060),hAPP(c_COMBK(tc_fun(X29064,tc_HOL_Obool),X29064),X29060))))
      | X29063 = X29062
      | hBOOL(hAPP(hAPP(c_member(X29064),X29063),X29060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).

fof(i_0_6916,plain,
    ! [X26614,X26615,X26616,X26617,X26618,X26619] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26619,tc_fun(X26618,tc_HOL_Obool))),X26617),X26616),X26615),X26614))
      | hBOOL(hAPP(hAPP(X26617,X26615),X26614))
      | hBOOL(hAPP(hAPP(X26616,X26615),X26614)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5477])]) ).

fof(i_0_6917,plain,
    ! [X31763,X31764,X31765] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31765)),hAPP(c_List_Ofilter(X31765,X31764),X31763))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31765)),hAPP(c_List_Ofilter(X31765,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31765),c_fNot),X31764)),X31763))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31765)),X31763),
    inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(i_0_6918,plain,
    ! [X28993,X28994,X28995,X28996,X28997] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28996),X28995)),c_Transitive__Closure_Ortrancl(X28997,X28994)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28995),X28993)),c_Transitive__Closure_Ortrancl(X28997,X28994)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28996),X28993)),c_Transitive__Closure_Ortrancl(X28997,X28994))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).

cnf(i_0_6919,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Otrancl(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5478]) ).

cnf(i_0_6920,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5479]) ).

fof(i_0_6921,plain,
    ! [X24749,X24750,X24751] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24751),X24750)),X24749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24751),X24749)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24750),X24749))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24751,X24749)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24750,X24749))),X24749)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(i_0_6922,plain,
    ! [X24886,X24887,X24888] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24888),X24887)),X24886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24888),X24886)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24887),X24886))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24888,X24886)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24887,X24886))),X24886)),
    inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).

fof(i_0_6923,plain,
    ! [X26620,X26621,X26622,X26623,X26624,X26625] :
      ( ( hBOOL(hAPP(hAPP(X26623,X26621),X26620))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26625,tc_fun(X26624,tc_HOL_Obool))),X26623),X26622),X26621),X26620)) )
      & ( hBOOL(hAPP(hAPP(X26622,X26621),X26620))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26625,tc_fun(X26624,tc_HOL_Obool))),X26623),X26622),X26621),X26620)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5480])])]) ).

fof(i_0_6924,plain,
    ! [X26693,X26694,X26695,X26696,X26697,X26698] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26698,tc_fun(X26697,tc_HOL_Obool))),X26696),X26695),X26694),X26693))
      | hBOOL(hAPP(hAPP(X26696,X26694),X26693)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).

fof(i_0_6925,plain,
    ! [X26687,X26688,X26689,X26690,X26691,X26692] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26692,tc_fun(X26691,tc_HOL_Obool))),X26690),X26689),X26688),X26687))
      | hBOOL(hAPP(hAPP(X26689,X26688),X26687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).

cnf(i_0_6926,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk430_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))
    | c_List_Oconcat(X1,X2) != c_List_Oconcat(X1,X3)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5278]) ).

cnf(i_0_6927,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk429_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))
    | X3 = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)
    | c_List_Oconcat(X1,X3) != c_List_Oconcat(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5279]) ).

fof(i_0_6928,plain,
    ! [X32391,X32392,X32393,X32394] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk448_4(X32391,X32392,X32393,X32394)),X32394))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32392)),X32391)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32392)),c_List_OtakeWhile(X32392,X32393,X32391)))) )
      & ( ~ hBOOL(hAPP(X32393,hAPP(hAPP(c_List_Onth(X32392),X32391),esk448_4(X32391,X32392,X32393,X32394))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32392)),X32391)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32392)),c_List_OtakeWhile(X32392,X32393,X32391)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__takeWhile__less__P__nth])])])]) ).

cnf(i_0_6929,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5481]) ).

cnf(i_0_6930,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5482]) ).

cnf(i_0_6931,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5483]) ).

cnf(i_0_6932,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5484]) ).

fof(i_0_6933,plain,
    ! [X29003,X29004,X29005,X29006,X29007] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29006),X29005)),X29004))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29005),X29003)),c_Transitive__Closure_Ortrancl(X29007,X29004)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29006),X29003)),c_Transitive__Closure_Ortrancl(X29007,X29004))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).

fof(i_0_6934,plain,
    ! [X28998,X28999,X29000,X29001,X29002] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29001),X29000)),c_Transitive__Closure_Ortrancl(X29002,X28999)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29000),X28998)),X28999))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29001),X28998)),c_Transitive__Closure_Ortrancl(X29002,X28999))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).

fof(i_0_6935,plain,
    ! [X29686,X29687,X29688,X29689] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29689),tc_List_Olist(X29689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29689),tc_List_Olist(X29689)),X29688),X29687)),c_List_Olistrel(X29689,X29686)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29689),tc_List_Olist(X29689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29689),tc_List_Olist(X29689)),X29688),X29687)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29689),c_List_Olistrel1(X29689,X29686)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).

fof(i_0_6936,plain,
    ! [X28606,X28607,X28608,X28609,X28610,X28611,X28612,X28613,X28614,X28615,X28616] :
      ( ~ c_Finite__Set_Ofolding(X28616,X28615,X28614,X28613)
      | hAPP(c_Fun_Ocomp(X28612,X28611,X28610,X28609),hAPP(c_Fun_Ocomp(X28608,X28612,X28610,X28607),X28606)) = hAPP(c_Fun_Ocomp(X28608,X28611,X28610,hAPP(c_Fun_Ocomp(X28612,X28611,X28608,X28609),X28607)),X28606) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).

cnf(i_0_6937,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_OremoveAll(X1,X3),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5485]) ).

fof(i_0_6938,plain,
    ! [X23231,X23232,X23233,X23234,X23235,X23236] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23236),X23235)),X23234) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23233),X23232)),X23231)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23233),X23232)),X23231)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23234),X23236))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23233))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23233),X23236))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23232),X23235)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).

fof(i_0_6939,plain,
    ! [X25432] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X25432)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X25432),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(i_0_6940,plain,
    ! [X29679,X29680,X29681,X29682] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29682),tc_List_Olist(X29682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29682),tc_List_Olist(X29682)),X29681),X29680)),c_List_Olistrel1(X29682,X29679)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29682),tc_List_Olist(X29682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29682),tc_List_Olist(X29682)),X29681),X29680)),c_List_Olistrel(X29682,c_Transitive__Closure_Ortrancl(X29682,X29679)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).

fof(i_0_6941,plain,
    ! [X29594,X29595,X29596,X29597] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29597),tc_List_Olist(X29597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29597),tc_List_Olist(X29597)),X29596),X29595)),c_List_Olexord(X29597,X29594)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29597),tc_List_Olist(X29597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29597),tc_List_Olist(X29597)),X29596),X29595)),c_List_Olex(X29597,X29594))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29596) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29595)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29597),tc_List_Olist(X29597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29597),tc_List_Olist(X29597)),X29596),X29595)),c_List_Olex(X29597,X29594))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29597),tc_List_Olist(X29597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29597),tc_List_Olist(X29597)),X29596),X29595)),c_List_Olexord(X29597,X29594)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29596) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29595)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29597),tc_List_Olist(X29597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29597),tc_List_Olist(X29597)),X29596),X29595)),c_List_Olex(X29597,X29594))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).

fof(i_0_6942,plain,
    ! [X31790,X31791,X31792,X31793,X31794] : hAPP(c_List_Ofilter(X31794,X31793),hAPP(hAPP(c_List_Omap(X31792,X31794),X31791),X31790)) = hAPP(hAPP(c_List_Omap(X31792,X31794),X31791),hAPP(c_List_Ofilter(X31792,hAPP(c_Fun_Ocomp(X31794,tc_HOL_Obool,X31792,X31793),X31791)),X31790)),
    inference(variable_rename,[status(thm)],[fact_filter__map]) ).

fof(i_0_6943,plain,
    ! [X28295,X28296,X28297] :
      ( ( hAPP(X28296,esk322_3(X28295,X28296,X28297)) != hAPP(X28296,esk323_3(X28295,X28296,X28297))
        | c_Wellfounded_OwfP(X28297,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28295,tc_fun(X28297,tc_fun(X28297,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28295,tc_HOL_Obool))),X28296))
        | ~ c_Wellfounded_OwfP(X28297,hAPP(X28296,esk321_3(X28295,X28296,X28297))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28297,tc_HOL_Obool)),c_Predicate_ODomainP(X28297,X28297,hAPP(X28296,esk322_3(X28295,X28296,X28297)))),c_Predicate_ORangeP(X28297,X28297,hAPP(X28296,esk323_3(X28295,X28296,X28297)))) != c_Orderings_Obot__class_Obot(tc_fun(X28297,tc_HOL_Obool))
        | c_Wellfounded_OwfP(X28297,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28295,tc_fun(X28297,tc_fun(X28297,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28295,tc_HOL_Obool))),X28296))
        | ~ c_Wellfounded_OwfP(X28297,hAPP(X28296,esk321_3(X28295,X28296,X28297))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__SUP])])])]) ).

fof(i_0_6944,plain,
    ! [X31847,X31848,X31849] : c_List_Opartition(X31849,X31848,X31847) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31849),tc_List_Olist(X31849)),hAPP(c_List_Ofilter(X31849,X31848),X31847)),hAPP(c_List_Ofilter(X31849,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31849,c_fNot),X31848)),X31847)),
    inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).

cnf(i_0_6945,plain,
    ( hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5)) = hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_5486]) ).

fof(i_0_6946,plain,
    ! [X30342,X30343,X30344] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk404_3(X30342,X30343,X30344)),esk405_3(X30342,X30343,X30344))))
        | hBOOL(hAPP(hAPP(X30342,X30344),X30343))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30344),X30343))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk404_3(X30342,X30343,X30344)),esk405_3(X30342,X30343,X30344)))
        | hBOOL(hAPP(hAPP(X30342,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk404_3(X30342,X30343,X30344)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk405_3(X30342,X30343,X30344)))
        | hBOOL(hAPP(hAPP(X30342,X30344),X30343))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30344),X30343))) )
      & ( ~ hBOOL(hAPP(hAPP(X30342,esk404_3(X30342,X30343,X30344)),esk405_3(X30342,X30343,X30344)))
        | hBOOL(hAPP(hAPP(X30342,X30344),X30343))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30344),X30343))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto_Opinduct])])])]) ).

fof(i_0_6947,plain,
    ! [X31440,X31441,X31442,X31443,X31444,X31445,X31446] :
      ( ( ~ c_List_Olist__all2(X31446,X31445,X31444,hAPP(hAPP(c_List_Omap(X31443,X31446),X31442),X31441),X31440)
        | c_List_Olist__all2(X31443,X31445,hAPP(hAPP(c_COMBB(X31446,tc_fun(X31445,tc_HOL_Obool),X31443),X31444),X31442),X31441,X31440) )
      & ( ~ c_List_Olist__all2(X31443,X31445,hAPP(hAPP(c_COMBB(X31446,tc_fun(X31445,tc_HOL_Obool),X31443),X31444),X31442),X31441,X31440)
        | c_List_Olist__all2(X31446,X31445,X31444,hAPP(hAPP(c_List_Omap(X31443,X31446),X31442),X31441),X31440) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])]) ).

cnf(i_0_6948,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5487]) ).

fof(i_0_6949,plain,
    ! [X32445,X32446,X32447,X32448,X32449] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X32449,X32448)),hAPP(X32449,X32447)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32446,X32446)),hAPP(hAPP(c_Product__Type_OPair(X32446,X32446),X32448),X32447)),c_List_Omeasures(X32446,X32445)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32446,X32446)),hAPP(hAPP(c_Product__Type_OPair(X32446,X32446),X32448),X32447)),c_List_Omeasures(X32446,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32446,tc_Nat_Onat)),X32449),X32445)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).

fof(i_0_6950,plain,
    ! [X33214,X33215,X33216,X33217,X33218,X33219,X33220] :
      ( ( ~ c_Relation_Otrans(X33215,X33214)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33215,X33215)),hAPP(hAPP(c_Product__Type_OPair(X33215,X33215),X33216),X33217)),X33214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33215,X33215)),hAPP(hAPP(c_Product__Type_OPair(X33215,X33215),X33217),X33218)),X33214))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33215,X33215)),hAPP(hAPP(c_Product__Type_OPair(X33215,X33215),X33216),X33218)),X33214)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33220,X33220)),hAPP(hAPP(c_Product__Type_OPair(X33220,X33220),esk507_2(X33219,X33220)),esk508_2(X33219,X33220))),X33219))
        | c_Relation_Otrans(X33220,X33219) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33220,X33220)),hAPP(hAPP(c_Product__Type_OPair(X33220,X33220),esk508_2(X33219,X33220)),esk509_2(X33219,X33220))),X33219))
        | c_Relation_Otrans(X33220,X33219) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33220,X33220)),hAPP(hAPP(c_Product__Type_OPair(X33220,X33220),esk507_2(X33219,X33220)),esk509_2(X33219,X33220))),X33219))
        | c_Relation_Otrans(X33220,X33219) ) ),
    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_trans__def])])])])])]) ).

fof(i_0_6951,plain,
    ! [X33209,X33210,X33211,X33212,X33213] :
      ( ~ c_Relation_Otrans(X33213,X33212)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33213,X33213)),hAPP(hAPP(c_Product__Type_OPair(X33213,X33213),X33211),X33210)),X33212))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33213,X33213)),hAPP(hAPP(c_Product__Type_OPair(X33213,X33213),X33210),X33209)),X33212))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33213,X33213)),hAPP(hAPP(c_Product__Type_OPair(X33213,X33213),X33211),X33209)),X33212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).

fof(i_0_6952,plain,
    ! [X22819,X22820] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22820),c_Groups_Oone__class_Oone(X22820)),X22819)),X22819)),c_Groups_Ozero__class_Ozero(X22820)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),X22819),c_Groups_Ozero__class_Ozero(X22820)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22820),X22819),c_Int_Oring__1__class_OInts(X22820)))
        | ~ class_Rings_Olinordered__idom(X22820) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),X22819),c_Groups_Ozero__class_Ozero(X22820)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22820),c_Groups_Oone__class_Oone(X22820)),X22819)),X22819)),c_Groups_Ozero__class_Ozero(X22820)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22820),X22819),c_Int_Oring__1__class_OInts(X22820)))
        | ~ class_Rings_Olinordered__idom(X22820) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

cnf(i_0_6953,plain,
    ( hBOOL(hAPP(X4,X2))
    | c_List_OdropWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5)) = hAPP(hAPP(c_List_Oappend(X1),c_List_OdropWhile(X1,X4,X3)),X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5488]) ).

fof(i_0_6954,plain,
    ! [X24793,X24794,X24795] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24795),X24794)),X24794)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24795,X24794))),X24793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24795),X24793),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).

cnf(i_0_6955,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk458_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))
    | c_List_OdropWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2)) = c_List_OdropWhile(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5489]) ).

cnf(i_0_6956,plain,
    ( hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5)) = hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_5490]) ).

fof(i_0_6957,plain,
    ! [X32301,X32302,X32303] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32303)),c_List_OtakeWhile(X32303,X32302,X32301))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32303)),X32301)))
      | ~ hBOOL(hAPP(X32302,hAPP(hAPP(c_List_Onth(X32303),X32301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32303)),c_List_OtakeWhile(X32303,X32302,X32301))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5491])]) ).

cnf(i_0_6958,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)) = c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

cnf(i_0_6959,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk346_3(X3,X2,X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5493]) ).

fof(i_0_6960,plain,
    ! [X30875,X30876,X30877,X30878] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30878)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30877,X30878),hAPP(c_List_Oset(X30877),X30876)),X30875) = hAPP(c_List_Ofoldl(X30878,X30877,hAPP(c_COMBC(X30877,X30878,X30878),hAPP(hAPP(c_COMBB(X30878,tc_fun(X30878,X30878),X30877),c_Lattices_Osemilattice__inf__class_Oinf(X30878)),X30875)),c_Orderings_Otop__class_Otop(X30878)),X30876) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).

fof(i_0_6961,plain,
    ! [X30871,X30872,X30873,X30874] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30874)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30873,X30874),hAPP(c_List_Oset(X30873),X30872)),X30871) = hAPP(c_List_Ofoldl(X30874,X30873,hAPP(c_COMBC(X30873,X30874,X30874),hAPP(hAPP(c_COMBB(X30874,tc_fun(X30874,X30874),X30873),c_Lattices_Osemilattice__sup__class_Osup(X30874)),X30871)),c_Orderings_Obot__class_Obot(X30874)),X30872) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])]) ).

cnf(i_0_6962,plain,
    c_List_Oconcat(X1,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oconcat(X1,X2)),c_List_Oconcat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_5494]) ).

fof(i_0_6963,plain,
    ! [X25496,X25497,X25498,X25499] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25499),esk245_4(X25496,X25497,X25498,X25499)),X25498))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25499,tc_fun(X25497,tc_HOL_Obool)),X25498),X25496)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25499),X25498)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25497),hAPP(X25496,esk245_4(X25496,X25497,X25498,X25499))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25499,tc_fun(X25497,tc_HOL_Obool)),X25498),X25496)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25499),X25498)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN__I])])])]) ).

fof(i_0_6964,plain,
    ! [X20594,X20595,X20596,X20597,X20598] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20597,tc_fun(X20595,tc_HOL_Obool)),X20596),X20594)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20597),X20598),X20596))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(X20594,X20598)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20597),X20596)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20597),esk88_4(X20594,X20595,X20596,X20597)),X20596))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20597,tc_fun(X20595,tc_HOL_Obool)),X20596),X20594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20597),X20596)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(X20594,esk88_4(X20594,X20595,X20596,X20597))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20597,tc_fun(X20595,tc_HOL_Obool)),X20596),X20594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20597),X20596)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN])])])])]) ).

fof(i_0_6965,plain,
    ! [X27350,X27351,X27352,X27353,X27354,X27355,X27356] : hAPP(hAPP(c_Relation_Orel__comp(X27356,X27355,X27354),X27353),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27352,tc_fun(tc_prod(X27355,X27354),tc_HOL_Obool)),X27351),X27350)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27352,tc_fun(tc_prod(X27356,X27354),tc_HOL_Obool)),X27351),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27355,X27354),tc_HOL_Obool),tc_fun(tc_prod(X27356,X27354),tc_HOL_Obool),X27352),hAPP(c_Relation_Orel__comp(X27356,X27355,X27354),X27353)),X27350)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(i_0_6966,plain,
    ! [X28361,X28362,X28363,X28364,X28365,X28366,X28367] : hAPP(c_Fun_Ocomp(X28367,X28366,X28365,X28364),hAPP(c_Fun_Ocomp(X28363,X28367,X28365,X28362),X28361)) = hAPP(c_Fun_Ocomp(X28363,X28366,X28365,hAPP(c_Fun_Ocomp(X28367,X28366,X28363,X28364),X28362)),X28361),
    inference(variable_rename,[status(thm)],[fact_o__assoc]) ).

fof(i_0_6967,plain,
    ! [X19818,X19819,X19820,X19821] :
      ( hAPP(c_Set_Oimage(X19821,X19820,X19819),c_Orderings_Otop__class_Otop(tc_fun(X19821,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19820,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19820,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19820,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19821,X19820,X19819),X19818))),hAPP(c_Set_Oimage(X19821,X19820,X19819),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19821,tc_HOL_Obool)),X19818)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).

fof(i_0_6968,plain,
    ! [X33659,X33660,X33661,X33662,X33663,X33664] :
      ( ~ c_Fun_Obij__betw(X33664,X33663,X33662,c_Orderings_Otop__class_Otop(tc_fun(X33664,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33663,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33664,X33663,X33662),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33661,tc_fun(X33664,tc_HOL_Obool)),X33660),X33659)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33661,tc_fun(X33663,tc_HOL_Obool)),X33660),hAPP(hAPP(c_COMBB(tc_fun(X33664,tc_HOL_Obool),tc_fun(X33663,tc_HOL_Obool),X33661),c_Set_Oimage(X33664,X33663,X33662)),X33659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__INT])]) ).

fof(i_0_6969,plain,
    ! [X27084,X27085,X27086,X27087,X27088,X27089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27089,X27089)),hAPP(hAPP(c_Product__Type_OPair(X27089,X27089),X27088),X27087)),hAPP(hAPP(c_Relation_Oinv__image(X27086,X27089),X27085),X27084)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27086,X27086)),hAPP(hAPP(c_Product__Type_OPair(X27086,X27086),hAPP(X27084,X27088)),hAPP(X27084,X27087))),X27085)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27086,X27086)),hAPP(hAPP(c_Product__Type_OPair(X27086,X27086),hAPP(X27084,X27088)),hAPP(X27084,X27087))),X27085))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27089,X27089)),hAPP(hAPP(c_Product__Type_OPair(X27089,X27089),X27088),X27087)),hAPP(hAPP(c_Relation_Oinv__image(X27086,X27089),X27085),X27084))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).

fof(i_0_6970,plain,
    ! [X33379,X33380] :
      ( ~ c_Relation_Osym(X33380,X33379)
      | ~ c_Relation_Otrans(X33380,X33379)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33380,X33380),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X33380,X33380,X33380),hAPP(c_Relation_Oconverse(X33380,X33380),X33379)),X33379)),X33379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trans__comp__subset])]) ).

fof(i_0_6971,plain,
    ! [X28586,X28587,X28588,X28589,X28590,X28591] :
      ( ~ c_Finite__Set_Ofolding(X28591,X28590,X28589,X28588)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28591),X28587))
      | ~ hBOOL(hAPP(hAPP(c_member(X28591),X28586),X28587))
      | hAPP(X28588,X28587) = hAPP(c_Fun_Ocomp(X28590,X28590,X28590,hAPP(X28588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28591,tc_HOL_Obool)),X28587),hAPP(hAPP(c_Set_Oinsert(X28591),X28586),c_Orderings_Obot__class_Obot(tc_fun(X28591,tc_HOL_Obool)))))),hAPP(X28589,X28586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).

fof(i_0_6972,plain,
    ! [X27945,X27946,X27947,X27948,X27949,X27950] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27950,X27949),tc_HOL_Obool)),X27948),hAPP(hAPP(c_Product__Type_OSigma(X27950,X27949),X27947),hAPP(c_COMBK(tc_fun(X27949,tc_HOL_Obool),X27950),X27946))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27949,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27950,X27949,X27948),X27945)),X27946)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).

fof(i_0_6973,plain,
    ! [X30783,X30784,X30785] : hAPP(c_List_Otl(X30785),hAPP(hAPP(c_List_Oappend(X30785),X30784),X30783)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X30785),X30785,hAPP(c_List_Otl(X30785),X30783),hAPP(c_COMBK(tc_fun(tc_List_Olist(X30785),tc_List_Olist(X30785)),X30785),hAPP(hAPP(c_COMBC(tc_List_Olist(X30785),tc_List_Olist(X30785),tc_List_Olist(X30785)),c_List_Oappend(X30785)),X30783))),X30784),
    inference(variable_rename,[status(thm)],[fact_tl__append]) ).

fof(i_0_6974,plain,
    ! [X32781,X32782,X32783,X32784] : c_New__Random__Sequence_Opos__map(X32784,X32783,X32782,X32781) = c_New__Random__Sequence_Opos__bind(X32784,X32783,X32781,hAPP(c_Fun_Ocomp(X32783,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32783))))),X32784,c_New__Random__Sequence_Opos__single(X32783)),X32782)),
    inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).

fof(i_0_6975,plain,
    ! [X19315,X19316,X19317,X19318] :
      ( ~ c_Fun_Oinj__on(X19318,X19317,X19316,c_Orderings_Otop__class_Otop(tc_fun(X19318,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19317,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19318,X19317,X19316),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19318,tc_HOL_Obool)),X19315))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19317,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19318,X19317,X19316),X19315)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).

fof(i_0_6976,plain,
    ! [X33651,X33652,X33653] :
      ( ~ c_Fun_Obij__betw(X33653,X33652,X33651,c_Orderings_Otop__class_Otop(tc_fun(X33653,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33652,tc_HOL_Obool)))
      | c_Fun_Obij__betw(X33652,X33653,c_Hilbert__Choice_Oinv__into(X33653,X33652,c_Orderings_Otop__class_Otop(tc_fun(X33653,tc_HOL_Obool)),X33651),c_Orderings_Otop__class_Otop(tc_fun(X33652,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33653,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__imp__bij__inv])]) ).

fof(i_0_6977,plain,
    ! [X28721,X28722,X28723,X28724,X28725,X28726] :
      ( ~ c_Finite__Set_Ofolding(X28726,X28725,X28724,X28723)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28726),X28722))
      | hAPP(X28723,hAPP(hAPP(c_Set_Oinsert(X28726),X28721),X28722)) = hAPP(c_Fun_Ocomp(X28725,X28725,X28725,hAPP(X28723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28726,tc_HOL_Obool)),X28722),hAPP(hAPP(c_Set_Oinsert(X28726),X28721),c_Orderings_Obot__class_Obot(tc_fun(X28726,tc_HOL_Obool)))))),hAPP(X28724,X28721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).

fof(i_0_6978,plain,
    ! [X31538,X31539,X31540,X31541,X31542,X31543,X31544,X31545] :
      ( ~ c_List_Olist__all2(X31545,X31544,X31543,X31542,X31541)
      | ~ hBOOL(hAPP(hAPP(X31543,X31540),X31539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31538),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31544)),X31541)))
      | c_List_Olist__all2(X31545,X31544,X31543,hAPP(hAPP(c_List_Olist__update(X31545,X31542),X31538),X31540),hAPP(hAPP(c_List_Olist__update(X31544,X31541),X31538),X31539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2])]) ).

fof(i_0_6979,plain,
    ! [X31530,X31531,X31532,X31533,X31534,X31535,X31536,X31537] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31537),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31536)),X31535)))
      | ~ c_List_Olist__all2(X31536,X31534,X31533,X31535,X31532)
      | ~ hBOOL(hAPP(hAPP(X31533,X31531),X31530))
      | c_List_Olist__all2(X31536,X31534,X31533,hAPP(hAPP(c_List_Olist__update(X31536,X31535),X31537),X31531),hAPP(hAPP(c_List_Olist__update(X31534,X31532),X31537),X31530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])]) ).

fof(i_0_6980,plain,
    ! [X33620,X33621,X33622,X33623] :
      ( ~ c_Fun_Obij__betw(X33623,X33622,X33621,c_Orderings_Otop__class_Otop(tc_fun(X33623,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33622,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33623,X33622,X33621),hAPP(c_Set_OCollect(X33623),X33620)) = hAPP(c_Set_OCollect(X33622),hAPP(hAPP(c_COMBB(X33623,tc_HOL_Obool,X33622),X33620),c_Hilbert__Choice_Oinv__into(X33623,X33622,c_Orderings_Otop__class_Otop(tc_fun(X33623,tc_HOL_Obool)),X33621))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Collect__eq])]) ).

fof(i_0_6981,plain,
    ! [X30118,X30119,X30120,X30121] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30121),X30120))
      | hBOOL(hAPP(hAPP(c_member(X30121),X30119),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30121,tc_HOL_Obool)),hAPP(c_List_Oset(X30121),X30120)),hAPP(hAPP(c_Set_Oinsert(X30121),hAPP(hAPP(c_List_Onth(X30121),X30120),X30118)),c_Orderings_Obot__class_Obot(tc_fun(X30121,tc_HOL_Obool))))))
      | hBOOL(hAPP(c_List_Odistinct(X30121),hAPP(hAPP(c_List_Olist__update(X30121,X30120),X30118),X30119))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5495])]) ).

fof(i_0_6982,plain,
    ! [X19691,X19692,X19693,X19694] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19694),hAPP(c_Set_Oimage(X19693,X19694,X19692),X19691))),hAPP(c_Finite__Set_Ocard(X19693),X19691)))
      | ~ c_Fun_Oinj__on(X19693,X19694,X19692,X19691) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5496])]) ).

fof(i_0_6983,plain,
    ! [X29496,X29497,X29498,X29499] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29498),esk378_4(X29496,X29497,X29498,X29499)),X29497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29499),c_Groups_Ozero__class_Ozero(X29499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29498,X29499),X29496),X29497)))
        | ~ class_Rings_Olinordered__semidom(X29499) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29499),c_Groups_Ozero__class_Ozero(X29499)),hAPP(X29496,esk378_4(X29496,X29497,X29498,X29499))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29499),c_Groups_Ozero__class_Ozero(X29499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29498,X29499),X29496),X29497)))
        | ~ class_Rings_Olinordered__semidom(X29499) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos])])])]) ).

fof(i_0_6984,plain,
    ! [X29522,X29523,X29524,X29525] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29524),esk379_4(X29522,X29523,X29524,X29525)),X29523))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29525),c_Groups_Ozero__class_Ozero(X29525)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29524,X29525),X29522),X29523)))
        | ~ class_Rings_Olinordered__semidom(X29525) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29525),c_Groups_Ozero__class_Ozero(X29525)),hAPP(X29522,esk379_4(X29522,X29523,X29524,X29525))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29525),c_Groups_Ozero__class_Ozero(X29525)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29524,X29525),X29522),X29523)))
        | ~ class_Rings_Olinordered__semidom(X29525) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__nonneg])])])]) ).

fof(i_0_6985,plain,
    ! [X32837,X32838,X32839,X32840,X32841] : c_Predicate_Oconversep(X32841,X32840,c_Predicate_Opred__comp(X32841,X32839,X32840,X32838,X32837)) = c_Predicate_Opred__comp(X32840,X32839,X32841,c_Predicate_Oconversep(X32839,X32840,X32837),c_Predicate_Oconversep(X32841,X32839,X32838)),
    inference(variable_rename,[status(thm)],[fact_converse__pred__comp]) ).

cnf(i_0_6986,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5478]) ).

cnf(i_0_6987,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5497]) ).

fof(i_0_6988,plain,
    ! [X28684,X28685,X28686,X28687,X28688,X28689,X28690,X28691] :
      ( ~ c_Finite__Set_Ofolding(X28691,X28690,X28689,X28688)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28691),X28687))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28691),X28686))
      | hAPP(c_Fun_Ocomp(X28690,X28690,X28685,hAPP(X28688,X28686)),hAPP(c_Fun_Ocomp(X28690,X28690,X28685,hAPP(X28688,X28687)),X28684)) = hAPP(c_Fun_Ocomp(X28690,X28690,X28685,hAPP(X28688,X28687)),hAPP(c_Fun_Ocomp(X28690,X28690,X28685,hAPP(X28688,X28686)),X28684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).

fof(i_0_6989,plain,
    ! [X33475,X33476,X33477,X33478] : hAPP(c_Hilbert__Choice_Oinv__into(X33478,X33477,c_Orderings_Otop__class_Otop(tc_fun(X33478,tc_HOL_Obool)),X33476),X33475) = c_Hilbert__Choice_OEps(X33478,hAPP(hAPP(c_COMBC(X33478,X33477,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X33477,tc_fun(X33477,tc_HOL_Obool),X33478),c_fequal),X33476)),X33475)),
    inference(variable_rename,[status(thm)],[fact_inv__def]) ).

fof(i_0_6990,plain,
    ! [X28063,X28064,X28065,X28066] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28066),esk305_4(X28063,X28064,X28065,X28066)),X28065))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28066,X28064)),hAPP(hAPP(c_Product__Type_OSigma(X28066,X28064),X28065),X28063)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28066),X28065)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28064),hAPP(X28063,esk305_4(X28063,X28064,X28065,X28066))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28066,X28064)),hAPP(hAPP(c_Product__Type_OSigma(X28066,X28064),X28065),X28063)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28066),X28065)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__SigmaI])])])]) ).

fof(i_0_6991,plain,
    ! [X22728,X22729,X22730,X22731,X22732,X22733] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X22733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22733),X22732),X22731))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22733),X22730),X22731))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22733),c_Groups_Ozero__class_Ozero(X22733)),X22729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22733),c_Groups_Ozero__class_Ozero(X22733)),X22728))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22733),X22729),X22728) != c_Groups_Oone__class_Oone(X22733)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22733),X22729),X22732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22733),X22728),X22730))),X22731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).

fof(i_0_6992,plain,
    ! [X22684,X22685,X22686,X22687,X22688,X22689] :
      ( ~ class_Rings_Olinordered__semiring__1(X22689)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22689),X22688),X22687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22689),X22686),X22687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22689),c_Groups_Ozero__class_Ozero(X22689)),X22685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22689),c_Groups_Ozero__class_Ozero(X22689)),X22684))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22689),X22685),X22684) != c_Groups_Oone__class_Oone(X22689)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22689),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22689),X22685),X22688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22689),X22684),X22686))),X22687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).

fof(i_0_6993,plain,
    ! [X24389,X24390,X24391,X24392] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk175_4(X24389,X24390,X24391,X24392)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24391)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24392),X24390))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24392),X24391)),X24390))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24390),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24389))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24391)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_4(X24389,X24390,X24391,X24392)),X24389))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24392),X24390))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24392),X24391)),X24390))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24390),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24389))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24391)) )
      & ( X24392 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk176_4(X24389,X24390,X24391,X24392)),esk175_4(X24389,X24390,X24391,X24392))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24392),X24390))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24392),X24391)),X24390))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24390),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24389))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24391)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I6_J])])])])]) ).

fof(i_0_6994,plain,
    ! [X32386,X32387,X32388,X32389] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32389),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32388)),X32387)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X32386,X32387,X32388,X32389)),X32389)) )
      & ( hBOOL(hAPP(X32386,hAPP(hAPP(c_List_Onth(X32388),X32387),X32389)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X32386,X32387,X32388,X32389)),X32389)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32389),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32388)),X32387)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X32386,X32387,X32388,X32389)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32388)),X32387))) )
      & ( hBOOL(hAPP(X32386,hAPP(hAPP(c_List_Onth(X32388),X32387),X32389)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X32386,X32387,X32388,X32389)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32388)),X32387))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32389),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32388)),X32387)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | ~ hBOOL(hAPP(X32386,hAPP(hAPP(c_List_Onth(X32388),X32387),esk447_4(X32386,X32387,X32388,X32389)))) )
      & ( hBOOL(hAPP(X32386,hAPP(hAPP(c_List_Onth(X32388),X32387),X32389)))
        | c_List_OtakeWhile(X32388,X32386,X32387) = hAPP(hAPP(c_List_Otake(X32388),X32389),X32387)
        | ~ hBOOL(hAPP(X32386,hAPP(hAPP(c_List_Onth(X32388),X32387),esk447_4(X32386,X32387,X32388,X32389)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5498])])])]) ).

fof(i_0_6995,plain,
    ! [X33614,X33615,X33616,X33617,X33618,X33619] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33619,X33618,X33617,X33616,c_Lazy__Sequence_Olazy__sequence_OInsert(X33618,X33615,X33614)) = hAPP(hAPP(hAPP(X33616,X33615),X33614),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33619,X33618,X33617,X33616,X33614)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I2_J]) ).

fof(i_0_6996,plain,
    ! [X33311,X33312,X33313,X33314,X33316] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33314),esk515_4(X33311,X33312,X33313,X33314)),X33313))
        | c_Wellfounded_Omax__extp(X33314,X33311,X33313,X33312)
        | X33312 = c_Orderings_Obot__class_Obot(tc_fun(X33314,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33314),X33312))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33314),X33313)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33314),X33316),X33312))
        | ~ hBOOL(hAPP(hAPP(X33311,esk515_4(X33311,X33312,X33313,X33314)),X33316))
        | c_Wellfounded_Omax__extp(X33314,X33311,X33313,X33312)
        | X33312 = c_Orderings_Obot__class_Obot(tc_fun(X33314,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33314),X33312))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33314),X33313)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp_Ointros])])])])]) ).

fof(i_0_6997,plain,
    ! [X28670,X28671,X28672,X28673,X28674,X28675,X28676,X28677] :
      ( ~ c_Finite__Set_Ofolding(X28677,X28676,X28675,X28674)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28677),X28673))
      | hAPP(c_Fun_Ocomp(X28676,X28676,X28672,hAPP(X28675,X28671)),hAPP(c_Fun_Ocomp(X28676,X28676,X28672,hAPP(X28674,X28673)),X28670)) = hAPP(c_Fun_Ocomp(X28676,X28676,X28672,hAPP(X28674,X28673)),hAPP(c_Fun_Ocomp(X28676,X28676,X28672,hAPP(X28675,X28671)),X28670)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).

fof(i_0_6998,plain,
    ! [X30535,X30536,X30537,X30538,X30539,X30540,X30541,X30542] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30542,X30542)),hAPP(hAPP(c_Product__Type_OPair(X30542,X30542),X30541),X30540)),X30539))
      | X30538 != hAPP(hAPP(c_List_Oappend(X30542),X30537),hAPP(hAPP(c_List_Olist_OCons(X30542),X30541),X30536))
      | X30535 != hAPP(hAPP(c_List_Oappend(X30542),X30537),hAPP(hAPP(c_List_Olist_OCons(X30542),X30540),X30536))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30542),tc_List_Olist(X30542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30542),tc_List_Olist(X30542)),X30538),X30535)),c_List_Olistrel1(X30542,X30539))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).

fof(i_0_6999,plain,
    ! [X33854,X33855,X33856,X33857,X33859] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33857),esk546_4(X33854,X33855,X33856,X33857)),c_Quotient_ORespects(X33857,X33856)))
        | ~ hBOOL(hAPP(X33855,X33859))
        | hBOOL(hAPP(X33855,esk545_4(X33854,X33855,X33856,X33857)))
        | ~ c_Equiv__Relations_Oequivp(X33857,X33856) )
      & ( hBOOL(hAPP(X33854,esk546_4(X33854,X33855,X33856,X33857)))
        | ~ hBOOL(hAPP(X33855,X33859))
        | hBOOL(hAPP(X33855,esk545_4(X33854,X33855,X33856,X33857)))
        | ~ c_Equiv__Relations_Oequivp(X33857,X33856) )
      & ( hBOOL(hAPP(hAPP(c_member(X33857),esk546_4(X33854,X33855,X33856,X33857)),c_Quotient_ORespects(X33857,X33856)))
        | ~ hBOOL(hAPP(X33855,X33859))
        | ~ hBOOL(hAPP(X33854,esk545_4(X33854,X33855,X33856,X33857)))
        | ~ c_Equiv__Relations_Oequivp(X33857,X33856) )
      & ( hBOOL(hAPP(X33854,esk546_4(X33854,X33855,X33856,X33857)))
        | ~ hBOOL(hAPP(X33855,X33859))
        | ~ hBOOL(hAPP(X33854,esk545_4(X33854,X33855,X33856,X33857)))
        | ~ c_Equiv__Relations_Oequivp(X33857,X33856) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__reg__right])])])])]) ).

cnf(i_0_7000,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5499]) ).

fof(i_0_7001,plain,
    ! [X31589,X31590,X31591,X31592] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk426_4(X31589,X31590,X31591,X31592)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31592)),X31591)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31592),X31589),hAPP(c_List_Oset(X31592),X31591)))
        | hBOOL(hAPP(X31590,X31589)) )
      & ( ~ hBOOL(hAPP(X31590,hAPP(hAPP(c_List_Onth(X31592),X31591),esk426_4(X31589,X31590,X31591,X31592))))
        | ~ hBOOL(hAPP(hAPP(c_member(X31592),X31589),hAPP(c_List_Oset(X31592),X31591)))
        | hBOOL(hAPP(X31590,X31589)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set])])])]) ).

fof(i_0_7002,plain,
    ! [X25634,X25635,X25636,X25637] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25637),esk255_4(X25634,X25635,X25636,X25637)),X25636))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25637),X25635),X25634)),hAPP(hAPP(c_Finite__Set_Ofold(X25637,X25637,c_Lattices_Osemilattice__inf__class_Oinf(X25637)),X25634),X25636)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25637),X25636))
        | ~ class_Lattices_Osemilattice__inf(X25637) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25637),X25635),esk255_4(X25634,X25635,X25636,X25637)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25637),X25635),X25634)),hAPP(hAPP(c_Finite__Set_Ofold(X25637,X25637,c_Lattices_Osemilattice__inf__class_Oinf(X25637)),X25634),X25636)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25637),X25636))
        | ~ class_Lattices_Osemilattice__inf(X25637) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf])])])]) ).

fof(i_0_7003,plain,
    ! [X19303,X19304,X19305,X19306] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19306),esk65_4(X19303,X19304,X19305,X19306)),X19305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19306),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19306),X19304),X19303)),hAPP(hAPP(c_Finite__Set_Ofold(X19306,X19306,c_Orderings_Oord__class_Omin(X19306)),X19303),X19305)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19306),X19305))
        | ~ class_Orderings_Olinorder(X19306) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19306),X19304),esk65_4(X19303,X19304,X19305,X19306)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19306),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19306),X19304),X19303)),hAPP(hAPP(c_Finite__Set_Ofold(X19306,X19306,c_Orderings_Oord__class_Omin(X19306)),X19303),X19305)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19306),X19305))
        | ~ class_Orderings_Olinorder(X19306) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf])])])]) ).

fof(i_0_7004,plain,
    ! [X23131,X23132,X23133,X23134,X23135] :
      ( ~ class_Groups_Ocomm__monoid__add(X23135)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23135),X23134),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23133),X23132)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23131),X23132))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23135),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23135,tc_Nat_Onat),X23134),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23132))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23133),X23131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).

fof(i_0_7005,plain,
    ! [X33726,X33727,X33728,X33729,X33730,X33731,X33732] :
      ( ~ c_Fun_Obij__betw(X33732,X33731,X33730,X33729,X33728)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33732,tc_HOL_Obool)),X33727),X33729))
      | hAPP(c_Set_Oimage(X33732,X33731,X33730),X33727) != X33726
      | c_Fun_Obij__betw(X33732,X33731,X33730,X33727,X33726) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__subset])]) ).

fof(i_0_7006,plain,
    ! [X28965,X28966,X28967,X28968] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28968,X28968)),X28967),c_Transitive__Closure_Ortrancl(X28968,X28966)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28968,X28968)),X28967),c_Transitive__Closure_Ortrancl(X28968,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28968,X28968),tc_HOL_Obool)),X28966),X28965)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28968,X28968)),X28967),c_Transitive__Closure_Ortrancl(X28968,X28965)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28968,X28968)),X28967),c_Transitive__Closure_Ortrancl(X28968,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28968,X28968),tc_HOL_Obool)),X28966),X28965)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).

fof(i_0_7007,plain,
    ! [X28623,X28624,X28625,X28626,X28627,X28628,X28629,X28630] :
      ( ~ c_Finite__Set_Ofolding(X28630,X28629,X28628,X28627)
      | hAPP(c_Fun_Ocomp(X28629,X28629,X28626,hAPP(X28628,X28625)),hAPP(c_Fun_Ocomp(X28629,X28629,X28626,hAPP(X28628,X28624)),X28623)) = hAPP(c_Fun_Ocomp(X28629,X28629,X28626,hAPP(X28628,X28624)),hAPP(c_Fun_Ocomp(X28629,X28629,X28626,hAPP(X28628,X28625)),X28623)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).

cnf(i_0_7008,plain,
    ( c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = c_List_OdropWhile(X4,X1,X2)
    | ~ hBOOL(hAPP(X1,esk458_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5489]) ).

fof(i_0_7009,plain,
    ! [X19791,X19792,X19793,X19794,X19796,X19797] :
      ( ( X19791 = hAPP(X19792,esk73_4(X19791,X19792,X19793,X19794))
        | ~ hBOOL(hAPP(hAPP(c_member(X19793),X19791),hAPP(c_Set_Oimage(X19794,X19793,X19792),c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19794,X19793,X19792,c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool))) )
      & ( X19791 != hAPP(X19792,X19796)
        | X19796 = esk73_4(X19791,X19792,X19793,X19794)
        | ~ hBOOL(hAPP(hAPP(c_member(X19793),X19791),hAPP(c_Set_Oimage(X19794,X19793,X19792),c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19794,X19793,X19792,c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool))) )
      & ( X19791 = hAPP(X19792,esk74_5(X19791,X19792,X19793,X19794,X19797))
        | X19791 != hAPP(X19792,X19797)
        | hBOOL(hAPP(hAPP(c_member(X19793),X19791),hAPP(c_Set_Oimage(X19794,X19793,X19792),c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19794,X19793,X19792,c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool))) )
      & ( esk74_5(X19791,X19792,X19793,X19794,X19797) != X19797
        | X19791 != hAPP(X19792,X19797)
        | hBOOL(hAPP(hAPP(c_member(X19793),X19791),hAPP(c_Set_Oimage(X19794,X19793,X19792),c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19794,X19793,X19792,c_Orderings_Otop__class_Otop(tc_fun(X19794,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).

fof(i_0_7010,plain,
    ! [X21065,X21066,X21067,X21068,X21069] :
      ( ~ class_Groups_Oab__group__add(X21069)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21068),X21067))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21068),X21066))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21068,X21069),X21065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21068,tc_HOL_Obool)),X21067),X21066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21068,X21069),X21065),X21067)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21068,X21069),X21065),X21066))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21068,X21069),X21065),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21068,tc_HOL_Obool)),X21067),X21066))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).

fof(i_0_7011,plain,
    ! [X32223,X32224,X32225,X32226] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32225)),X32224)))
      | hAPP(c_List_Orev(X32225),hAPP(hAPP(c_List_Olist__update(X32225,X32224),X32226),X32223)) = hAPP(hAPP(c_List_Olist__update(X32225,hAPP(c_List_Orev(X32225),X32224)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32225)),X32224)),X32226)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32223) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).

cnf(i_0_7012,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | c_Groups_Oone__class_Oone(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5454]) ).

cnf(i_0_7013,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5453]) ).

fof(i_0_7014,plain,
    ! [X25360,X25361,X25362] : hAPP(c_Set_OCollect(X25362),hAPP(hAPP(c_COMBS(X25362,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25362),c_fimplies),X25361)),X25360)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25362,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25362,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25362),X25361))),hAPP(c_Set_OCollect(X25362),X25360)),
    inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).

fof(i_0_7015,plain,
    ! [X25804,X25805,X25806,X25807] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)),X25806))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)),X25806))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)),X25806))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25805))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25805),c_Groups_Ozero__class_Ozero(X25807)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)),X25806))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)),X25806))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),X25806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25807),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)),X25805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25807),X25806),X25805)),hAPP(c_Int_Onumber__class_Onumber__of(X25807),X25804)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25807)
        | ~ class_Int_Onumber(X25807) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5500])])]) ).

fof(i_0_7016,plain,
    ! [X25830,X25831,X25832,X25833] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)),X25832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),c_Groups_Ozero__class_Ozero(X25833)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),c_Groups_Ozero__class_Ozero(X25833)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)),X25832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),c_Groups_Ozero__class_Ozero(X25833)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)),X25832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),c_Groups_Ozero__class_Ozero(X25833)),X25831))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),c_Groups_Ozero__class_Ozero(X25833)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25833),X25831),c_Groups_Ozero__class_Ozero(X25833)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)),X25832))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),c_Groups_Ozero__class_Ozero(X25833)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)),X25832))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),X25832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25833),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)),X25831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25833),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25833),X25832),X25831)),hAPP(c_Int_Onumber__class_Onumber__of(X25833),X25830)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25833)
        | ~ class_Int_Onumber(X25833) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5501])])]) ).

fof(i_0_7017,plain,
    ! [X29242,X29243,X29244,X29245,X29246,X29247,X29248,X29249,X29250] :
      ( ( ~ c_Relation_Osingle__valued(X29244,X29243,X29242)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29244,X29243)),hAPP(hAPP(c_Product__Type_OPair(X29244,X29243),X29245),X29246)),X29242))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29244,X29243)),hAPP(hAPP(c_Product__Type_OPair(X29244,X29243),X29245),X29247)),X29242))
        | X29246 = X29247 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29250,X29249)),hAPP(hAPP(c_Product__Type_OPair(X29250,X29249),esk342_3(X29248,X29249,X29250)),esk343_3(X29248,X29249,X29250))),X29248))
        | c_Relation_Osingle__valued(X29250,X29249,X29248) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29250,X29249)),hAPP(hAPP(c_Product__Type_OPair(X29250,X29249),esk342_3(X29248,X29249,X29250)),esk344_3(X29248,X29249,X29250))),X29248))
        | c_Relation_Osingle__valued(X29250,X29249,X29248) )
      & ( esk343_3(X29248,X29249,X29250) != esk344_3(X29248,X29249,X29250)
        | c_Relation_Osingle__valued(X29250,X29249,X29248) ) ),
    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_single__valued__def])])])])])]) ).

fof(i_0_7018,plain,
    ! [X25808,X25809,X25810,X25811] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),c_Groups_Ozero__class_Ozero(X25811)),X25808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),c_Groups_Ozero__class_Ozero(X25811)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25808),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),c_Groups_Ozero__class_Ozero(X25811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),X25809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),X25808)),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25811),hAPP(c_Int_Onumber__class_Onumber__of(X25811),X25810)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25811),X25809),X25808)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25811)
        | ~ class_Int_Onumber(X25811) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5502])])]) ).

fof(i_0_7019,plain,
    ! [X25826,X25827,X25828,X25829] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),X25827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),X25827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),X25827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),c_Groups_Ozero__class_Ozero(X25829)),X25826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),c_Groups_Ozero__class_Ozero(X25829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25829),X25826),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),X25827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),c_Groups_Ozero__class_Ozero(X25829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),X25827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),X25826)),X25827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25829),hAPP(c_Int_Onumber__class_Onumber__of(X25829),X25828)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25829),X25827),X25826)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25829)
        | ~ class_Int_Onumber(X25829) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5503])])]) ).

fof(i_0_7020,plain,
    ! [X27049,X27050,X27051,X27052,X27053] : c_Product__Type_Oprod_Oprod__size(X27053,X27052,X27051,X27050,X27049) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X27051,hAPP(c_Product__Type_Ofst(X27053,X27052),X27049))),hAPP(X27050,hAPP(c_Product__Type_Osnd(X27053,X27052),X27049)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_prod__size__simp]) ).

fof(i_0_7021,plain,
    ! [X24177,X24178,X24179,X24180,X24181] :
      ( ~ class_Groups_Ocomm__monoid__add(X24181)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24181),X24180),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24179),X24178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24177),X24178))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24181),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24181,tc_Nat_Onat),X24180),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24178))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24179,X24177)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).

fof(i_0_7022,plain,
    ! [X24395,X24396,X24397,X24398] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_4(X24395,X24396,X24397,X24398)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24397)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),X24398))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24398),X24397)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24396),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24395))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24397)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_4(X24395,X24396,X24397,X24398)),X24395))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),X24398))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24398),X24397)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24396),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24395))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24397)) )
      & ( X24398 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk178_4(X24395,X24396,X24397,X24398)),esk177_4(X24395,X24396,X24397,X24398))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),X24398))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24398),X24397)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24396),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24395))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24397)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I8_J])])])])]) ).

fof(i_0_7023,plain,
    ! [X27981,X27982,X27983,X27984] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27984),X27983))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27984,X27984),tc_HOL_Obool)),X27982),hAPP(hAPP(c_Product__Type_OSigma(X27984,X27984),X27983),hAPP(c_COMBK(tc_fun(X27984,tc_HOL_Obool),X27984),X27983))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27984,tc_HOL_Obool)),X27981),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27984),X27983),X27982)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27984),X27981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).

fof(i_0_7024,plain,
    ! [X17921,X17922,X17923,X17924,X17925,X17926] :
      ( ~ c_Fun_Oinj__on(X17926,X17925,X17924,X17923)
      | hBOOL(hAPP(hAPP(c_member(X17925),X17922),hAPP(c_Set_Oimage(X17926,X17925,X17924),X17923)))
      | c_Fun_Oinj__on(X17926,X17925,c_Fun_Ofun__upd(X17926,X17925,X17924,X17921,X17922),X17923) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5504])]) ).

fof(i_0_7025,plain,
    ! [X26520,X26521,X26522,X26523,X26524,X26525,X26526] :
      ( ~ c_Equiv__Relations_Oequiv(X26526,X26525,X26524)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26526,tc_HOL_Obool)),X26523),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26526),X26525),X26524)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26526,tc_HOL_Obool)),X26522),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26526),X26525),X26524)))
      | ~ hBOOL(hAPP(hAPP(c_member(X26526),X26521),X26523))
      | ~ hBOOL(hAPP(hAPP(c_member(X26526),X26520),X26522))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26526,X26526)),hAPP(hAPP(c_Product__Type_OPair(X26526,X26526),X26521),X26520)),X26524))
      | X26523 = X26522 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).

fof(i_0_7026,plain,
    ! [X26527,X26528,X26529,X26530,X26531,X26532,X26533] :
      ( ( X26530 != X26529
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26533,X26533)),hAPP(hAPP(c_Product__Type_OPair(X26533,X26533),X26528),X26527)),X26531))
        | ~ hBOOL(hAPP(hAPP(c_member(X26533),X26527),X26529))
        | ~ hBOOL(hAPP(hAPP(c_member(X26533),X26528),X26530))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26533,tc_HOL_Obool)),X26529),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26533),X26532),X26531)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26533,tc_HOL_Obool)),X26530),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26533),X26532),X26531)))
        | ~ c_Equiv__Relations_Oequiv(X26533,X26532,X26531) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26533,X26533)),hAPP(hAPP(c_Product__Type_OPair(X26533,X26533),X26528),X26527)),X26531))
        | X26530 = X26529
        | ~ hBOOL(hAPP(hAPP(c_member(X26533),X26527),X26529))
        | ~ hBOOL(hAPP(hAPP(c_member(X26533),X26528),X26530))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26533,tc_HOL_Obool)),X26529),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26533),X26532),X26531)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26533,tc_HOL_Obool)),X26530),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26533),X26532),X26531)))
        | ~ c_Equiv__Relations_Oequiv(X26533,X26532,X26531) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).

fof(i_0_7027,plain,
    ! [X24564,X24565,X24566] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24566),c_Groups_Ozero__class_Ozero(X24566)),esk208_3(X24564,X24565,X24566)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24566),X24565),X24564))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24566) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24566),esk208_3(X24564,X24565,X24566)),c_Groups_Oone__class_Oone(X24566)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24566),X24565),X24564))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24566) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24566),esk208_3(X24564,X24565,X24566)),X24565)),X24564))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24566),X24565),X24564))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24566) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval])])])]) ).

fof(i_0_7028,plain,
    ! [X32979,X32980] : c_Predicate_Opred__comp(X32980,X32980,X32980,c_fequal,c_Predicate_Opred__comp(X32980,X32980,X32980,X32979,c_fequal)) = X32979,
    inference(variable_rename,[status(thm)],[fact_eq__comp__r]) ).

fof(i_0_7029,plain,
    ! [X33699,X33700,X33701,X33702,X33703] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33703,X33702,tc_HOL_Obool,X33701),X33700),X33699))
      | hBOOL(hAPP(X33701,hAPP(hAPP(c_Product__Type_OPair(X33703,X33702),X33700),X33699))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).

fof(i_0_7030,plain,
    ! [X33694,X33695,X33696,X33697,X33698] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33698,X33697,tc_HOL_Obool,X33696),X33695),X33694))
      | hBOOL(hAPP(X33696,hAPP(hAPP(c_Product__Type_OPair(X33698,X33697),X33695),X33694))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).

fof(i_0_7031,plain,
    ! [X25508,X25509,X25510,X25511] : hAPP(c_Relation_OImage(X25511,X25510,X25509),X25508) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25511,tc_fun(X25510,tc_HOL_Obool)),X25508),hAPP(hAPP(c_COMBB(tc_fun(X25511,tc_HOL_Obool),tc_fun(X25510,tc_HOL_Obool),X25511),c_Relation_OImage(X25511,X25510,X25509)),hAPP(hAPP(c_COMBC(X25511,tc_fun(X25511,tc_HOL_Obool),tc_fun(X25511,tc_HOL_Obool)),c_Set_Oinsert(X25511)),c_Orderings_Obot__class_Obot(tc_fun(X25511,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).

fof(i_0_7032,plain,
    ! [X21135,X21136,X21137,X21138] : hAPP(c_Set_Ovimage(X21138,X21137,X21136),X21135) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21137,tc_fun(X21138,tc_HOL_Obool)),X21135),hAPP(hAPP(c_COMBB(tc_fun(X21137,tc_HOL_Obool),tc_fun(X21138,tc_HOL_Obool),X21137),c_Set_Ovimage(X21138,X21137,X21136)),hAPP(hAPP(c_COMBC(X21137,tc_fun(X21137,tc_HOL_Obool),tc_fun(X21137,tc_HOL_Obool)),c_Set_Oinsert(X21137)),c_Orderings_Obot__class_Obot(tc_fun(X21137,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).

fof(i_0_7033,plain,
    ! [X20833,X20834,X20835,X20836] :
      ( ~ class_Lattices_Olattice(X20836)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20836),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20836),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20836),X20835),X20834)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20836),X20835),X20833))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20836),X20835),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20836),X20834),X20833)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).

fof(i_0_7034,plain,
    ! [X18704,X18705,X18706,X18707] :
      ( ~ class_Orderings_Olinorder(X18707)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18707),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18707),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18707),X18706),X18705)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18707),X18706),X18704))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18707),X18706),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18707),X18705),X18704)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).

fof(i_0_7035,plain,
    ! [X33637,X33638,X33639,X33640,X33641] :
      ( ~ c_Fun_Obij__betw(X33641,X33640,X33639,X33638,X33637)
      | c_Fun_Obij__betw(X33640,X33641,c_Hilbert__Choice_Oinv__into(X33641,X33640,X33638,X33639),X33637,X33638) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__inv__into])]) ).

fof(i_0_7036,plain,
    ! [X33757,X33758,X33759,X33760,X33761] :
      ( ~ c_Fun_Obij__betw(X33761,X33760,X33759,X33758,X33757)
      | c_Fun_Obij__betw(X33760,X33761,c_Fun_Othe__inv__into(X33761,X33760,X33758,X33759),X33757,X33758) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__the__inv__into])]) ).

fof(i_0_7037,plain,
    ! [X33642,X33643,X33644,X33645,X33646,X33647] :
      ( ~ c_Fun_Obij__betw(X33647,X33646,X33645,X33644,X33643)
      | ~ hBOOL(hAPP(hAPP(c_member(X33647),X33642),X33644))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33646,X33647,X33643,c_Hilbert__Choice_Oinv__into(X33647,X33646,X33644,X33645)),X33642) = hAPP(X33645,X33642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__inv__into__eq])]) ).

fof(i_0_7038,plain,
    ! [X20471,X20472,X20473,X20474,X20475,X20476,X20477,X20478] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20478),X20477),X20476))
      | ~ hBOOL(hAPP(hAPP(hAPP(X20475,X20477),X20474),X20473))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20478,tc_fun(X20472,tc_fun(X20471,tc_HOL_Obool))),X20476),X20475),X20474),X20473)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).

fof(i_0_7039,plain,
    ! [X26653,X26654,X26655,X26656,X26657,X26658,X26659] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26659,X26658,tc_fun(X26657,tc_HOL_Obool)),X26656),hAPP(hAPP(c_Product__Type_OPair(X26659,X26658),X26655),X26654)),X26653))
      | hBOOL(hAPP(hAPP(hAPP(X26656,X26655),X26654),X26653)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).

fof(i_0_7040,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_5])]) ).

fof(i_0_7041,plain,
    ! [X27378,X27379,X27380,X27381,X27382,X27383] : hAPP(hAPP(c_Relation_Orel__comp(X27383,X27382,X27381),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27383,X27382),tc_HOL_Obool)),X27380),X27379)),X27378) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27383,X27381),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27383,X27382,X27381),X27380),X27378)),hAPP(hAPP(c_Relation_Orel__comp(X27383,X27382,X27381),X27379),X27378)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(i_0_7042,plain,
    ! [X21992,X21993,X21994,X21995,X21996] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21996)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21995),X21994))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21996),X21993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21995,X21996),X21994),X21992)) = hAPP(hAPP(c_Finite__Set_Ofold(X21995,X21996,hAPP(hAPP(c_COMBB(X21996,tc_fun(X21996,X21996),X21995),c_Lattices_Osemilattice__inf__class_Oinf(X21996)),X21992)),X21993),X21994) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).

fof(i_0_7043,plain,
    ! [X21080,X21081,X21082,X21083,X21084] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21084)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21083),X21082))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21084),X21081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21083,X21084),X21082),X21080)) = hAPP(hAPP(c_Finite__Set_Ofold(X21083,X21084,hAPP(hAPP(c_COMBB(X21084,tc_fun(X21084,X21084),X21083),c_Lattices_Osemilattice__sup__class_Osup(X21084)),X21080)),X21081),X21082) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).

fof(i_0_7044,plain,
    ! [X21131,X21132,X21133,X21134] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21134),X21133))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21134),X21132))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21134,tc_Nat_Onat),X21131),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21134,tc_HOL_Obool)),X21133),X21132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21134,tc_Nat_Onat),X21131),X21133)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21134,tc_Nat_Onat),X21131),X21132))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21134,tc_Nat_Onat),X21131),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21134,tc_HOL_Obool)),X21133),X21132))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).

fof(i_0_7045,plain,
    ! [X25349,X25350] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),hAPP(c_Set_OCollect(X25350),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25350),c_fNot),X25349))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),c_Orderings_Otop__class_Otop(tc_fun(X25350,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),hAPP(c_Set_OCollect(X25350),X25349))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),c_Orderings_Otop__class_Otop(tc_fun(X25350,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),hAPP(c_Set_OCollect(X25350),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25350),c_fNot),X25349))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25350),hAPP(c_Set_OCollect(X25350),X25349))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).

fof(i_0_7046,plain,
    ! [X33815,X33816,X33817,X33818] :
      ( ~ c_Fun_Obij__betw(X33818,X33817,X33816,c_Orderings_Otop__class_Otop(tc_fun(X33818,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33817,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X33818,X33817,X33816),X33815) = hAPP(c_Set_Oimage(X33817,X33818,c_Hilbert__Choice_Oinv__into(X33818,X33817,c_Orderings_Otop__class_Otop(tc_fun(X33818,tc_HOL_Obool)),X33816)),X33815) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__vimage__eq__inv__image])]) ).

fof(i_0_7047,plain,
    ! [X24810,X24811,X24812,X24813] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24813))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24812),X24811))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24811),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24812),X24813)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24812),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24810,X24813))),X24811))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).

fof(i_0_7048,plain,
    ! [X20235,X20236,X20237,X20238,X20239] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20239),X20238))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20239),X20237)),X20236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20238),X20237)),X20235)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20236),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20238),X20239)),X20237)),X20235)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).

fof(i_0_7049,plain,
    ! [X24996,X24997,X24998,X24999] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24999)
      | hAPP(c_Groups_Oabs__class_Oabs(X24999),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24998,X24999),hAPP(hAPP(c_COMBB(X24999,X24999,X24998),c_Groups_Oabs__class_Oabs(X24999)),X24997)),X24996)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24998,X24999),hAPP(hAPP(c_COMBB(X24999,X24999,X24998),c_Groups_Oabs__class_Oabs(X24999)),X24997)),X24996) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).

fof(i_0_7050,plain,
    ! [X19808,X19809,X19810,X19811,X19812] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19811,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19812,X19811,X19810),X19809)),hAPP(c_Set_Oimage(X19812,X19811,X19810),X19808)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19812,tc_HOL_Obool)),X19809),X19808))
        | ~ c_Fun_Oinj__on(X19812,X19811,X19810,c_Orderings_Otop__class_Otop(tc_fun(X19812,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19812,tc_HOL_Obool)),X19809),X19808))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19811,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19812,X19811,X19810),X19809)),hAPP(c_Set_Oimage(X19812,X19811,X19810),X19808)))
        | ~ c_Fun_Oinj__on(X19812,X19811,X19810,c_Orderings_Otop__class_Otop(tc_fun(X19812,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).

cnf(i_0_7051,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk453_2(X2,X1))),hAPP(c_List_Oset(X1),esk454_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7052,plain,
    ! [X23949,X23950,X23951] :
      ( ~ class_Fields_Olinordered__field(X23951)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23951),X23950),X23949))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23951),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23951),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23951),X23950),X23949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23951),c_Groups_Oone__class_Oone(X23951)),c_Groups_Oone__class_Oone(X23951)))),X23949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_7053,plain,
    ! [X33510,X33511,X33512,X33513,X33514,X33515] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X33515,X33514,X33513,X33512),X33511) != hAPP(c_Hilbert__Choice_Oinv__into(X33515,X33514,X33513,X33512),X33510)
      | ~ hBOOL(hAPP(hAPP(c_member(X33514),X33511),hAPP(c_Set_Oimage(X33515,X33514,X33512),X33513)))
      | ~ hBOOL(hAPP(hAPP(c_member(X33514),X33510),hAPP(c_Set_Oimage(X33515,X33514,X33512),X33513)))
      | X33511 = X33510 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_7054,plain,
    ! [X31474,X31475,X31476,X31477,X31478,X31479,X31480] :
      ( ( hBOOL(hAPP(hAPP(X31478,X31477),X31475))
        | ~ c_List_Olist__all2(X31480,X31479,X31478,hAPP(hAPP(c_List_Olist_OCons(X31480),X31477),X31476),hAPP(hAPP(c_List_Olist_OCons(X31479),X31475),X31474)) )
      & ( c_List_Olist__all2(X31480,X31479,X31478,X31476,X31474)
        | ~ c_List_Olist__all2(X31480,X31479,X31478,hAPP(hAPP(c_List_Olist_OCons(X31480),X31477),X31476),hAPP(hAPP(c_List_Olist_OCons(X31479),X31475),X31474)) )
      & ( ~ hBOOL(hAPP(hAPP(X31478,X31477),X31475))
        | ~ c_List_Olist__all2(X31480,X31479,X31478,X31476,X31474)
        | c_List_Olist__all2(X31480,X31479,X31478,hAPP(hAPP(c_List_Olist_OCons(X31480),X31477),X31476),hAPP(hAPP(c_List_Olist_OCons(X31479),X31475),X31474)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])]) ).

fof(i_0_7055,plain,
    ! [X23212,X23213,X23214] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23214),X23213)),X23212)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23214))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23213),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).

fof(i_0_7056,plain,
    ! [X25340,X25341,X25342] :
      ( ( ~ hBOOL(hAPP(X25342,X25341))
        | hAPP(c_Set_OCollect(X25340),hAPP(hAPP(c_COMBS(X25340,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25340),c_fconj),hAPP(c_fequal,X25341))),X25342)) = hAPP(hAPP(c_Set_Oinsert(X25340),X25341),c_Orderings_Obot__class_Obot(tc_fun(X25340,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X25342,X25341))
        | hAPP(c_Set_OCollect(X25340),hAPP(hAPP(c_COMBS(X25340,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25340),c_fconj),hAPP(c_fequal,X25341))),X25342)) = c_Orderings_Obot__class_Obot(tc_fun(X25340,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5506])]) ).

cnf(i_0_7057,plain,
    hAPP(c_List_Orotate(X1,X2),X3) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_5507]) ).

cnf(i_0_7058,plain,
    ( ~ c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5508]) ).

fof(i_0_7059,plain,
    ! [X29952,X29953,X29954,X29955] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29955),X29954),hAPP(c_List_Oset(X29955),X29952)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29955,X29955)),hAPP(hAPP(c_Product__Type_OPair(X29955,X29955),X29954),X29953)),hAPP(c_List_Oset(tc_prod(X29955,X29955)),hAPP(hAPP(c_List_Ozip(X29955,X29955),X29952),X29952)))) )
      & ( X29954 = X29953
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29955,X29955)),hAPP(hAPP(c_Product__Type_OPair(X29955,X29955),X29954),X29953)),hAPP(c_List_Oset(tc_prod(X29955,X29955)),hAPP(hAPP(c_List_Ozip(X29955,X29955),X29952),X29952)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29955),X29954),hAPP(c_List_Oset(X29955),X29952)))
        | X29954 != X29953
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29955,X29955)),hAPP(hAPP(c_Product__Type_OPair(X29955,X29955),X29954),X29953)),hAPP(c_List_Oset(tc_prod(X29955,X29955)),hAPP(hAPP(c_List_Ozip(X29955,X29955),X29952),X29952)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).

fof(i_0_7060,plain,
    ! [X29968,X29969,X29970,X29971,X29972,X29973] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29973),X29971),hAPP(c_List_Oset(X29973),X29969)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29973,X29972)),hAPP(hAPP(c_Product__Type_OPair(X29973,X29972),X29971),X29970)),hAPP(c_List_Oset(tc_prod(X29973,X29972)),hAPP(hAPP(c_List_Ozip(X29973,X29972),X29969),X29968)))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29972),X29970),hAPP(c_List_Oset(X29972),X29968)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29973,X29972)),hAPP(hAPP(c_Product__Type_OPair(X29973,X29972),X29971),X29970)),hAPP(c_List_Oset(tc_prod(X29973,X29972)),hAPP(hAPP(c_List_Ozip(X29973,X29972),X29969),X29968)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5509])])]) ).

fof(i_0_7061,plain,
    ! [X29956,X29957,X29958,X29959,X29960,X29961] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29961,X29960)),hAPP(hAPP(c_Product__Type_OPair(X29961,X29960),X29959),X29958)),hAPP(c_List_Oset(tc_prod(X29961,X29960)),hAPP(hAPP(c_List_Ozip(X29961,X29960),X29957),X29956))))
      | hBOOL(hAPP(hAPP(c_member(X29961),X29959),hAPP(c_List_Oset(X29961),X29957))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).

fof(i_0_7062,plain,
    ! [X29962,X29963,X29964,X29965,X29966,X29967] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29967,X29966)),hAPP(hAPP(c_Product__Type_OPair(X29967,X29966),X29965),X29964)),hAPP(c_List_Oset(tc_prod(X29967,X29966)),hAPP(hAPP(c_List_Ozip(X29967,X29966),X29963),X29962))))
      | hBOOL(hAPP(hAPP(c_member(X29966),X29964),hAPP(c_List_Oset(X29966),X29962))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).

fof(i_0_7063,plain,
    ! [X28715,X28716,X28717,X28718,X28719,X28720] :
      ( ~ c_Finite__Set_Ofolding(X28720,X28719,X28718,X28717)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28720),X28716))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28720),X28715))
      | hAPP(c_Fun_Ocomp(X28719,X28719,X28719,hAPP(X28717,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28720,tc_HOL_Obool)),X28716),X28715))),hAPP(X28717,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28720,tc_HOL_Obool)),X28716),X28715))) = hAPP(c_Fun_Ocomp(X28719,X28719,X28719,hAPP(X28717,X28716)),hAPP(X28717,X28715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).

fof(i_0_7064,plain,
    ! [X25062,X25063,X25064] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25064)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25064),hAPP(c_Groups_Oabs__class_Oabs(X25064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25064),hAPP(c_Groups_Oabs__class_Oabs(X25064),X25063)),hAPP(c_Groups_Oabs__class_Oabs(X25064),X25062)))),hAPP(c_Groups_Oabs__class_Oabs(X25064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25064),X25063),X25062)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).

cnf(i_0_7065,plain,
    ( X1 = X2
    | hAPP(c_List_OremoveAll(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_OremoveAll(X3,X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5510]) ).

fof(i_0_7066,plain,
    ! [X23082] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23082)),X23082)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23082),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23082),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23082)),X23082)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).

fof(i_0_7067,plain,
    ! [X21452,X21453,X21454,X21455] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21455)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21454),X21453))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21454,X21455),X21453),X21452) = hAPP(hAPP(c_Finite__Set_Ofold(X21454,X21455,hAPP(hAPP(c_COMBB(X21455,tc_fun(X21455,X21455),X21454),c_Lattices_Osemilattice__inf__class_Oinf(X21455)),X21452)),c_Orderings_Otop__class_Otop(X21455)),X21453) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).

fof(i_0_7068,plain,
    ! [X20436,X20437,X20438,X20439] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X20439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20438),X20437))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20438,X20439),X20437),X20436) = hAPP(hAPP(c_Finite__Set_Ofold(X20438,X20439,hAPP(hAPP(c_COMBB(X20439,tc_fun(X20439,X20439),X20438),c_Lattices_Osemilattice__sup__class_Osup(X20439)),X20436)),c_Orderings_Obot__class_Obot(X20439)),X20437) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).

fof(i_0_7069,plain,
    ! [X29054,X29055,X29056,X29057] :
      ( ( c_Wellfounded_Oacyclic(X29057,X29054)
        | ~ c_Wellfounded_Oacyclic(X29057,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29057,X29057)),hAPP(hAPP(c_Product__Type_OPair(X29057,X29057),X29056),X29055)),X29054)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29057,X29057)),hAPP(hAPP(c_Product__Type_OPair(X29057,X29057),X29055),X29056)),c_Transitive__Closure_Ortrancl(X29057,X29054)))
        | ~ c_Wellfounded_Oacyclic(X29057,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29057,X29057)),hAPP(hAPP(c_Product__Type_OPair(X29057,X29057),X29056),X29055)),X29054)) )
      & ( ~ c_Wellfounded_Oacyclic(X29057,X29054)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29057,X29057)),hAPP(hAPP(c_Product__Type_OPair(X29057,X29057),X29055),X29056)),c_Transitive__Closure_Ortrancl(X29057,X29054)))
        | c_Wellfounded_Oacyclic(X29057,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29057,X29057)),hAPP(hAPP(c_Product__Type_OPair(X29057,X29057),X29056),X29055)),X29054)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5511])])]) ).

fof(i_0_7070,plain,
    ! [X29050,X29051,X29052,X29053] :
      ( ( c_Wellfounded_Owf(X29053,X29050)
        | ~ c_Wellfounded_Owf(X29053,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29053,X29053)),hAPP(hAPP(c_Product__Type_OPair(X29053,X29053),X29052),X29051)),X29050)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29053,X29053)),hAPP(hAPP(c_Product__Type_OPair(X29053,X29053),X29051),X29052)),c_Transitive__Closure_Ortrancl(X29053,X29050)))
        | ~ c_Wellfounded_Owf(X29053,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29053,X29053)),hAPP(hAPP(c_Product__Type_OPair(X29053,X29053),X29052),X29051)),X29050)) )
      & ( ~ c_Wellfounded_Owf(X29053,X29050)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29053,X29053)),hAPP(hAPP(c_Product__Type_OPair(X29053,X29053),X29051),X29052)),c_Transitive__Closure_Ortrancl(X29053,X29050)))
        | c_Wellfounded_Owf(X29053,hAPP(hAPP(c_Set_Oinsert(tc_prod(X29053,X29053)),hAPP(hAPP(c_Product__Type_OPair(X29053,X29053),X29052),X29051)),X29050)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5512])])]) ).

cnf(i_0_7071,plain,
    c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5513]) ).

fof(i_0_7072,plain,
    ! [X29236,X29237,X29238,X29239,X29240,X29241] :
      ( ~ c_Relation_Osingle__valued(X29241,X29240,X29239)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29241,X29240)),hAPP(hAPP(c_Product__Type_OPair(X29241,X29240),X29238),X29237)),X29239))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29241,X29240)),hAPP(hAPP(c_Product__Type_OPair(X29241,X29240),X29238),X29236)),X29239))
      | X29237 = X29236 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).

fof(i_0_7073,plain,
    ! [X25275,X25276,X25277] : hAPP(c_Set_OCollect(X25277),hAPP(hAPP(c_COMBS(X25277,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25277),c_fdisj),X25276)),X25275)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25277,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25277),X25276)),hAPP(c_Set_OCollect(X25277),X25275)),
    inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).

fof(i_0_7074,plain,
    ! [X25278,X25279,X25280] : hAPP(c_Set_OCollect(X25280),hAPP(hAPP(c_COMBS(X25280,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25280),c_fconj),X25279)),X25278)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25280,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25280),X25279)),hAPP(c_Set_OCollect(X25280),X25278)),
    inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).

fof(i_0_7075,plain,
    ! [X29453,X29454,X29455,X29456,X29458,X29459,X29460,X29463] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29454),esk366_3(X29453,X29454,X29455)),X29455))
        | ~ hBOOL(hAPP(hAPP(c_member(X29454),X29456),X29455))
        | ~ c_Wellfounded_Owf(X29454,X29453) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29454,X29454)),hAPP(hAPP(c_Product__Type_OPair(X29454,X29454),X29458),esk366_3(X29453,X29454,X29455))),X29453))
        | ~ hBOOL(hAPP(hAPP(c_member(X29454),X29458),X29455))
        | ~ hBOOL(hAPP(hAPP(c_member(X29454),X29456),X29455))
        | ~ c_Wellfounded_Owf(X29454,X29453) )
      & ( hBOOL(hAPP(hAPP(c_member(X29460),esk368_2(X29459,X29460)),esk367_2(X29459,X29460)))
        | c_Wellfounded_Owf(X29460,X29459) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29460,X29460)),hAPP(hAPP(c_Product__Type_OPair(X29460,X29460),esk369_3(X29459,X29460,X29463)),X29463)),X29459))
        | ~ hBOOL(hAPP(hAPP(c_member(X29460),X29463),esk367_2(X29459,X29460)))
        | c_Wellfounded_Owf(X29460,X29459) )
      & ( hBOOL(hAPP(hAPP(c_member(X29460),esk369_3(X29459,X29460,X29463)),esk367_2(X29459,X29460)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29460),X29463),esk367_2(X29459,X29460)))
        | c_Wellfounded_Owf(X29460,X29459) ) ),
    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)],[i_0_5514])])])])])]) ).

cnf(i_0_7076,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5515]) ).

cnf(i_0_7077,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5516]) ).

cnf(i_0_7078,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5517]) ).

cnf(i_0_7079,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5518]) ).

cnf(i_0_7080,plain,
    c_Nitpick_Oint__lcm(X1,X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_5519]) ).

cnf(i_0_7081,plain,
    c_Nitpick_Onat__lcm(X1,X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),c_Nitpick_Onat__gcd(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5520]) ).

cnf(i_0_7082,plain,
    c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),X6) = hAPP(hAPP(X3,X4),c_List_Ofoldr(X1,X2,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_5521]) ).

fof(i_0_7083,plain,
    ! [X31454,X31455,X31456,X31457,X31458,X31459] :
      ( ~ c_List_Olist__all2(X31459,X31458,X31457,X31456,X31455)
      | c_List_Olist__all2(X31459,X31458,X31457,hAPP(hAPP(c_List_Odrop(X31459),X31454),X31456),hAPP(hAPP(c_List_Odrop(X31458),X31454),X31455)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__dropI])]) ).

fof(i_0_7084,plain,
    ! [X31481,X31482,X31483,X31484,X31485,X31486] :
      ( ~ c_List_Olist__all2(X31486,X31485,X31484,X31483,X31482)
      | c_List_Olist__all2(X31486,X31485,X31484,hAPP(hAPP(c_List_Otake(X31486),X31481),X31483),hAPP(hAPP(c_List_Otake(X31485),X31481),X31482)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])]) ).

fof(i_0_7085,plain,
    ! [X29162,X29163,X29164,X29165] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29165,X29165)),hAPP(hAPP(c_Product__Type_OPair(X29165,X29165),X29164),X29163)),c_Transitive__Closure_Ortrancl(X29165,hAPP(c_Relation_Oconverse(X29165,X29165),X29162))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29165,X29165)),hAPP(hAPP(c_Product__Type_OPair(X29165,X29165),X29163),X29164)),c_Transitive__Closure_Ortrancl(X29165,X29162))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).

fof(i_0_7086,plain,
    ! [X33365,X33366,X33367,X33368] :
      ( ~ c_Relation_Oantisym(X33368,X33367)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33368,X33368)),hAPP(hAPP(c_Product__Type_OPair(X33368,X33368),X33366),X33365)),X33367))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33368,X33368)),hAPP(hAPP(c_Product__Type_OPair(X33368,X33368),X33365),X33366)),X33367))
      | X33366 = X33365 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisymD])]) ).

fof(i_0_7087,plain,
    ! [X33357,X33358,X33359,X33360,X33361,X33362] :
      ( ( ~ c_Relation_Oantisym(X33358,X33357)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33358,X33358)),hAPP(hAPP(c_Product__Type_OPair(X33358,X33358),X33359),X33360)),X33357))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33358,X33358)),hAPP(hAPP(c_Product__Type_OPair(X33358,X33358),X33360),X33359)),X33357))
        | X33359 = X33360 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33362,X33362)),hAPP(hAPP(c_Product__Type_OPair(X33362,X33362),esk518_2(X33361,X33362)),esk519_2(X33361,X33362))),X33361))
        | c_Relation_Oantisym(X33362,X33361) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33362,X33362)),hAPP(hAPP(c_Product__Type_OPair(X33362,X33362),esk519_2(X33361,X33362)),esk518_2(X33361,X33362))),X33361))
        | c_Relation_Oantisym(X33362,X33361) )
      & ( esk518_2(X33361,X33362) != esk519_2(X33361,X33362)
        | c_Relation_Oantisym(X33362,X33361) ) ),
    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_antisym__def])])])])])]) ).

fof(i_0_7088,plain,
    ! [X27552,X27553,X27554,X27555] :
      ( ~ c_Wellfounded_Owf(X27555,X27554)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27555,X27555)),hAPP(hAPP(c_Product__Type_OPair(X27555,X27555),X27553),X27552)),X27554))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27555,X27555)),hAPP(hAPP(c_Product__Type_OPair(X27555,X27555),X27552),X27553)),X27554)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5522])]) ).

fof(i_0_7089,plain,
    ! [X27548,X27549,X27550,X27551] :
      ( ~ c_Wellfounded_Owf(X27551,X27550)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27551,X27551)),hAPP(hAPP(c_Product__Type_OPair(X27551,X27551),X27549),X27548)),X27550))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27551,X27551)),hAPP(hAPP(c_Product__Type_OPair(X27551,X27551),X27548),X27549)),X27550)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5523])]) ).

fof(i_0_7090,plain,
    ! [X31126,X31127,X31128,X31129,X31130] :
      ( ~ class_Rings_Osemiring__0(X31130)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31130),hAPP(hAPP(c_List_Omap(X31129,X31130),hAPP(hAPP(c_COMBB(X31130,X31130,X31129),hAPP(c_Groups_Otimes__class_Otimes(X31130),X31128)),X31127)),X31126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31130),X31128),hAPP(c_List_Omonoid__add__class_Olistsum(X31130),hAPP(hAPP(c_List_Omap(X31129,X31130),X31127),X31126))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).

fof(i_0_7091,plain,
    ! [X25532,X25533,X25534,X25535,X25536,X25537] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X25537,X25536),tc_HOL_Obool)),X25535),X25534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25537,tc_HOL_Obool)),X25533),X25532))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25536,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25537,X25536,X25535),X25533)),hAPP(c_Relation_OImage(X25537,X25536,X25534),X25532))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).

fof(i_0_7092,plain,
    ! [X27067,X27068,X27069] :
      ( ( X27069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( X27068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27068),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( X27068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27068),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27068),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068))
        | X27068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( X27068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27068),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27068),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X27069 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X27067)),X27068)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X27067))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27069,X27068),X27067)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5524])])]) ).

fof(i_0_7093,plain,
    ! [X27074,X27075,X27076,X27077,X27078] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X27078,X27077)),hAPP(X27078,X27076)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27075,X27075)),hAPP(hAPP(c_Product__Type_OPair(X27075,X27075),X27077),X27076)),X27074))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27075,X27075)),hAPP(hAPP(c_Product__Type_OPair(X27075,X27075),X27077),X27076)),c_Wellfounded_Omlex__prod(X27075,X27078,X27074))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

fof(i_0_7094,plain,
    ! [X25800,X25801,X25802,X25803] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25802))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),X25800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),X25800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25802))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),X25800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25802))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),X25800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801)),c_Groups_Ozero__class_Ozero(X25803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),c_Groups_Ozero__class_Ozero(X25803)),X25800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25803),X25800),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25803),X25802),hAPP(c_Int_Onumber__class_Onumber__of(X25803),X25801))),X25800))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25803)
        | ~ class_Int_Onumber(X25803) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5525])])]) ).

fof(i_0_7095,plain,
    ! [X25834,X25835,X25836,X25837] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25836))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),c_Groups_Ozero__class_Ozero(X25837)),X25834))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),c_Groups_Ozero__class_Ozero(X25837)),X25834))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25836))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),c_Groups_Ozero__class_Ozero(X25837)),X25834))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25836))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),c_Groups_Ozero__class_Ozero(X25837)),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),c_Groups_Ozero__class_Ozero(X25837)),X25834))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835)),c_Groups_Ozero__class_Ozero(X25837)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25836))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),c_Groups_Ozero__class_Ozero(X25837)),X25834))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25836))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),X25836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25837),X25834),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25837),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25837),X25836),hAPP(c_Int_Onumber__class_Onumber__of(X25837),X25835))),X25834))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25837)
        | ~ class_Int_Onumber(X25837) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5526])])]) ).

cnf(i_0_7096,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),c_Transitive__Closure_Otrancl(X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5493]) ).

fof(i_0_7097,plain,
    ! [X27856,X27857,X27858,X27859] : hAPP(c_Set_Oimage(tc_prod(X27859,X27858),tc_prod(X27858,X27859),hAPP(c_Product__Type_Oprod_Oprod__case(X27859,X27858,tc_prod(X27858,X27859)),hAPP(c_COMBC(X27858,X27859,tc_prod(X27858,X27859)),c_Product__Type_OPair(X27858,X27859)))),hAPP(hAPP(c_Product__Type_OSigma(X27859,X27858),X27857),hAPP(c_COMBK(tc_fun(X27858,tc_HOL_Obool),X27859),X27856))) = hAPP(hAPP(c_Product__Type_OSigma(X27858,X27859),X27856),hAPP(c_COMBK(tc_fun(X27859,tc_HOL_Obool),X27858),X27857)),
    inference(variable_rename,[status(thm)],[fact_swap__product]) ).

cnf(i_0_7098,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X1)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_5527]) ).

fof(i_0_7099,plain,
    ! [X25504,X25505,X25506,X25507] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25507),X25506),X25505))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X25507,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25507,X25507,X25504),hAPP(hAPP(c_Set_Oinsert(X25507),X25506),c_Orderings_Obot__class_Obot(tc_fun(X25507,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25507),X25505),X25504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).

fof(i_0_7100,plain,
    ! [X26510,X26511,X26512,X26513,X26514] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26514),X26513),hAPP(c_Relation_OImage(X26512,X26514,X26511),hAPP(hAPP(c_Set_Oinsert(X26512),X26510),c_Orderings_Obot__class_Obot(tc_fun(X26512,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26512,X26514)),hAPP(hAPP(c_Product__Type_OPair(X26512,X26514),X26510),X26513)),X26511)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26512,X26514)),hAPP(hAPP(c_Product__Type_OPair(X26512,X26514),X26510),X26513)),X26511))
        | hBOOL(hAPP(hAPP(c_member(X26514),X26513),hAPP(c_Relation_OImage(X26512,X26514,X26511),hAPP(hAPP(c_Set_Oinsert(X26512),X26510),c_Orderings_Obot__class_Obot(tc_fun(X26512,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).

fof(i_0_7101,plain,
    ! [X32164,X32165,X32166,X32167,X32168] :
      ( ( ~ c_List_Olist__all2(X32168,X32167,X32166,hAPP(c_List_Orev(X32168),X32165),hAPP(c_List_Orev(X32167),X32164))
        | c_List_Olist__all2(X32168,X32167,X32166,X32165,X32164) )
      & ( ~ c_List_Olist__all2(X32168,X32167,X32166,X32165,X32164)
        | c_List_Olist__all2(X32168,X32167,X32166,hAPP(c_List_Orev(X32168),X32165),hAPP(c_List_Orev(X32167),X32164)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])]) ).

cnf(i_0_7102,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk453_2(X2,X1))),hAPP(c_List_Oset(X1),esk454_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7103,plain,
    ! [X26942,X26943,X26944] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk272_3(X26942,X26943,X26944)),esk273_3(X26942,X26943,X26944))))
        | hBOOL(hAPP(hAPP(X26942,X26944),X26943))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26944),X26943))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk273_3(X26942,X26943,X26944)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X26942,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk272_3(X26942,X26943,X26944))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk273_3(X26942,X26943,X26944))))
        | hBOOL(hAPP(hAPP(X26942,X26944),X26943))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26944),X26943))) )
      & ( ~ hBOOL(hAPP(hAPP(X26942,esk272_3(X26942,X26943,X26944)),esk273_3(X26942,X26943,X26944)))
        | hBOOL(hAPP(hAPP(X26942,X26944),X26943))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26944),X26943))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct])])])]) ).

fof(i_0_7104,plain,
    ! [X24429,X24430,X24431,X24432] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk189_4(X24429,X24430,X24431,X24432)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24431)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24432),X24430))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24432),X24431)),X24430))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24430),X24429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24431)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk190_4(X24429,X24430,X24431,X24432)),X24429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24432),X24430))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24432),X24431)),X24430))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24430),X24429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24431)) )
      & ( X24432 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk190_4(X24429,X24430,X24431,X24432)),esk189_4(X24429,X24430,X24431,X24432))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24432),X24430))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24432),X24431)),X24430))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24430),X24429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24431)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I5_J])])])])]) ).

fof(i_0_7105,plain,
    ! [X24761,X24762,X24763,X24764] :
      ( ~ class_Divides_Osemiring__div(X24764)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24764),X24763),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24764),X24762),X24763))),c_Divides_Odiv__class_Omod(X24764,X24762,X24763))),X24761) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24764),X24762),X24761) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).

fof(i_0_7106,plain,
    ! [X32169,X32170,X32171,X32172,X32173] :
      ( ( ~ c_List_Olist__all2(X32173,X32172,X32171,hAPP(c_List_Orev(X32173),X32170),X32169)
        | c_List_Olist__all2(X32173,X32172,X32171,X32170,hAPP(c_List_Orev(X32172),X32169)) )
      & ( ~ c_List_Olist__all2(X32173,X32172,X32171,X32170,hAPP(c_List_Orev(X32172),X32169))
        | c_List_Olist__all2(X32173,X32172,X32171,hAPP(c_List_Orev(X32173),X32170),X32169) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])]) ).

fof(i_0_7107,plain,
    ! [X30884,X30885,X30886,X30889,X30890,X30891,X30892,X30893] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30886),tc_List_Olist(X30886))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30886),tc_List_Olist(X30886)),c_List_Olist_ONil(X30886)),X30885)),c_List_Olexord(X30886,X30884)))
        | X30885 = hAPP(hAPP(c_List_Olist_OCons(X30886),esk416_3(X30884,X30885,X30886)),esk417_3(X30884,X30885,X30886)) )
      & ( X30890 != hAPP(hAPP(c_List_Olist_OCons(X30891),X30892),X30893)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30891),tc_List_Olist(X30891))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30891),tc_List_Olist(X30891)),c_List_Olist_ONil(X30891)),X30890)),c_List_Olexord(X30891,X30889))) ) ),
    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_lexord__Nil__left])])])])]) ).

fof(i_0_7108,plain,
    ! [X20878,X20879,X20880,X20881] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20881,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20880,X20881,X20879),hAPP(c_Set_Ovimage(X20880,X20881,X20879),X20878))),X20878)),
    inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).

fof(i_0_7109,plain,
    ! [X32119,X32120,X32121,X32122,X32123] :
      ( ~ class_Orderings_Olinorder(X32123)
      | ~ c_Fun_Oinj__on(X32122,X32123,X32121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32122,tc_HOL_Obool)),hAPP(c_List_Oset(X32122),X32120)),hAPP(c_List_Oset(X32122),X32119)))
      | ~ c_List_Olinorder__class_Osorted(X32123,hAPP(hAPP(c_List_Omap(X32122,X32123),X32121),X32120))
      | ~ hBOOL(hAPP(c_List_Odistinct(X32123),hAPP(hAPP(c_List_Omap(X32122,X32123),X32121),X32120)))
      | ~ c_List_Olinorder__class_Osorted(X32123,hAPP(hAPP(c_List_Omap(X32122,X32123),X32121),X32119))
      | ~ hBOOL(hAPP(c_List_Odistinct(X32123),hAPP(hAPP(c_List_Omap(X32122,X32123),X32121),X32119)))
      | hAPP(c_List_Oset(X32122),X32120) != hAPP(c_List_Oset(X32122),X32119)
      | X32120 = X32119 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).

fof(i_0_7110,plain,
    ! [X24818,X24819,X24820,X24821] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24821))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24820))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24820),X24819))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24819),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24818,X24821))),X24820))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).

fof(i_0_7111,plain,
    ! [X27997,X27998,X27999] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27999),X27998))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27999,X27999),tc_HOL_Obool)),X27997),hAPP(hAPP(c_Product__Type_OSigma(X27999,X27999),X27998),hAPP(c_COMBK(tc_fun(X27999,tc_HOL_Obool),X27999),X27998))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27999,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27999),X27998),X27997))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).

fof(i_0_7112,plain,
    ! [X30831,X30832,X30833,X30834,X30835,X30836] : hAPP(c_List_Ofoldl(X30836,X30835,X30834,X30833),hAPP(hAPP(c_List_Oappend(X30835),X30832),X30831)) = hAPP(c_List_Ofoldl(X30836,X30835,X30834,hAPP(c_List_Ofoldl(X30836,X30835,X30834,X30833),X30832)),X30831),
    inference(variable_rename,[status(thm)],[fact_foldl__append]) ).

cnf(i_0_7113,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk454_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

cnf(i_0_7114,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk453_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7115,plain,
    ! [X29158,X29159,X29160,X29161] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29161,X29161)),hAPP(hAPP(c_Product__Type_OPair(X29161,X29161),X29160),X29159)),c_Transitive__Closure_Ortrancl(X29161,X29158)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29161,X29161)),hAPP(hAPP(c_Product__Type_OPair(X29161,X29161),X29159),X29160)),c_Transitive__Closure_Ortrancl(X29161,hAPP(c_Relation_Oconverse(X29161,X29161),X29158)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).

fof(i_0_7116,plain,
    ! [X33019,X33020,X33021] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk490_3(X33019,X33020,X33021)),esk491_3(X33019,X33020,X33021))))
        | hBOOL(hAPP(hAPP(X33019,X33021),X33020))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X33021),X33020))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk490_3(X33019,X33020,X33021)),esk491_3(X33019,X33020,X33021)))
        | hBOOL(hAPP(hAPP(X33019,esk490_3(X33019,X33020,X33021)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk491_3(X33019,X33020,X33021)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(X33019,X33021),X33020))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X33021),X33020))) )
      & ( ~ hBOOL(hAPP(hAPP(X33019,esk490_3(X33019,X33020,X33021)),esk491_3(X33019,X33020,X33021)))
        | hBOOL(hAPP(hAPP(X33019,X33021),X33020))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X33021),X33020))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5528])])])]) ).

fof(i_0_7117,plain,
    ! [X30699,X30700,X30701,X30702,X30703] : hAPP(hAPP(c_List_Ozip(X30703,X30702),hAPP(hAPP(c_List_Oappend(X30703),X30701),X30700)),X30699) = hAPP(hAPP(c_List_Oappend(tc_prod(X30703,X30702)),hAPP(hAPP(c_List_Ozip(X30703,X30702),X30701),hAPP(hAPP(c_List_Otake(X30702),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30703)),X30701)),X30699))),hAPP(hAPP(c_List_Ozip(X30703,X30702),X30700),hAPP(hAPP(c_List_Odrop(X30702),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30703)),X30701)),X30699))),
    inference(variable_rename,[status(thm)],[fact_zip__append1]) ).

fof(i_0_7118,plain,
    ! [X19702,X19703,X19704,X19705] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19705,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19705,tc_HOL_Obool)),X19704),X19703)),X19702))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19705,tc_HOL_Obool)),X19704),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19705,tc_HOL_Obool)),X19703),X19702))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19705,tc_HOL_Obool)),X19704),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19705,tc_HOL_Obool)),X19703),X19702)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19705,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19705,tc_HOL_Obool)),X19704),X19703)),X19702)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).

cnf(i_0_7119,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_5529]) ).

fof(i_0_7120,plain,
    ! [X25548,X25549,X25550,X25551] :
      ( ( X25550 = hAPP(c_Relation_OImage(X25551,X25551,X25548),hAPP(hAPP(c_Set_Oinsert(X25551),esk247_4(X25548,X25549,X25550,X25551)),c_Orderings_Obot__class_Obot(tc_fun(X25551,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25551,tc_HOL_Obool)),X25550),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25551),X25549),X25548))) )
      & ( hBOOL(hAPP(hAPP(c_member(X25551),esk247_4(X25548,X25549,X25550,X25551)),X25549))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25551,tc_HOL_Obool)),X25550),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25551),X25549),X25548))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5530])])])]) ).

cnf(i_0_7121,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5531]) ).

cnf(i_0_7122,plain,
    c_Divides_Odivmod__nat(X1,X2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5532]) ).

cnf(i_0_7123,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5533]) ).

fof(i_0_7124,plain,
    ! [X33516,X33517,X33518,X33519] :
      ( hAPP(c_Set_Oimage(X33519,X33518,X33517),c_Orderings_Otop__class_Otop(tc_fun(X33519,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33518,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X33519,X33518,X33517),hAPP(c_Set_Oimage(X33518,X33519,c_Hilbert__Choice_Oinv__into(X33519,X33518,c_Orderings_Otop__class_Otop(tc_fun(X33519,tc_HOL_Obool)),X33517)),X33516)) = X33516 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_7125,plain,
    ! [X24455,X24456,X24457,X24458] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk199_4(X24455,X24456,X24457,X24458)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24457)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24458),X24455))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24458),X24457)),X24455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24457)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk200_4(X24455,X24456,X24457,X24458)),X24456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24458),X24455))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24458),X24457)),X24455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24457)) )
      & ( X24458 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk200_4(X24455,X24456,X24457,X24458)),esk199_4(X24455,X24456,X24457,X24458))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24458),X24455))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24458),X24457)),X24455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24457)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I5_J])])])])]) ).

fof(i_0_7126,plain,
    ! [X24435,X24436,X24437,X24438] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk191_4(X24435,X24436,X24437,X24438)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24437)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24438),X24435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24438),X24437)),X24435))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24437)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk192_4(X24435,X24436,X24437,X24438)),X24436))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24438),X24435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24438),X24437)),X24435))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24437)) )
      & ( X24438 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk192_4(X24435,X24436,X24437,X24438)),esk191_4(X24435,X24436,X24437,X24438))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24438),X24435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24438),X24437)),X24435))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24437)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I6_J])])])])]) ).

fof(i_0_7127,plain,
    ! [X30672,X30673,X30674,X30675,X30676] :
      ( ( X30675 = hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) != hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( X30674 = hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)),X30672)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) != hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675) = X30673
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) != hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675)),X30674) = X30672
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) != hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) = hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675) != X30673
        | hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675)),X30674) != X30672
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) = hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)))
        | X30675 != hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)
        | X30674 != hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)),X30672)
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) = hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) )
      & ( hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675) != X30673
        | hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30673)),X30675)),X30674) != X30672
        | X30675 != hAPP(hAPP(c_List_Otake(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)
        | X30674 != hAPP(hAPP(c_List_Oappend(X30676),hAPP(hAPP(c_List_Odrop(X30676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30676)),X30675)),X30673)),X30672)
        | hAPP(hAPP(c_List_Oappend(X30676),X30675),X30674) = hAPP(hAPP(c_List_Oappend(X30676),X30673),X30672) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5534])])]) ).

fof(i_0_7128,plain,
    ! [X21022,X21023,X21024,X21025,X21026] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21026)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21025),X21024))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21025),X21023))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21026),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21025,X21026),X21022),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21025,tc_HOL_Obool)),X21024),X21023))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21025,X21026),X21022),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21025,tc_HOL_Obool)),X21024),X21023))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21026),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21025,X21026),X21022),X21024)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21025,X21026),X21022),X21023)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).

fof(i_0_7129,plain,
    ! [X21017,X21018,X21019,X21020,X21021] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21021)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21020),X21019))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21020),X21018))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21021),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21020,X21021),X21017),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21020,tc_HOL_Obool)),X21019),X21018))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21020,X21021),X21017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21020,tc_HOL_Obool)),X21019),X21018))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21021),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21020,X21021),X21017),X21019)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21020,X21021),X21017),X21018)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).

fof(i_0_7130,plain,
    ! [X21007,X21008,X21009,X21010,X21011] :
      ( ~ class_Groups_Ocomm__monoid__add(X21011)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21010),X21009))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21010),X21008))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21010,X21011),X21007),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21010,tc_HOL_Obool)),X21009),X21008))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21010,X21011),X21007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21010,tc_HOL_Obool)),X21009),X21008))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21010,X21011),X21007),X21009)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21010,X21011),X21007),X21008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])]) ).

cnf(i_0_7131,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5535]) ).

cnf(i_0_7132,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5536]) ).

cnf(i_0_7133,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5537]) ).

cnf(i_0_7134,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5538]) ).

cnf(i_0_7135,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5539]) ).

fof(i_0_7136,plain,
    ! [X26626,X26627,X26628,X26629,X26630,X26631] :
      ( ~ hBOOL(hAPP(hAPP(X26631,X26630),X26629))
      | ~ hBOOL(hAPP(hAPP(X26628,X26630),X26629))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26627,tc_fun(X26626,tc_HOL_Obool))),X26631),X26628),X26630),X26629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).

fof(i_0_7137,plain,
    ! [X20953,X20954,X20955,X20956,X20957] :
      ( hAPP(c_Set_Oimage(X20957,X20956,X20955),c_Orderings_Otop__class_Otop(tc_fun(X20957,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20956,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20957,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20957,X20956,X20955),X20954)),X20953))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20956,tc_HOL_Obool)),X20954),hAPP(c_Set_Oimage(X20957,X20956,X20955),X20953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).

fof(i_0_7138,plain,
    ! [X24413,X24414,X24415,X24416] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X24413,X24414,X24415,X24416)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24415)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),X24416))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24416),X24415)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24414),X24413))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24415)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X24413,X24414,X24415,X24416)),X24413))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),X24416))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24416),X24415)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24414),X24413))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24415)) )
      & ( X24416 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk184_4(X24413,X24414,X24415,X24416)),esk183_4(X24413,X24414,X24415,X24416))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),X24416))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24416),X24415)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24414),X24413))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24415)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I7_J])])])])]) ).

fof(i_0_7139,plain,
    ! [X23220,X23221,X23222,X23223,X23224,X23225] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23225),X23224)),X23223) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23222),X23221)),X23220)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23222),X23221)),X23220)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23220),X23222))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23222))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23222),X23225))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23224),X23221)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).

fof(i_0_7140,plain,
    ! [X29135,X29136,X29137,X29138,X29139] : hAPP(c_Relation_Oconverse(X29139,X29138),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29137,tc_fun(tc_prod(X29139,X29138),tc_HOL_Obool)),X29136),X29135)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29137,tc_fun(tc_prod(X29138,X29139),tc_HOL_Obool)),X29136),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29139,X29138),tc_HOL_Obool),tc_fun(tc_prod(X29138,X29139),tc_HOL_Obool),X29137),c_Relation_Oconverse(X29139,X29138)),X29135)),
    inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).

fof(i_0_7141,plain,
    ! [X29085,X29086,X29087,X29088,X29089] : hAPP(c_Relation_Oconverse(X29089,X29088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29087,tc_fun(tc_prod(X29089,X29088),tc_HOL_Obool)),X29086),X29085)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29087,tc_fun(tc_prod(X29088,X29089),tc_HOL_Obool)),X29086),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29089,X29088),tc_HOL_Obool),tc_fun(tc_prod(X29088,X29089),tc_HOL_Obool),X29087),c_Relation_Oconverse(X29089,X29088)),X29085)),
    inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).

fof(i_0_7142,plain,
    ! [X27323] : X27323 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk282_1(X27323)),esk283_1(X27323))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ])])]) ).

fof(i_0_7143,plain,
    ! [X17106,X17107,X17108,X17109,X17110,X17112,X17113,X17114,X17115,X17116,X17117] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17108),esk4_4(X17106,X17107,X17108,X17109)),X17106))
        | ~ hBOOL(hAPP(hAPP(c_member(X17110),X17109),hAPP(c_Set_Oimage(X17108,X17110,X17107),X17106))) )
      & ( X17109 = hAPP(X17107,esk4_4(X17106,X17107,X17108,X17109))
        | ~ hBOOL(hAPP(hAPP(c_member(X17110),X17109),hAPP(c_Set_Oimage(X17108,X17110,X17107),X17106))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17114),X17116),X17112))
        | X17115 != hAPP(X17113,X17116)
        | hBOOL(hAPP(hAPP(c_member(X17117),X17115),hAPP(c_Set_Oimage(X17114,X17117,X17113),X17112))) ) ),
    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_image__iff])])])])])]) ).

fof(i_0_7144,plain,
    ! [X26560,X26561,X26562,X26563,X26564] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X26564),hAPP(hAPP(c_Set_Oinsert(X26564),X26561),c_Orderings_Obot__class_Obot(tc_fun(X26564,tc_HOL_Obool)))),X26562) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X26564),hAPP(hAPP(c_Set_Oinsert(X26564),X26560),c_Orderings_Obot__class_Obot(tc_fun(X26564,tc_HOL_Obool)))),X26562)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26564,X26564)),hAPP(hAPP(c_Product__Type_OPair(X26564,X26564),X26561),X26560)),X26562))
        | ~ hBOOL(hAPP(hAPP(c_member(X26564),X26560),X26563))
        | ~ hBOOL(hAPP(hAPP(c_member(X26564),X26561),X26563))
        | ~ c_Equiv__Relations_Oequiv(X26564,X26563,X26562) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26564,X26564)),hAPP(hAPP(c_Product__Type_OPair(X26564,X26564),X26561),X26560)),X26562))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X26564),hAPP(hAPP(c_Set_Oinsert(X26564),X26561),c_Orderings_Obot__class_Obot(tc_fun(X26564,tc_HOL_Obool)))),X26562) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X26564),hAPP(hAPP(c_Set_Oinsert(X26564),X26560),c_Orderings_Obot__class_Obot(tc_fun(X26564,tc_HOL_Obool)))),X26562)
        | ~ hBOOL(hAPP(hAPP(c_member(X26564),X26560),X26563))
        | ~ hBOOL(hAPP(hAPP(c_member(X26564),X26561),X26563))
        | ~ c_Equiv__Relations_Oequiv(X26564,X26563,X26562) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).

fof(i_0_7145,plain,
    ! [X33532,X33533,X33534,X33535,X33536,X33537] :
      ( hAPP(c_Set_Oimage(X33537,X33536,X33535),X33534) != X33533
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33536,tc_HOL_Obool)),X33532),X33533))
      | hAPP(c_Set_Oimage(X33537,X33536,X33535),hAPP(c_Set_Oimage(X33536,X33537,c_Hilbert__Choice_Oinv__into(X33537,X33536,X33534,X33535)),X33532)) = X33532 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_7146,plain,
    ! [X33469,X33470,X33471] :
      ( ( ~ c_Fun_Oinj__on(X33471,X33470,X33469,c_Orderings_Otop__class_Otop(tc_fun(X33471,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(X33470,X33471,X33471,c_Hilbert__Choice_Oinv__into(X33471,X33470,c_Orderings_Otop__class_Otop(tc_fun(X33471,tc_HOL_Obool)),X33469)),X33469) = c_Fun_Oid(X33471) )
      & ( hAPP(c_Fun_Ocomp(X33470,X33471,X33471,c_Hilbert__Choice_Oinv__into(X33471,X33470,c_Orderings_Otop__class_Otop(tc_fun(X33471,tc_HOL_Obool)),X33469)),X33469) != c_Fun_Oid(X33471)
        | c_Fun_Oinj__on(X33471,X33470,X33469,c_Orderings_Otop__class_Otop(tc_fun(X33471,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__iff])]) ).

cnf(i_0_7147,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,c_List_Oconcat(X1,X2))) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5540]) ).

fof(i_0_7148,plain,
    ! [X28657,X28658,X28659,X28660,X28661,X28662,X28663] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28663,X28662,X28661),hAPP(c_Fun_Ocomp(X28660,tc_fun(X28662,X28661),X28663,X28659),X28658)),X28657) = hAPP(hAPP(X28659,hAPP(X28658,hAPP(c_Product__Type_Ofst(X28663,X28662),X28657))),hAPP(c_Product__Type_Osnd(X28663,X28662),X28657)),
    inference(variable_rename,[status(thm)],[fact_split__comp]) ).

fof(i_0_7149,plain,
    ! [X33648,X33649,X33650] :
      ( ~ c_Fun_Obij__betw(X33650,X33649,X33648,c_Orderings_Otop__class_Otop(tc_fun(X33650,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33649,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X33649,X33650,c_Orderings_Otop__class_Otop(tc_fun(X33649,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X33650,X33649,c_Orderings_Otop__class_Otop(tc_fun(X33650,tc_HOL_Obool)),X33648)) = X33648 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__inv__eq])]) ).

cnf(i_0_7150,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5541]) ).

cnf(i_0_7151,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5542]) ).

fof(i_0_7152,plain,
    ! [X23023,X23024] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23024),X23023))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23024)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23023))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23024)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23023)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23024),X23023)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).

fof(i_0_7153,plain,
    ! [X23017,X23018] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23018),X23017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23018)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23017))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23018)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23017)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23018),X23017)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).

fof(i_0_7154,plain,
    ! [X19278,X19279,X19280] :
      ( ~ class_Orderings_Olinorder(X19280)
      | hAPP(X19279,hAPP(hAPP(c_Orderings_Oord__class_Omin(X19280),esk56_3(X19278,X19279,X19280)),esk57_3(X19278,X19279,X19280))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X19280),hAPP(X19279,esk56_3(X19278,X19279,X19280))),hAPP(X19279,esk57_3(X19278,X19279,X19280)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19280),X19278))
      | X19278 = c_Orderings_Obot__class_Obot(tc_fun(X19280,tc_HOL_Obool))
      | hAPP(X19279,c_Big__Operators_Olattice_OInf__fin(X19280,c_Orderings_Oord__class_Omin(X19280),X19278)) = c_Big__Operators_Olattice_OInf__fin(X19280,c_Orderings_Oord__class_Omin(X19280),hAPP(c_Set_Oimage(X19280,X19280,X19279),X19278)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])]) ).

fof(i_0_7155,plain,
    ! [X19273,X19274,X19275] :
      ( ~ class_Orderings_Olinorder(X19275)
      | hAPP(X19274,hAPP(hAPP(c_Orderings_Oord__class_Omax(X19275),esk54_3(X19273,X19274,X19275)),esk55_3(X19273,X19274,X19275))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X19275),hAPP(X19274,esk54_3(X19273,X19274,X19275))),hAPP(X19274,esk55_3(X19273,X19274,X19275)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19275),X19273))
      | X19273 = c_Orderings_Obot__class_Obot(tc_fun(X19275,tc_HOL_Obool))
      | hAPP(X19274,c_Big__Operators_Olattice_OSup__fin(X19275,c_Orderings_Oord__class_Omax(X19275),X19273)) = c_Big__Operators_Olattice_OSup__fin(X19275,c_Orderings_Oord__class_Omax(X19275),hAPP(c_Set_Oimage(X19275,X19275,X19274),X19273)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])]) ).

fof(i_0_7156,plain,
    ! [X31518,X31519,X31520,X31521,X31522,X31523] :
      ( ~ c_List_Olist__all2(X31523,X31522,X31521,X31520,X31519)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31518),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31523)),X31520)))
      | hBOOL(hAPP(hAPP(X31521,hAPP(hAPP(c_List_Onth(X31523),X31520),X31518)),hAPP(hAPP(c_List_Onth(X31522),X31519),X31518))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD])]) ).

fof(i_0_7157,plain,
    ! [X31524,X31525,X31526,X31527,X31528,X31529] :
      ( ~ c_List_Olist__all2(X31529,X31528,X31527,X31526,X31525)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31528)),X31525)))
      | hBOOL(hAPP(hAPP(X31527,hAPP(hAPP(c_List_Onth(X31529),X31526),X31524)),hAPP(hAPP(c_List_Onth(X31528),X31525),X31524))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2])]) ).

fof(i_0_7158,plain,
    ! [X21012,X21013,X21014,X21015,X21016] :
      ( ~ c_Fun_Oinj__on(X21016,X21015,X21014,c_Orderings_Otop__class_Otop(tc_fun(X21016,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21015,tc_HOL_Obool)),X21013),hAPP(c_Set_Oimage(X21016,X21015,X21014),X21012)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21016,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X21016,X21015,X21014),X21013)),X21012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetI])]) ).

cnf(i_0_7159,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5481]) ).

cnf(i_0_7160,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5482]) ).

cnf(i_0_7161,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5483]) ).

cnf(i_0_7162,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5484]) ).

fof(i_0_7163,plain,
    ! [X25812,X25813,X25814,X25815] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),c_Groups_Ozero__class_Ozero(X25815)),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),c_Groups_Ozero__class_Ozero(X25815)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812)),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),c_Groups_Ozero__class_Ozero(X25815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))),X25813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25815),X25814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25815),X25813),hAPP(c_Int_Onumber__class_Onumber__of(X25815),X25812))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25815)
        | ~ class_Int_Onumber(X25815) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5543])])]) ).

fof(i_0_7164,plain,
    ! [X25822,X25823,X25824,X25825] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),c_Groups_Ozero__class_Ozero(X25825)),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),c_Groups_Ozero__class_Ozero(X25825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25825),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822)),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),c_Groups_Ozero__class_Ozero(X25825)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25825),X25824),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))),X25823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25825),X25824),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25825),X25823),hAPP(c_Int_Onumber__class_Onumber__of(X25825),X25822))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25825)
        | ~ class_Int_Onumber(X25825) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5544])])]) ).

fof(i_0_7165,plain,
    ! [X29127,X29128,X29129,X29130,X29131] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29131,X29130)),hAPP(hAPP(c_Product__Type_OPair(X29131,X29130),X29129),X29128)),hAPP(c_Relation_Oconverse(X29130,X29131),X29127)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29130,X29131)),hAPP(hAPP(c_Product__Type_OPair(X29130,X29131),X29128),X29129)),X29127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).

fof(i_0_7166,plain,
    ! [X29117,X29118,X29119,X29120,X29121] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29121,X29120)),hAPP(hAPP(c_Product__Type_OPair(X29121,X29120),X29119),X29118)),hAPP(c_Relation_Oconverse(X29120,X29121),X29117)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29120,X29121)),hAPP(hAPP(c_Product__Type_OPair(X29120,X29121),X29118),X29119)),X29117)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29120,X29121)),hAPP(hAPP(c_Product__Type_OPair(X29120,X29121),X29118),X29119)),X29117))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29121,X29120)),hAPP(hAPP(c_Product__Type_OPair(X29121,X29120),X29119),X29118)),hAPP(c_Relation_Oconverse(X29120,X29121),X29117))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).

fof(i_0_7167,plain,
    ! [X33718,X33719,X33720,X33721] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33721),hAPP(c_Set_Ovimage(X33721,X33720,X33719),X33718)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33720),X33718))
        | ~ c_Fun_Obij__betw(X33721,X33720,X33719,c_Orderings_Otop__class_Otop(tc_fun(X33721,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33720,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33720),X33718))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33721),hAPP(c_Set_Ovimage(X33721,X33720,X33719),X33718)))
        | ~ c_Fun_Obij__betw(X33721,X33720,X33719,c_Orderings_Otop__class_Otop(tc_fun(X33721,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33720,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimage__iff])])]) ).

fof(i_0_7168,plain,
    ! [X26669,X26670,X26671,X26672,X26673,X26674] :
      ( ~ hBOOL(hAPP(hAPP(X26674,X26673),X26672))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26671,tc_fun(X26670,tc_HOL_Obool))),X26674),X26669),X26673),X26672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).

fof(i_0_7169,plain,
    ! [X26608,X26609,X26610,X26611,X26612,X26613] :
      ( ( ~ hBOOL(hAPP(hAPP(X26613,X26612),X26611))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26609,tc_fun(X26608,tc_HOL_Obool))),X26610),X26613),X26612),X26611)) )
      & ( ~ hBOOL(hAPP(hAPP(X26610,X26612),X26611))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26609,tc_fun(X26608,tc_HOL_Obool))),X26610),X26613),X26612),X26611)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5545])])]) ).

fof(i_0_7170,plain,
    ! [X26663,X26664,X26665,X26666,X26667,X26668] :
      ( ~ hBOOL(hAPP(hAPP(X26668,X26667),X26666))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26665,tc_fun(X26664,tc_HOL_Obool))),X26663),X26668),X26667),X26666)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).

fof(i_0_7171,plain,
    ! [X20769,X20770,X20771,X20772,X20773] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20773,tc_HOL_Obool)),X20772),X20771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20773,tc_HOL_Obool)),X20770),X20769))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20773,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20773,tc_HOL_Obool)),X20772),X20770)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20773,tc_HOL_Obool)),X20771),X20769))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).

fof(i_0_7172,plain,
    ! [X19619,X19620,X19621,X19622,X19623] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19623,tc_HOL_Obool)),X19622),X19621))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19623,tc_HOL_Obool)),X19620),X19619))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19623,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19623,tc_HOL_Obool)),X19622),X19620)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19623,tc_HOL_Obool)),X19621),X19619))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).

fof(i_0_7173,plain,
    ! [X17836,X17837,X17838,X17839,X17840] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17840,tc_HOL_Obool)),X17839),X17838))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17840,tc_HOL_Obool)),X17837),X17836))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17840,tc_HOL_Obool)),X17839),X17836)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17840,tc_HOL_Obool)),X17838),X17837))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).

fof(i_0_7174,plain,
    ! [X19293,X19294,X19295] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19295)
      | hAPP(X19294,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19295),esk62_3(X19293,X19294,X19295)),esk63_3(X19293,X19294,X19295))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19295),hAPP(X19294,esk62_3(X19293,X19294,X19295))),hAPP(X19294,esk63_3(X19293,X19294,X19295)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19295),X19293))
      | X19293 = c_Orderings_Obot__class_Obot(tc_fun(X19295,tc_HOL_Obool))
      | hAPP(X19294,hAPP(c_Finite__Set_Ofold1(X19295,c_Groups_Otimes__class_Otimes(X19295)),X19293)) = hAPP(c_Finite__Set_Ofold1(X19295,c_Groups_Otimes__class_Otimes(X19295)),hAPP(c_Set_Oimage(X19295,X19295,X19294),X19293)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).

fof(i_0_7175,plain,
    ! [X28567,X28568,X28569,X28570,X28571] :
      ( ~ class_Groups_Ocomm__monoid__mult(X28571)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28570),X28569))
      | ~ c_Fun_Oinj__on(X28570,X28570,X28568,X28569)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28570,X28571),X28567),hAPP(c_Set_Oimage(X28570,X28570,X28568),X28569)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28570,X28571),hAPP(c_Fun_Ocomp(X28570,X28571,X28570,X28567),X28568)),X28569) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).

fof(i_0_7176,plain,
    ! [X28562,X28563,X28564,X28565,X28566] :
      ( ~ class_Groups_Ocomm__monoid__add(X28566)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28565),X28564))
      | ~ c_Fun_Oinj__on(X28565,X28565,X28563,X28564)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28565,X28566),X28562),hAPP(c_Set_Oimage(X28565,X28565,X28563),X28564)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28565,X28566),hAPP(c_Fun_Ocomp(X28565,X28566,X28565,X28562),X28563)),X28564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).

fof(i_0_7177,plain,
    ! [X28808,X28809,X28810] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28810,X28810)),hAPP(hAPP(c_Product__Type_OPair(X28810,X28810),esk335_3(X28808,X28809,X28810)),X28809)),X28808))
        | hBOOL(hAPP(hAPP(c_member(X28810),X28809),c_Wellfounded_Oacc(X28810,X28808))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28810),esk335_3(X28808,X28809,X28810)),c_Wellfounded_Oacc(X28810,X28808)))
        | hBOOL(hAPP(hAPP(c_member(X28810),X28809),c_Wellfounded_Oacc(X28810,X28808))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).

fof(i_0_7178,plain,
    ! [X28804,X28805,X28806] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28806,X28806)),hAPP(hAPP(c_Product__Type_OPair(X28806,X28806),esk334_3(X28804,X28805,X28806)),X28805)),X28804))
        | hBOOL(hAPP(hAPP(c_member(X28806),X28805),c_Wellfounded_Oacc(X28806,X28804))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28806),esk334_3(X28804,X28805,X28806)),c_Wellfounded_Oacc(X28806,X28804)))
        | hBOOL(hAPP(hAPP(c_member(X28806),X28805),c_Wellfounded_Oacc(X28806,X28804))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5546])])])]) ).

fof(i_0_7179,plain,
    ! [X27409,X27410,X27411,X27412,X27413,X27414,X27415] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27411),X27410),c_Wellfounded_Oacc(X27411,X27409)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27411,X27411)),hAPP(hAPP(c_Product__Type_OPair(X27411,X27411),X27412),X27410)),X27409))
        | hBOOL(hAPP(hAPP(c_member(X27411),X27412),c_Wellfounded_Oacc(X27411,X27409))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27415,X27415)),hAPP(hAPP(c_Product__Type_OPair(X27415,X27415),esk284_3(X27413,X27414,X27415)),X27414)),X27413))
        | hBOOL(hAPP(hAPP(c_member(X27415),X27414),c_Wellfounded_Oacc(X27415,X27413))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27415),esk284_3(X27413,X27414,X27415)),c_Wellfounded_Oacc(X27415,X27413)))
        | hBOOL(hAPP(hAPP(c_member(X27415),X27414),c_Wellfounded_Oacc(X27415,X27413))) ) ),
    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_acc_Osimps])])])])])]) ).

fof(i_0_7180,plain,
    ! [X29629,X29630,X29631,X29632] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29632),tc_List_Olist(X29632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29632),tc_List_Olist(X29632)),X29631),X29630)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29632),c_List_Olistrel1(X29632,X29629))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29632)),X29631) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29632)),X29630) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).

cnf(i_0_7181,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk454_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

cnf(i_0_7182,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk453_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7183,plain,
    ! [X30056,X30057,X30058,X30059,X30060] : hAPP(hAPP(c_List_Olist__update(X30060,hAPP(hAPP(c_List_Olist_OCons(X30060),X30059),X30058)),X30057),X30056) = c_Nat_Onat_Onat__case(tc_List_Olist(X30060),hAPP(hAPP(c_List_Olist_OCons(X30060),X30056),X30058),hAPP(hAPP(c_COMBB(tc_List_Olist(X30060),tc_List_Olist(X30060),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X30060),X30059)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X30060,tc_List_Olist(X30060)),c_List_Olist__update(X30060,X30058)),X30056)),X30057),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(i_0_7184,plain,
    ! [X26754,X26755,X26756,X26757] : hAPP(c_Product__Type_Oprod_Oprod__case(X26757,X26756,X26755),hAPP(hAPP(c_COMBB(tc_fun(X26756,tc_prod(X26757,X26756)),tc_fun(X26756,X26755),X26757),hAPP(c_COMBB(tc_prod(X26757,X26756),X26755,X26756),X26754)),c_Product__Type_OPair(X26757,X26756))) = X26754,
    inference(variable_rename,[status(thm)],[fact_split__eta]) ).

fof(i_0_7185,plain,
    ! [X24461,X24462,X24463,X24464] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk201_4(X24461,X24462,X24463,X24464)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),X24464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24464),X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24463)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_4(X24461,X24462,X24463,X24464)),X24462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),X24464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24464),X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24463)) )
      & ( X24464 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk202_4(X24461,X24462,X24463,X24464)),esk201_4(X24461,X24462,X24463,X24464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),X24464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24464),X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24463)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I7_J])])])])]) ).

fof(i_0_7186,plain,
    ! [X24441,X24442,X24443,X24444] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_4(X24441,X24442,X24443,X24444)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),X24444))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24444),X24443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24443)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_4(X24441,X24442,X24443,X24444)),X24442))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),X24444))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24444),X24443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24443)) )
      & ( X24444 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk194_4(X24441,X24442,X24443,X24444)),esk193_4(X24441,X24442,X24443,X24444))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),X24444))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24444),X24443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24443)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I8_J])])])])]) ).

fof(i_0_7187,plain,
    ! [X17984,X17985,X17986] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17986,tc_HOL_Obool)),X17985),hAPP(hAPP(c_Set_Oinsert(X17986),X17984),c_Orderings_Obot__class_Obot(tc_fun(X17986,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X17986,X17984,X17985) = X17984 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17986,tc_HOL_Obool)),X17985),hAPP(hAPP(c_Set_Oinsert(X17986),X17984),c_Orderings_Obot__class_Obot(tc_fun(X17986,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X17986,X17984,X17985) = c_HOL_OThe(X17986,hAPP(hAPP(c_COMBC(X17986,tc_fun(X17986,tc_HOL_Obool),tc_HOL_Obool),c_member(X17986)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17986,tc_HOL_Obool)),X17985),hAPP(hAPP(c_Set_Oinsert(X17986),X17984),c_Orderings_Obot__class_Obot(tc_fun(X17986,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5547])]) ).

fof(i_0_7188,plain,
    ! [X30161,X30162,X30163,X30164] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X30161,X30162,X30163,X30164)),X30164))
        | hAPP(hAPP(c_List_Otake(X30163),X30164),X30162) = hAPP(hAPP(c_List_Otake(X30163),X30164),X30161)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30163)),X30161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30163)),X30162))) )
      & ( hAPP(hAPP(c_List_Onth(X30163),X30162),esk403_4(X30161,X30162,X30163,X30164)) != hAPP(hAPP(c_List_Onth(X30163),X30161),esk403_4(X30161,X30162,X30163,X30164))
        | hAPP(hAPP(c_List_Otake(X30163),X30164),X30162) = hAPP(hAPP(c_List_Otake(X30163),X30164),X30161)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30163)),X30161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30163)),X30162))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take__lemma])])])]) ).

fof(i_0_7189,plain,
    ! [X29336,X29337,X29338,X29339] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29339,X29339)),hAPP(hAPP(c_Product__Type_OPair(X29339,X29339),X29338),X29337)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29339,X29339),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29336)))
      | X29338 = X29337 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).

fof(i_0_7190,plain,
    ! [X27054,X27055,X27056,X27057,X27058] :
      ( ~ hBOOL(hAPP(hAPP(X27058,X27057),X27056))
      | hBOOL(hAPP(hAPP(X27058,hAPP(c_Product__Type_Osnd(X27055,X27054),hAPP(hAPP(c_Product__Type_OPair(X27055,X27054),X27056),X27057))),hAPP(c_Product__Type_Ofst(X27055,X27054),hAPP(hAPP(c_Product__Type_OPair(X27055,X27054),X27056),X27057)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).

fof(i_0_7191,plain,
    ! [X28480,X28481,X28482,X28483,X28484,X28485] :
      ( ( ~ c_Fun_Oinj__on(X28484,X28481,X28480,hAPP(c_Set_Oimage(X28485,X28484,X28483),X28482))
        | c_Fun_Oinj__on(X28485,X28481,hAPP(c_Fun_Ocomp(X28484,X28481,X28485,X28480),X28483),X28482)
        | ~ c_Fun_Oinj__on(X28485,X28484,X28483,X28482) )
      & ( ~ c_Fun_Oinj__on(X28485,X28481,hAPP(c_Fun_Ocomp(X28484,X28481,X28485,X28480),X28483),X28482)
        | c_Fun_Oinj__on(X28484,X28481,X28480,hAPP(c_Set_Oimage(X28485,X28484,X28483),X28482))
        | ~ c_Fun_Oinj__on(X28485,X28484,X28483,X28482) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).

fof(i_0_7192,plain,
    ! [X28475,X28476,X28477,X28478,X28479] :
      ( hAPP(c_Set_Oimage(X28479,X28478,X28477),c_Orderings_Otop__class_Otop(tc_fun(X28479,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28478,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X28478,X28476,X28475),c_Orderings_Otop__class_Otop(tc_fun(X28478,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28476,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X28479,X28476,hAPP(c_Fun_Ocomp(X28478,X28476,X28479,X28475),X28477)),c_Orderings_Otop__class_Otop(tc_fun(X28479,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28476,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).

fof(i_0_7193,plain,
    ! [X24790,X24791,X24792] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24792),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24791),X24792))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24791,X24792))),X24790) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24791),X24790),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(i_0_7194,plain,
    ! [X28541,X28542,X28543,X28544,X28545,X28546] :
      ( ~ class_Groups_Ocomm__monoid__mult(X28546)
      | ~ c_Fun_Oinj__on(X28545,X28544,X28543,X28542)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28544,X28546),X28541),hAPP(c_Set_Oimage(X28545,X28544,X28543),X28542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28545,X28546),hAPP(c_Fun_Ocomp(X28544,X28546,X28545,X28541),X28543)),X28542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).

fof(i_0_7195,plain,
    ! [X28535,X28536,X28537,X28538,X28539,X28540] :
      ( ~ class_Groups_Ocomm__monoid__add(X28540)
      | ~ c_Fun_Oinj__on(X28539,X28538,X28537,X28536)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28538,X28540),X28535),hAPP(c_Set_Oimage(X28539,X28538,X28537),X28536)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28539,X28540),hAPP(c_Fun_Ocomp(X28538,X28540,X28539,X28535),X28537)),X28536) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).

fof(i_0_7196,plain,
    ! [X21125,X21126,X21127] :
      ( ~ class_Orderings_Olinorder(X21127)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21127),X21126))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21127),X21125))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21127,tc_HOL_Obool)),X21126),X21125) = c_Orderings_Obot__class_Obot(tc_fun(X21127,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X21127),c_Big__Operators_Olattice_OSup__fin(X21127,c_Orderings_Oord__class_Omax(X21127),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21127,tc_HOL_Obool)),X21126),X21125))),c_Big__Operators_Olattice_OSup__fin(X21127,c_Orderings_Oord__class_Omax(X21127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21127,tc_HOL_Obool)),X21126),X21125))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X21127),c_Big__Operators_Olattice_OSup__fin(X21127,c_Orderings_Oord__class_Omax(X21127),X21126)),c_Big__Operators_Olattice_OSup__fin(X21127,c_Orderings_Oord__class_Omax(X21127),X21125)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).

fof(i_0_7197,plain,
    ! [X21119,X21120,X21121] :
      ( ~ class_Orderings_Olinorder(X21121)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21121),X21120))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21121),X21119))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21121,tc_HOL_Obool)),X21120),X21119) = c_Orderings_Obot__class_Obot(tc_fun(X21121,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21121),c_Big__Operators_Olattice_OInf__fin(X21121,c_Orderings_Oord__class_Omin(X21121),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21121,tc_HOL_Obool)),X21120),X21119))),c_Big__Operators_Olattice_OInf__fin(X21121,c_Orderings_Oord__class_Omin(X21121),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21121,tc_HOL_Obool)),X21120),X21119))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21121),c_Big__Operators_Olattice_OInf__fin(X21121,c_Orderings_Oord__class_Omin(X21121),X21120)),c_Big__Operators_Olattice_OInf__fin(X21121,c_Orderings_Oord__class_Omin(X21121),X21119)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).

fof(i_0_7198,plain,
    ! [X29541,X29542,X29543,X29544,X29545] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29545)),X29544) = X29541
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29545),tc_List_Olist(X29545))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29545),tc_List_Olist(X29545)),X29544),X29543)),hAPP(c_List_Olexn(X29545,X29542),X29541))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29545)),X29543) = X29541
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29545),tc_List_Olist(X29545))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29545),tc_List_Olist(X29545)),X29544),X29543)),hAPP(c_List_Olexn(X29545,X29542),X29541))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).

fof(i_0_7199,plain,
    ! [X29122,X29123,X29124,X29125,X29126] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29126,X29125)),hAPP(hAPP(c_Product__Type_OPair(X29126,X29125),X29124),X29123)),X29122))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29125,X29126)),hAPP(hAPP(c_Product__Type_OPair(X29125,X29126),X29123),X29124)),hAPP(c_Relation_Oconverse(X29126,X29125),X29122))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).

fof(i_0_7200,plain,
    ! [X27372,X27373,X27374,X27375,X27376,X27377] : hAPP(hAPP(c_Relation_Orel__comp(X27377,X27376,X27375),X27374),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27376,X27375),tc_HOL_Obool)),X27373),X27372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27377,X27375),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27377,X27376,X27375),X27374),X27373)),hAPP(hAPP(c_Relation_Orel__comp(X27377,X27376,X27375),X27374),X27372)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib]) ).

cnf(i_0_7201,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5548]) ).

fof(i_0_7202,plain,
    ! [X26411,X26412,X26413,X26414] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X26414,tc_fun(X26413,tc_HOL_Obool))),X26412),X26411))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26414,X26413)),hAPP(hAPP(c_Product__Type_OPair(X26414,X26413),X26412),X26411)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26414,X26413),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26414,X26413)),hAPP(hAPP(c_Product__Type_OPair(X26414,X26413),X26412),X26411)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26414,X26413),tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X26414,tc_fun(X26413,tc_HOL_Obool))),X26412),X26411)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).

fof(i_0_7203,plain,
    ! [X32239,X32240] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32240),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32240))),X32239)))
      | c_List_Otranspose(X32240,c_List_Otranspose(X32240,X32239)) = c_List_OtakeWhile(tc_List_Olist(X32240),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32240)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32240),tc_List_Olist(X32240),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32240))),X32239) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).

fof(i_0_7204,plain,
    ! [X22025,X22026,X22027] :
      ( ~ class_Lattices_Olattice(X22027)
      | hAPP(X22026,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22027),esk117_3(X22025,X22026,X22027)),esk118_3(X22025,X22026,X22027))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22027),hAPP(X22026,esk117_3(X22025,X22026,X22027))),hAPP(X22026,esk118_3(X22025,X22026,X22027)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22027),X22025))
      | X22025 = c_Orderings_Obot__class_Obot(tc_fun(X22027,tc_HOL_Obool))
      | hAPP(X22026,c_Big__Operators_Olattice__class_OInf__fin(X22027,X22025)) = c_Big__Operators_Olattice__class_OInf__fin(X22027,hAPP(c_Set_Oimage(X22027,X22027,X22026),X22025)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).

fof(i_0_7205,plain,
    ! [X20431,X20432,X20433] :
      ( ~ class_Lattices_Olattice(X20433)
      | hAPP(X20432,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20433),esk84_3(X20431,X20432,X20433)),esk85_3(X20431,X20432,X20433))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20433),hAPP(X20432,esk84_3(X20431,X20432,X20433))),hAPP(X20432,esk85_3(X20431,X20432,X20433)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20433),X20431))
      | X20431 = c_Orderings_Obot__class_Obot(tc_fun(X20433,tc_HOL_Obool))
      | hAPP(X20432,c_Big__Operators_Olattice__class_OSup__fin(X20433,X20431)) = c_Big__Operators_Olattice__class_OSup__fin(X20433,hAPP(c_Set_Oimage(X20433,X20433,X20432),X20431)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).

fof(i_0_7206,plain,
    ! [X19288,X19289,X19290] :
      ( ~ class_Orderings_Olinorder(X19290)
      | hAPP(X19289,hAPP(hAPP(c_Orderings_Oord__class_Omin(X19290),esk60_3(X19288,X19289,X19290)),esk61_3(X19288,X19289,X19290))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X19290),hAPP(X19289,esk60_3(X19288,X19289,X19290))),hAPP(X19289,esk61_3(X19288,X19289,X19290)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19290),X19288))
      | X19288 = c_Orderings_Obot__class_Obot(tc_fun(X19290,tc_HOL_Obool))
      | hAPP(X19289,c_Big__Operators_Olinorder__class_OMin(X19290,X19288)) = c_Big__Operators_Olinorder__class_OMin(X19290,hAPP(c_Set_Oimage(X19290,X19290,X19289),X19288)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).

fof(i_0_7207,plain,
    ! [X19283,X19284,X19285] :
      ( ~ class_Orderings_Olinorder(X19285)
      | hAPP(X19284,hAPP(hAPP(c_Orderings_Oord__class_Omax(X19285),esk58_3(X19283,X19284,X19285)),esk59_3(X19283,X19284,X19285))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X19285),hAPP(X19284,esk58_3(X19283,X19284,X19285))),hAPP(X19284,esk59_3(X19283,X19284,X19285)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19285),X19283))
      | X19283 = c_Orderings_Obot__class_Obot(tc_fun(X19285,tc_HOL_Obool))
      | hAPP(X19284,c_Big__Operators_Olinorder__class_OMax(X19285,X19283)) = c_Big__Operators_Olinorder__class_OMax(X19285,hAPP(c_Set_Oimage(X19285,X19285,X19284),X19283)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).

fof(i_0_7208,plain,
    ! [X24447,X24448,X24451,X24453] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_2(X24447,X24448)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24448)))
        | ~ hBOOL(hAPP(X24447,X24451))
        | ~ hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) )
      & ( hBOOL(hAPP(X24447,esk197_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,X24451))
        | ~ hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24453),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24448)))
        | ~ hBOOL(hAPP(X24447,X24453))
        | hBOOL(hAPP(X24447,esk198_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_2(X24447,X24448)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24448)))
        | ~ hBOOL(hAPP(X24447,X24451))
        | hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) )
      & ( hBOOL(hAPP(X24447,esk197_2(X24447,X24448)))
        | ~ hBOOL(hAPP(X24447,X24451))
        | hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24453),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24448)))
        | ~ hBOOL(hAPP(X24447,X24453))
        | hBOOL(hAPP(X24447,esk198_2(X24447,X24448)))
        | hBOOL(hAPP(X24447,esk195_2(X24447,X24448)))
        | hBOOL(hAPP(X24447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X24447,X24448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X24447,X24448)),X24448))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24448)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex])])])])]) ).

fof(i_0_7209,plain,
    ! [X30175,X30176,X30177] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30177),tc_List_Olist(X30177))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30177),tc_List_Olist(X30177)),c_List_Olist_ONil(X30177)),X30176)),c_List_Olistrel(X30177,X30175)))
      | X30176 = c_List_Olist_ONil(X30177) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).

cnf(i_0_7210,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk452_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))
    | esk453_2(X1,X2) != esk454_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7211,plain,
    ! [X17245,X17246] : c_Set_Othe__elem(X17246,X17245) = c_HOL_OThe(X17246,hAPP(hAPP(c_COMBB(tc_fun(X17246,tc_HOL_Obool),tc_HOL_Obool,X17246),hAPP(c_fequal,X17245)),hAPP(hAPP(c_COMBC(X17246,tc_fun(X17246,tc_HOL_Obool),tc_fun(X17246,tc_HOL_Obool)),c_Set_Oinsert(X17246)),c_Orderings_Obot__class_Obot(tc_fun(X17246,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).

cnf(i_0_7212,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk353_2(X2,X1)),esk353_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5549]) ).

cnf(i_0_7213,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk340_2(X2,X1)),esk340_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5508]) ).

fof(i_0_7214,plain,
    ! [X30270,X30271,X30272] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30272),tc_List_Olist(X30272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30272),tc_List_Olist(X30272)),c_List_Olist_ONil(X30272)),X30271)),c_List_Olistrel1(X30272,X30270))),
    inference(variable_rename,[status(thm)],[i_0_5550]) ).

fof(i_0_7215,plain,
    ! [X30281,X30282,X30283] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30283),tc_List_Olist(X30283))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30283),tc_List_Olist(X30283)),c_List_Olist_ONil(X30283)),X30282)),c_List_Olex(X30283,X30281))),
    inference(variable_rename,[status(thm)],[i_0_5551]) ).

fof(i_0_7216,plain,
    ! [X23999,X24000] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24000),X23999))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24000)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23999)))
        | ~ c_Nat__Transfer_Onat__set(X23999)
        | ~ c_Nat__Transfer_Onat__set(X24000) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24000)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23999)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24000),X23999))
        | ~ c_Nat__Transfer_Onat__set(X23999)
        | ~ c_Nat__Transfer_Onat__set(X24000) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J])])]) ).

fof(i_0_7217,plain,
    ! [X23997,X23998] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23998),X23997))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23998)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23997)))
        | ~ c_Nat__Transfer_Onat__set(X23997)
        | ~ c_Nat__Transfer_Onat__set(X23998) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23998)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23997)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23998),X23997))
        | ~ c_Nat__Transfer_Onat__set(X23997)
        | ~ c_Nat__Transfer_Onat__set(X23998) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J])])]) ).

fof(i_0_7218,plain,
    ! [X27398,X27399,X27400,X27401] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27401,X27401,X27401),X27400),X27399) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27401,X27401),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27401,X27401,X27401),X27398),X27399) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27401,X27401),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27401,X27401,X27401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27401,X27401),tc_HOL_Obool)),X27400),X27398)),X27399) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27401,X27401),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).

fof(i_0_7219,plain,
    ! [X27307] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27307) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27307),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_int__def]) ).

fof(i_0_7220,plain,
    ! [X20837,X20838,X20839,X20840] :
      ( ~ class_Lattices_Olattice(X20840)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20840),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20840),X20839),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20840),X20838),X20837))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20840),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20840),X20839),X20838)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20840),X20839),X20837)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).

fof(i_0_7221,plain,
    ! [X18700,X18701,X18702,X18703] :
      ( ~ class_Orderings_Olinorder(X18703)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18703),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18703),X18702),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18703),X18701),X18700))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18703),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18703),X18702),X18701)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18703),X18702),X18700)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).

fof(i_0_7222,plain,
    ! [X20995,X20996,X20997,X20998] :
      ( ~ class_Lattices_Osemilattice__inf(X20998)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20998),X20997))
      | ~ hBOOL(hAPP(hAPP(c_member(X20998),X20996),X20997))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20998),hAPP(hAPP(c_Finite__Set_Ofold(X20998,X20998,c_Lattices_Osemilattice__inf__class_Oinf(X20998)),X20995),X20997)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20998),X20996),X20995))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).

fof(i_0_7223,plain,
    ! [X19125,X19126,X19127,X19128] :
      ( ~ class_Orderings_Olinorder(X19128)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19128),X19127))
      | ~ hBOOL(hAPP(hAPP(c_member(X19128),X19126),X19127))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19128),hAPP(hAPP(c_Finite__Set_Ofold(X19128,X19128,c_Orderings_Oord__class_Omin(X19128)),X19125),X19127)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19128),X19126),X19125))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).

fof(i_0_7224,plain,
    ! [X30073,X30074,X30075,X30076,X30077] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30077,tc_HOL_Obool)),hAPP(c_List_Oset(X30077),X30076)),X30075))
      | ~ hBOOL(hAPP(hAPP(c_member(X30077),X30074),X30075))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30077,tc_HOL_Obool)),hAPP(c_List_Oset(X30077),hAPP(hAPP(c_List_Olist__update(X30077,X30076),X30073),X30074))),X30075)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).

fof(i_0_7225,plain,
    ! [X24245,X24246,X24247,X24248,X24249] :
      ( ~ class_Groups_Ocomm__monoid__add(X24249)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24248),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24247),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24249),X24246),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24248,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24247),X24245))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24249),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24249),X24246),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24248,X24247))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24249),X24246),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24247),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24247),X24245)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).

fof(i_0_7226,plain,
    ! [X33226,X33227] :
      ( ~ c_Relation_Otrans(X33227,X33226)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33227,X33227),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X33227,X33227,X33227),X33226),X33226)),X33226)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__O__subset])]) ).

fof(i_0_7227,plain,
    ! [X27872,X27873,X27874,X27875,X27876] : hAPP(hAPP(c_Product__Type_OSigma(X27876,X27875),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27876,tc_HOL_Obool)),X27874),X27873)),hAPP(c_COMBK(tc_fun(X27875,tc_HOL_Obool),X27876),X27872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27876,X27875),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27876,X27875),X27874),hAPP(c_COMBK(tc_fun(X27875,tc_HOL_Obool),X27876),X27872))),hAPP(hAPP(c_Product__Type_OSigma(X27876,X27875),X27873),hAPP(c_COMBK(tc_fun(X27875,tc_HOL_Obool),X27876),X27872))),
    inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(i_0_7228,plain,
    ! [X27838,X27839,X27840,X27841,X27842] : hAPP(hAPP(c_Product__Type_OSigma(X27842,X27841),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27842,tc_HOL_Obool)),X27840),X27839)),hAPP(c_COMBK(tc_fun(X27841,tc_HOL_Obool),X27842),X27838)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27842,X27841),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27842,X27841),X27840),hAPP(c_COMBK(tc_fun(X27841,tc_HOL_Obool),X27842),X27838))),hAPP(hAPP(c_Product__Type_OSigma(X27842,X27841),X27839),hAPP(c_COMBK(tc_fun(X27841,tc_HOL_Obool),X27842),X27838))),
    inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(i_0_7229,plain,
    ! [X27889,X27890,X27891,X27892,X27893] : hAPP(hAPP(c_Product__Type_OSigma(X27893,X27892),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27893,tc_HOL_Obool)),X27891),X27890)),hAPP(c_COMBK(tc_fun(X27892,tc_HOL_Obool),X27893),X27889)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27893,X27892),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27893,X27892),X27891),hAPP(c_COMBK(tc_fun(X27892,tc_HOL_Obool),X27893),X27889))),hAPP(hAPP(c_Product__Type_OSigma(X27893,X27892),X27890),hAPP(c_COMBK(tc_fun(X27892,tc_HOL_Obool),X27893),X27889))),
    inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(i_0_7230,plain,
    ! [X19841,X19842,X19843,X19844,X19845] :
      ( ~ c_Fun_Oinj__on(X19845,X19844,X19843,X19842)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19844,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19845,X19844,X19843),X19842)),X19841))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19844),X19841))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19845),X19842)),hAPP(c_Finite__Set_Ocard(X19844),X19841))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_7231,plain,
    ! [X25579,X25580,X25581,X25582] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25581),esk250_4(X25579,X25580,X25581,X25582)),X25580))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25582,X25581,c_Groups_Otimes__class_Otimes(X25582)),X25579),c_Groups_Oone__class_Oone(X25582)),X25580) = c_Groups_Oone__class_Oone(X25582)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25581),X25580))
        | ~ class_Groups_Ocomm__monoid__mult(X25582) )
      & ( hAPP(X25579,esk250_4(X25579,X25580,X25581,X25582)) != c_Groups_Oone__class_Oone(X25582)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25582,X25581,c_Groups_Otimes__class_Otimes(X25582)),X25579),c_Groups_Oone__class_Oone(X25582)),X25580) = c_Groups_Oone__class_Oone(X25582)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25581),X25580))
        | ~ class_Groups_Ocomm__monoid__mult(X25582) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__1])])])]) ).

fof(i_0_7232,plain,
    ! [X32573,X32574,X32575,X32576] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32575),esk471_4(X32573,X32574,X32575,X32576)),hAPP(c_List_Oset(X32575),X32574)))
        | hBOOL(hAPP(X32573,hAPP(hAPP(c_List_Onth(X32575),X32574),X32576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32576),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32575)),X32574))) )
      & ( ~ hBOOL(hAPP(X32573,esk471_4(X32573,X32574,X32575,X32576)))
        | hBOOL(hAPP(X32573,hAPP(hAPP(c_List_Onth(X32575),X32574),X32576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32576),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32575)),X32574))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ball__nth])])])]) ).

fof(i_0_7233,plain,
    ! [X30178,X30179,X30180] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30180),tc_List_Olist(X30180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30180),tc_List_Olist(X30180)),X30179),c_List_Olist_ONil(X30180))),c_List_Olistrel(X30180,X30178)))
      | X30179 = c_List_Olist_ONil(X30180) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).

fof(i_0_7234,plain,
    ! [X21540,X21541,X21542,X21543,X21544,X21545] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21545)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21544,X21545),X21543),hAPP(hAPP(c_COMBB(tc_fun(X21542,X21545),X21545,X21544),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21542,X21545),X21541)),X21540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21542,X21545),X21541),hAPP(hAPP(c_COMBB(tc_fun(X21544,X21545),X21545,X21542),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21544,X21545),X21543)),hAPP(c_COMBC(X21544,X21542,X21545),X21540))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).

fof(i_0_7235,plain,
    ! [X21346,X21347,X21348,X21349,X21350,X21351] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21351)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21350,X21351),X21349),hAPP(hAPP(c_COMBB(tc_fun(X21348,X21351),X21351,X21350),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21348,X21351),X21347)),X21346)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21348,X21351),X21347),hAPP(hAPP(c_COMBB(tc_fun(X21350,X21351),X21351,X21348),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21350,X21351),X21349)),hAPP(c_COMBC(X21350,X21348,X21351),X21346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).

fof(i_0_7236,plain,
    ! [X30273,X30274,X30275] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30275),tc_List_Olist(X30275))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30275),tc_List_Olist(X30275)),X30274),c_List_Olist_ONil(X30275))),c_List_Olistrel1(X30275,X30273))),
    inference(variable_rename,[status(thm)],[i_0_5552]) ).

fof(i_0_7237,plain,
    ! [X30278,X30279,X30280] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30280),tc_List_Olist(X30280))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30280),tc_List_Olist(X30280)),X30279),c_List_Olist_ONil(X30280))),c_List_Olexord(X30280,X30278))),
    inference(variable_rename,[status(thm)],[i_0_5553]) ).

fof(i_0_7238,plain,
    ! [X30284,X30285,X30286] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30286),tc_List_Olist(X30286))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30286),tc_List_Olist(X30286)),X30285),c_List_Olist_ONil(X30286))),c_List_Olex(X30286,X30284))),
    inference(variable_rename,[status(thm)],[i_0_5554]) ).

fof(i_0_7239,plain,
    ! [X26545,X26546,X26547,X26548,X26549] :
      ( ( hAPP(c_Relation_OImage(X26549,X26549,X26547),hAPP(hAPP(c_Set_Oinsert(X26549),X26546),c_Orderings_Obot__class_Obot(tc_fun(X26549,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26549,X26549,X26547),hAPP(hAPP(c_Set_Oinsert(X26549),X26545),c_Orderings_Obot__class_Obot(tc_fun(X26549,tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26549,X26549)),hAPP(hAPP(c_Product__Type_OPair(X26549,X26549),X26546),X26545)),X26547))
        | ~ hBOOL(hAPP(hAPP(c_member(X26549),X26545),X26548))
        | ~ hBOOL(hAPP(hAPP(c_member(X26549),X26546),X26548))
        | ~ c_Equiv__Relations_Oequiv(X26549,X26548,X26547) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26549,X26549)),hAPP(hAPP(c_Product__Type_OPair(X26549,X26549),X26546),X26545)),X26547))
        | hAPP(c_Relation_OImage(X26549,X26549,X26547),hAPP(hAPP(c_Set_Oinsert(X26549),X26546),c_Orderings_Obot__class_Obot(tc_fun(X26549,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26549,X26549,X26547),hAPP(hAPP(c_Set_Oinsert(X26549),X26545),c_Orderings_Obot__class_Obot(tc_fun(X26549,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X26549),X26545),X26548))
        | ~ hBOOL(hAPP(hAPP(c_member(X26549),X26546),X26548))
        | ~ c_Equiv__Relations_Oequiv(X26549,X26548,X26547) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).

fof(i_0_7240,plain,
    ! [X24107,X24108,X24109] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24109),esk166_3(X24107,X24108,X24109)),X24108))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,tc_Int_Oint),X24107),X24108) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24109),c_Int_Onat),X24107)),X24108)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X24107,esk166_3(X24107,X24108,X24109)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,tc_Int_Oint),X24107),X24108) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24109),c_Int_Onat),X24107)),X24108)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J])])])]) ).

fof(i_0_7241,plain,
    ! [X24111,X24112,X24113] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24113),esk167_3(X24111,X24112,X24113)),X24112))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24113,tc_Int_Oint),X24111),X24112) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24113,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24113),c_Int_Onat),X24111)),X24112)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X24111,esk167_3(X24111,X24112,X24113)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24113,tc_Int_Oint),X24111),X24112) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24113,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24113),c_Int_Onat),X24111)),X24112)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J])])])]) ).

fof(i_0_7242,plain,
    ! [X29668,X29669,X29670,X29671] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29671),tc_List_Olist(X29671))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29671),tc_List_Olist(X29671)),X29670),X29669)),c_List_Olistrel(X29671,X29668)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29671)),X29670) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29671)),X29669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).

fof(i_0_7243,plain,
    ! [X29633,X29634,X29635,X29636] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29636),tc_List_Olist(X29636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29636),tc_List_Olist(X29636)),X29635),X29634)),c_List_Olistrel1(X29636,X29633)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29636)),X29635) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29636)),X29634) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).

fof(i_0_7244,plain,
    ! [X33385,X33386,X33387,X33388,X33389,X33390] :
      ( ( ~ c_Relation_Osym(X33386,X33385)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33386,X33386)),hAPP(hAPP(c_Product__Type_OPair(X33386,X33386),X33387),X33388)),X33385))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33386,X33386)),hAPP(hAPP(c_Product__Type_OPair(X33386,X33386),X33388),X33387)),X33385)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33390,X33390)),hAPP(hAPP(c_Product__Type_OPair(X33390,X33390),esk520_2(X33389,X33390)),esk521_2(X33389,X33390))),X33389))
        | c_Relation_Osym(X33390,X33389) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33390,X33390)),hAPP(hAPP(c_Product__Type_OPair(X33390,X33390),esk521_2(X33389,X33390)),esk520_2(X33389,X33390))),X33389))
        | c_Relation_Osym(X33390,X33389) ) ),
    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_sym__def])])])])])]) ).

fof(i_0_7245,plain,
    ! [X33381,X33382,X33383,X33384] :
      ( ~ c_Relation_Osym(X33384,X33383)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33384,X33384)),hAPP(hAPP(c_Product__Type_OPair(X33384,X33384),X33382),X33381)),X33383))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33384,X33384)),hAPP(hAPP(c_Product__Type_OPair(X33384,X33384),X33381),X33382)),X33383)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symD])]) ).

cnf(i_0_7246,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3,c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5555]) ).

cnf(i_0_7247,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5556]) ).

fof(i_0_7248,plain,
    ! [X17280,X17281,X17282] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17282),esk16_3(X17280,X17281,X17282)))
        | hBOOL(hAPP(X17280,X17281))
        | ~ hBOOL(hAPP(X17280,c_Orderings_Obot__class_Obot(tc_fun(X17282,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17282),X17281)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17282),esk15_3(X17280,X17281,X17282)),esk16_3(X17280,X17281,X17282)))
        | hBOOL(hAPP(X17280,X17281))
        | ~ hBOOL(hAPP(X17280,c_Orderings_Obot__class_Obot(tc_fun(X17282,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17282),X17281)) )
      & ( hBOOL(hAPP(X17280,esk16_3(X17280,X17281,X17282)))
        | hBOOL(hAPP(X17280,X17281))
        | ~ hBOOL(hAPP(X17280,c_Orderings_Obot__class_Obot(tc_fun(X17282,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17282),X17281)) )
      & ( ~ hBOOL(hAPP(X17280,hAPP(hAPP(c_Set_Oinsert(X17282),esk15_3(X17280,X17281,X17282)),esk16_3(X17280,X17281,X17282))))
        | hBOOL(hAPP(X17280,X17281))
        | ~ hBOOL(hAPP(X17280,c_Orderings_Obot__class_Obot(tc_fun(X17282,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17282),X17281)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5557])])])]) ).

fof(i_0_7249,plain,
    ! [X32306,X32307,X32308,X32309,X32310] :
      ( ~ class_Orderings_Olinorder(X32310)
      | ~ c_List_Olinorder__class_Osorted(X32310,hAPP(c_List_Orev(X32310),hAPP(hAPP(c_List_Omap(X32309,X32310),X32308),X32307)))
      | hAPP(c_List_Ofilter(X32309,hAPP(hAPP(c_COMBB(X32310,tc_HOL_Obool,X32309),hAPP(c_Orderings_Oord__class_Oless(X32310),X32306)),X32308)),X32307) = c_List_OtakeWhile(X32309,hAPP(hAPP(c_COMBB(X32310,tc_HOL_Obool,X32309),hAPP(c_Orderings_Oord__class_Oless(X32310),X32306)),X32308),X32307) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])]) ).

fof(i_0_7250,plain,
    ! [X27800,X27801,X27802,X27803] : hAPP(hAPP(c_Product__Type_OSigma(X27803,X27802),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27803,tc_HOL_Obool),X27801)),X27800) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X27803,tc_HOL_Obool),tc_fun(tc_prod(X27803,X27802),tc_HOL_Obool)),X27801),hAPP(hAPP(c_COMBC(tc_fun(X27803,tc_HOL_Obool),tc_fun(X27803,tc_fun(X27802,tc_HOL_Obool)),tc_fun(tc_prod(X27803,X27802),tc_HOL_Obool)),c_Product__Type_OSigma(X27803,X27802)),X27800)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).

fof(i_0_7251,plain,
    ! [X24407,X24408,X24409,X24410] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk181_4(X24407,X24408,X24409,X24410)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24409)))
        | X24410 = X24408
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24410),X24409) != X24408
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24408),X24407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24409)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X24407,X24408,X24409,X24410)),X24407))
        | X24410 = X24408
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24410),X24409) != X24408
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24408),X24407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24409)) )
      & ( X24410 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk182_4(X24407,X24408,X24409,X24410)),esk181_4(X24407,X24408,X24409,X24410))
        | X24410 = X24408
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24410),X24409) != X24408
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24408),X24407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24409)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I4_J])])])])]) ).

fof(i_0_7252,plain,
    ! [X24401,X24402,X24403,X24404] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_4(X24401,X24402,X24403,X24404)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24403)))
        | X24404 = X24402
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24404),X24403) != X24402
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24402),X24401))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24403)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk180_4(X24401,X24402,X24403,X24404)),X24401))
        | X24404 = X24402
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24404),X24403) != X24402
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24402),X24401))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24403)) )
      & ( X24404 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk180_4(X24401,X24402,X24403,X24404)),esk179_4(X24401,X24402,X24403,X24404))
        | X24404 = X24402
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24404),X24403) != X24402
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24402),X24401))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24403)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I4_J])])])])]) ).

fof(i_0_7253,plain,
    ! [X17720,X17721,X17722,X17723,X17724] : hAPP(hAPP(c_Finite__Set_Ofold(X17724,X17723,X17722),X17721),X17720) = c_HOL_OThe(X17723,c_Finite__Set_Ofold__graph(X17724,X17723,X17722,X17721,X17720)),
    inference(variable_rename,[status(thm)],[fact_fold__def]) ).

fof(i_0_7254,plain,
    ! [X26711,X26712,X26713,X26715,X26716,X26717,X26718,X26719,X26722] :
      ( ( ~ hBOOL(hAPP(X26713,esk261_3(X26711,X26712,X26713)))
        | hBOOL(hAPP(X26713,hAPP(hAPP(c_Product__Type_OPair(X26712,X26711),X26715),X26716))) )
      & ( ~ hBOOL(hAPP(X26719,hAPP(hAPP(c_Product__Type_OPair(X26718,X26717),esk262_3(X26717,X26718,X26719)),esk263_3(X26717,X26718,X26719))))
        | hBOOL(hAPP(X26719,X26722)) ) ),
    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_split__paired__All])])])])]) ).

fof(i_0_7255,plain,
    ! [X33630,X33631,X33632,X33633,X33634] :
      ( ~ hBOOL(hAPP(X33634,hAPP(hAPP(c_Product__Type_OPair(X33633,X33632),X33631),X33630)))
      | hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33633,X33632,tc_HOL_Obool,X33634),X33631),X33630)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).

fof(i_0_7256,plain,
    ! [X19779,X19780,X19781] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19781),X19780))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19781),X19779)),hAPP(c_Finite__Set_Ocard(X19781),X19780))),hAPP(c_Finite__Set_Ocard(X19781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19781,tc_HOL_Obool)),X19779),X19780)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).

fof(i_0_7257,plain,
    ! [X25200,X25201,X25202,X25203] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25202,tc_HOL_Obool)),esk222_4(X25200,X25201,X25202,X25203)),X25203))
        | c_Fun_Oinj__on(X25202,X25201,X25200,c_Complete__Lattice_OInf__class_OInf(tc_fun(X25202,tc_HOL_Obool),X25203))
        | X25203 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25202,tc_HOL_Obool),tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X25202,X25201,X25200,esk222_4(X25200,X25201,X25202,X25203))
        | c_Fun_Oinj__on(X25202,X25201,X25200,c_Complete__Lattice_OInf__class_OInf(tc_fun(X25202,tc_HOL_Obool),X25203))
        | X25203 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25202,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Inter])])])]) ).

cnf(i_0_7258,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5558]) ).

fof(i_0_7259,plain,
    ! [X32902,X32903,X32904,X32905,X32906,X32907,X32908,X32909,X32910] :
      ( ( hBOOL(hAPP(X32902,X32903))
        | ~ hBOOL(hAPP(hAPP(c_member(X32905),X32906),hAPP(c_List_Oset(X32905),c_List_Oreplicate(X32905,X32904,X32903))))
        | ~ hBOOL(hAPP(X32902,X32906)) )
      & ( X32904 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32905),X32906),hAPP(c_List_Oset(X32905),c_List_Oreplicate(X32905,X32904,X32903))))
        | ~ hBOOL(hAPP(X32902,X32906)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32910),esk487_4(X32907,X32908,X32909,X32910)),hAPP(c_List_Oset(X32910),c_List_Oreplicate(X32910,X32909,X32908))))
        | ~ hBOOL(hAPP(X32907,X32908))
        | X32909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(X32907,esk487_4(X32907,X32908,X32909,X32910)))
        | ~ hBOOL(hAPP(X32907,X32908))
        | X32909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    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_Bex__set__replicate])])])])])]) ).

cnf(i_0_7260,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).

fof(i_0_7261,plain,
    ! [X26785,X26786,X26787,X26788,X26789] :
      ( ( ~ c_Nitpick_Orefl_H(X26786,X26785)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26786,X26786)),hAPP(hAPP(c_Product__Type_OPair(X26786,X26786),X26787),X26787)),X26785)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26789,X26789)),hAPP(hAPP(c_Product__Type_OPair(X26789,X26789),esk264_2(X26788,X26789)),esk264_2(X26788,X26789))),X26788))
        | c_Nitpick_Orefl_H(X26789,X26788) ) ),
    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_Nitpick_Orefl_H__def])])])])]) ).

fof(i_0_7262,plain,
    ! [X24467,X24468,X24469,X24471] :
      ( ( hBOOL(hAPP(X24468,esk203_3(X24467,X24468,X24469)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24467))
        | ~ hBOOL(hAPP(X24468,X24471))
        | hBOOL(hAPP(X24468,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24467),X24469))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24469)) )
      & ( ~ hBOOL(hAPP(X24468,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk203_3(X24467,X24468,X24469)),X24469)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24467))
        | ~ hBOOL(hAPP(X24468,X24471))
        | hBOOL(hAPP(X24468,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24467),X24469))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24469)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma])])])])]) ).

fof(i_0_7263,plain,
    ! [X24271,X24272,X24273,X24275] :
      ( ( hBOOL(hAPP(X24272,esk173_3(X24271,X24272,X24273)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24271))
        | ~ hBOOL(hAPP(X24272,X24275))
        | hBOOL(hAPP(X24272,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24271),X24273))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24273)) )
      & ( ~ hBOOL(hAPP(X24272,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk173_3(X24271,X24272,X24273)),X24273)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24271))
        | ~ hBOOL(hAPP(X24272,X24275))
        | hBOOL(hAPP(X24272,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24271),X24273))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24273)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma])])])])]) ).

fof(i_0_7264,plain,
    ! [X32462,X32463,X32464,X32465,X32466] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32466,X32465)),hAPP(X32466,X32464)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32463,X32463)),hAPP(hAPP(c_Product__Type_OPair(X32463,X32463),X32465),X32464)),c_List_Omeasures(X32463,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32463,tc_Nat_Onat)),X32466),X32462)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).

cnf(i_0_7265,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).

fof(i_0_7266,plain,
    ! [X28770,X28771,X28772,X28773,X28774,X28775,X28776] :
      ( ~ c_Finite__Set_Ofolding__idem(X28776,X28775,X28774,X28773)
      | hAPP(c_Fun_Ocomp(X28775,X28775,X28772,hAPP(X28774,X28771)),hAPP(c_Fun_Ocomp(X28775,X28775,X28772,hAPP(X28774,X28771)),X28770)) = hAPP(c_Fun_Ocomp(X28775,X28775,X28772,hAPP(X28774,X28771)),X28770) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).

fof(i_0_7267,plain,
    ! [X26632,X26633,X26634,X26635,X26636,X26637,X26638] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26638),X26637),hAPP(hAPP(X26636,X26635),X26634)))
      | hBOOL(hAPP(hAPP(c_member(X26638),X26637),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26633,X26632,tc_fun(X26638,tc_HOL_Obool)),X26636),hAPP(hAPP(c_Product__Type_OPair(X26633,X26632),X26635),X26634)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).

fof(i_0_7268,plain,
    ! [X32912,X32913,X32914,X32915,X32917,X32918,X32919,X32920,X32921] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32915),esk488_4(X32912,X32913,X32914,X32915)),hAPP(c_List_Oset(X32915),c_List_Oreplicate(X32915,X32914,X32913))))
        | hBOOL(hAPP(X32912,X32913))
        | X32914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X32912,esk488_4(X32912,X32913,X32914,X32915)))
        | hBOOL(hAPP(X32912,X32913))
        | X32914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X32917,X32918))
        | ~ hBOOL(hAPP(hAPP(c_member(X32920),X32921),hAPP(c_List_Oset(X32920),c_List_Oreplicate(X32920,X32919,X32918))))
        | hBOOL(hAPP(X32917,X32921)) )
      & ( X32919 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32920),X32921),hAPP(c_List_Oset(X32920),c_List_Oreplicate(X32920,X32919,X32918))))
        | hBOOL(hAPP(X32917,X32921)) ) ),
    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_Ball__set__replicate])])])])])]) ).

fof(i_0_7269,plain,
    ! [X29652,X29653,X29654,X29655] : hAPP(c_Relation_OImage(tc_List_Olist(X29655),tc_List_Olist(X29655),c_List_Olistrel(X29655,X29654)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29655)),hAPP(hAPP(c_List_Olist_OCons(X29655),X29653),X29652)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29655),tc_HOL_Obool)))) = c_List_Oset__Cons(X29655,hAPP(c_Relation_OImage(X29655,X29655,X29654),hAPP(hAPP(c_Set_Oinsert(X29655),X29653),c_Orderings_Obot__class_Obot(tc_fun(X29655,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X29655),tc_List_Olist(X29655),c_List_Olistrel(X29655,X29654)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29655)),X29652),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29655),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).

fof(i_0_7270,plain,
    ! [X24359,X24360,X24361,X24362] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24362,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24361)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X24362,tc_HOL_Obool),tc_Nat_Onat),X24360),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24359))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24362,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24359,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24361),X24359))),X24360),
    inference(variable_rename,[status(thm)],[fact_UN__le__add__shift]) ).

cnf(i_0_7271,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2]) ).

cnf(i_0_7272,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).

fof(i_0_7273,plain,
    ! [X33722,X33723,X33724,X33725] :
      ( ~ c_Fun_Obij__betw(X33725,X33724,X33723,c_Orderings_Otop__class_Otop(tc_fun(X33725,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33724,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33725,X33724,X33723),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X33725,tc_HOL_Obool)),X33722)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X33724,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33725,X33724,X33723),X33722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Compl__eq])]) ).

cnf(i_0_7274,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_OremoveAll(X1,X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_5559]) ).

fof(i_0_7275,plain,
    ! [X17927,X17928,X17929,X17930,X17931,X17932] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17932),X17931),X17930))
      | hAPP(c_Fun_Ooverride__on(X17932,X17929,X17928,X17927,X17930),X17931) = hAPP(X17927,X17931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).

fof(i_0_7276,plain,
    ! [X17554,X17555,X17556,X17557,X17558,X17559] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17559),X17558),X17557))
        | hAPP(c_Fun_Ooverride__on(X17559,X17556,X17555,X17554,X17557),X17558) = hAPP(X17554,X17558) )
      & ( hBOOL(hAPP(hAPP(c_member(X17559),X17558),X17557))
        | hAPP(c_Fun_Ooverride__on(X17559,X17556,X17555,X17554,X17557),X17558) = hAPP(X17555,X17558) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5560])]) ).

cnf(i_0_7277,plain,
    ( c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5561]) ).

fof(i_0_7278,plain,
    ! [X30805,X30806,X30807,X30808,X30809,X30810] :
      ( X30808 != hAPP(hAPP(c_List_Olist_OCons(X30807),X30809),X30810)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30807),tc_List_Olist(X30807))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30807),tc_List_Olist(X30807)),X30806),hAPP(hAPP(c_List_Oappend(X30807),X30806),X30808))),c_List_Olexord(X30807,X30805))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).

fof(i_0_7279,plain,
    ! [X29944,X29945,X29946,X29947,X29948,X29949,X29950] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29944)),X29946) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29944)),X29945)
        | X29946 != X29945 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29944,X29944)),X29947),hAPP(c_List_Oset(tc_prod(X29944,X29944)),hAPP(hAPP(c_List_Ozip(X29944,X29944),X29946),X29945))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29944,X29944,tc_HOL_Obool),c_fequal),X29947))
        | X29946 != X29945 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29948,X29948)),esk396_3(X29948,X29949,X29950)),hAPP(c_List_Oset(tc_prod(X29948,X29948)),hAPP(hAPP(c_List_Ozip(X29948,X29948),X29950),X29949))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29948)),X29950) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29948)),X29949)
        | X29950 = X29949 )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29948,X29948,tc_HOL_Obool),c_fequal),esk396_3(X29948,X29949,X29950)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29948)),X29950) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29948)),X29949)
        | X29950 = X29949 ) ),
    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_list__eq__iff__zip__eq])])])])])]) ).

fof(i_0_7280,plain,
    ! [X26976,X26977,X26978] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk276_3(X26976,X26977,X26978)),esk277_3(X26976,X26977,X26978))))
        | hBOOL(hAPP(hAPP(X26976,X26978),X26977))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26978),X26977))) )
      & ( esk277_3(X26976,X26977,X26978) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(X26976,esk277_3(X26976,X26977,X26978)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk276_3(X26976,X26977,X26978),esk277_3(X26976,X26977,X26978))))
        | hBOOL(hAPP(hAPP(X26976,X26978),X26977))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26978),X26977))) )
      & ( ~ hBOOL(hAPP(hAPP(X26976,esk276_3(X26976,X26977,X26978)),esk277_3(X26976,X26977,X26978)))
        | hBOOL(hAPP(hAPP(X26976,X26978),X26977))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26978),X26977))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct])])])]) ).

fof(i_0_7281,plain,
    ! [X18491,X18492,X18493,X18494,X18495] :
      ( ~ c_Fun_Oinj__on(X18495,X18494,X18493,X18492)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18495,tc_HOL_Obool)),X18491),X18492))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18494,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18495,X18494,X18493),X18491)),hAPP(c_Set_Oimage(X18495,X18494,X18493),X18492))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_7282,plain,
    ! [X20966,X20967,X20968,X20969,X20970,X20971] :
      ( ~ c_Fun_Oinj__on(X20971,X20970,X20969,X20968)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20971,tc_HOL_Obool)),X20967),X20968))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20971,tc_HOL_Obool)),X20966),X20968))
      | hAPP(c_Set_Oimage(X20971,X20970,X20969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20971,tc_HOL_Obool)),X20967),X20966)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20970,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20971,X20970,X20969),X20967)),hAPP(c_Set_Oimage(X20971,X20970,X20969),X20966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).

fof(i_0_7283,plain,
    ! [X17731,X17732,X17733,X17734,X17735,X17736] :
      ( ~ c_Fun_Oinj__on(X17736,X17735,X17734,X17733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17736,tc_HOL_Obool)),X17732),X17733))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17736,tc_HOL_Obool)),X17731),X17733))
      | hAPP(c_Set_Oimage(X17736,X17735,X17734),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17736,tc_HOL_Obool)),X17732),X17731)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17735,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17736,X17735,X17734),X17732)),hAPP(c_Set_Oimage(X17736,X17735,X17734),X17731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).

fof(i_0_7284,plain,
    ! [X31853,X31854,X31855] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31855),X31854))
      | hAPP(c_List_Ofilter(X31855,hAPP(hAPP(c_COMBC(X31855,tc_fun(X31855,tc_HOL_Obool),tc_HOL_Obool),c_member(X31855)),hAPP(c_List_Oset(X31855),c_List_Osublist(X31855,X31854,X31853)))),X31854) = c_List_Osublist(X31855,X31854,X31853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__in__sublist])]) ).

cnf(i_0_7285,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5) = c_List_Ofoldr(X2,X1,hAPP(c_COMBC(X1,X2,X1),X3),hAPP(c_List_Orev(X2),X5),X4),
    inference(split_conjunct,[status(thm)],[i_0_5562]) ).

cnf(i_0_7286,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk346_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),c_Transitive__Closure_Otrancl(X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5493]) ).

cnf(i_0_7287,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | esk453_2(X1,X2) != esk454_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk452_2(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5505]) ).

fof(i_0_7288,plain,
    ! [X33524,X33525,X33526,X33527,X33528,X33529,X33530] :
      ( ( hAPP(c_Set_Oimage(X33526,X33525,X33524),c_Orderings_Otop__class_Otop(tc_fun(X33526,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33525,tc_HOL_Obool))
        | hAPP(X33524,hAPP(c_Hilbert__Choice_Oinv__into(X33526,X33525,c_Orderings_Otop__class_Otop(tc_fun(X33526,tc_HOL_Obool)),X33524),X33527)) = X33527 )
      & ( hAPP(X33528,hAPP(c_Hilbert__Choice_Oinv__into(X33530,X33529,c_Orderings_Otop__class_Otop(tc_fun(X33530,tc_HOL_Obool)),X33528),esk528_3(X33528,X33529,X33530))) != esk528_3(X33528,X33529,X33530)
        | hAPP(c_Set_Oimage(X33530,X33529,X33528),c_Orderings_Otop__class_Otop(tc_fun(X33530,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33529,tc_HOL_Obool)) ) ),
    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_surj__iff__all])])])])]) ).

fof(i_0_7289,plain,
    ! [X33066,X33067,X33068,X33070,X33071,X33072,X33073,X33074] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33068),esk493_3(X33066,X33067,X33068)),hAPP(c_List_Oset(X33068),X33066)))
        | ~ c_List_Olist__ex1(X33068,X33067,X33066) )
      & ( hBOOL(hAPP(X33067,esk493_3(X33066,X33067,X33068)))
        | ~ c_List_Olist__ex1(X33068,X33067,X33066) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33068),X33070),hAPP(c_List_Oset(X33068),X33066)))
        | ~ hBOOL(hAPP(X33067,X33070))
        | X33070 = esk493_3(X33066,X33067,X33068)
        | ~ c_List_Olist__ex1(X33068,X33067,X33066) )
      & ( hBOOL(hAPP(hAPP(c_member(X33073),esk494_4(X33071,X33072,X33073,X33074)),hAPP(c_List_Oset(X33073),X33071)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33073),X33074),hAPP(c_List_Oset(X33073),X33071)))
        | ~ hBOOL(hAPP(X33072,X33074))
        | c_List_Olist__ex1(X33073,X33072,X33071) )
      & ( hBOOL(hAPP(X33072,esk494_4(X33071,X33072,X33073,X33074)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33073),X33074),hAPP(c_List_Oset(X33073),X33071)))
        | ~ hBOOL(hAPP(X33072,X33074))
        | c_List_Olist__ex1(X33073,X33072,X33071) )
      & ( esk494_4(X33071,X33072,X33073,X33074) != X33074
        | ~ hBOOL(hAPP(hAPP(c_member(X33073),X33074),hAPP(c_List_Oset(X33073),X33071)))
        | ~ hBOOL(hAPP(X33072,X33074))
        | c_List_Olist__ex1(X33073,X33072,X33071) ) ),
    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_list__ex1__iff__raw])])])])])]) ).

fof(i_0_7290,plain,
    ! [X32705,X32706,X32707,X32709,X32710,X32711,X32712,X32713] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32707),esk485_3(X32705,X32706,X32707)),hAPP(c_List_Oset(X32707),X32705)))
        | ~ c_List_Olist__ex1(X32707,X32706,X32705) )
      & ( hBOOL(hAPP(X32706,esk485_3(X32705,X32706,X32707)))
        | ~ c_List_Olist__ex1(X32707,X32706,X32705) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32707),X32709),hAPP(c_List_Oset(X32707),X32705)))
        | ~ hBOOL(hAPP(X32706,X32709))
        | X32709 = esk485_3(X32705,X32706,X32707)
        | ~ c_List_Olist__ex1(X32707,X32706,X32705) )
      & ( hBOOL(hAPP(hAPP(c_member(X32712),esk486_4(X32710,X32711,X32712,X32713)),hAPP(c_List_Oset(X32712),X32710)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32712),X32713),hAPP(c_List_Oset(X32712),X32710)))
        | ~ hBOOL(hAPP(X32711,X32713))
        | c_List_Olist__ex1(X32712,X32711,X32710) )
      & ( hBOOL(hAPP(X32711,esk486_4(X32710,X32711,X32712,X32713)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32712),X32713),hAPP(c_List_Oset(X32712),X32710)))
        | ~ hBOOL(hAPP(X32711,X32713))
        | c_List_Olist__ex1(X32712,X32711,X32710) )
      & ( esk486_4(X32710,X32711,X32712,X32713) != X32713
        | ~ hBOOL(hAPP(hAPP(c_member(X32712),X32713),hAPP(c_List_Oset(X32712),X32710)))
        | ~ hBOOL(hAPP(X32711,X32713))
        | c_List_Olist__ex1(X32712,X32711,X32710) ) ),
    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_list__ex1__iff])])])])])]) ).

fof(i_0_7291,plain,
    ! [X17725,X17726,X17727] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17727),X17726))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17727,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17727,X17727,X17725),X17726)),X17726))
      | ~ c_Fun_Oinj__on(X17727,X17727,X17725,X17726)
      | hAPP(c_Set_Oimage(X17727,X17727,X17725),X17726) = X17726 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_7292,plain,
    ! [X17933,X17934,X17935,X17936,X17937,X17938] :
      ( hBOOL(hAPP(hAPP(c_member(X17938),X17937),X17936))
      | hAPP(c_Fun_Ooverride__on(X17938,X17935,X17934,X17933,X17936),X17937) = hAPP(X17934,X17937) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5563])]) ).

fof(i_0_7293,plain,
    ! [X30957,X30958,X30959,X30960,X30961] :
      ( ~ class_Orderings_Olinorder(X30961)
      | ~ hBOOL(hAPP(hAPP(c_member(X30961),hAPP(X30960,X30959)),hAPP(c_Set_Oimage(X30958,X30961,X30960),hAPP(c_List_Oset(X30958),X30957))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30958,X30961,X30960,X30959,X30957) = X30957 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).

fof(i_0_7294,plain,
    ! [X30954,X30955,X30956] :
      ( ~ class_Orderings_Olinorder(X30956)
      | hAPP(c_List_Oset(X30956),c_List_Olinorder__class_Oinsort__insert__key(X30956,X30956,c_COMBI(X30956),X30955,X30954)) = hAPP(hAPP(c_Set_Oinsert(X30956),X30955),hAPP(c_List_Oset(X30956),X30954)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).

fof(i_0_7295,plain,
    ! [X29683,X29684,X29685] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29685,X29685),tc_HOL_Obool)),X29684),X29683))
      | ~ c_Relation_Orefl__on(X29685,c_Orderings_Otop__class_Otop(tc_fun(X29685,tc_HOL_Obool)),X29683)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29685),tc_List_Olist(X29685)),tc_HOL_Obool)),c_List_Olistrel1(X29685,X29684)),c_List_Olistrel(X29685,X29683))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])]) ).

cnf(i_0_7296,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_OdropWhile(X1,X3,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5564]) ).

cnf(i_0_7297,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5548]) ).

fof(i_0_7298,plain,
    ! [X19827,X19828,X19829,X19830,X19831,X19832,X19833] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19832),X19828))
        | hAPP(hAPP(X19829,X19827),X19828) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19833,X19832,X19831),X19827),X19830),X19828)
        | ~ c_Big__Operators_Ocomm__monoid__big(X19833,X19832,X19831,X19830,X19829) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19832),X19828))
        | hAPP(hAPP(X19829,X19827),X19828) = X19830
        | ~ c_Big__Operators_Ocomm__monoid__big(X19833,X19832,X19831,X19830,X19829) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5565])])]) ).

fof(i_0_7299,plain,
    ! [X28702,X28703,X28704,X28705,X28706,X28707,X28708] :
      ( ~ c_Finite__Set_Ofolding__image(X28708,X28707,X28706,X28705,X28704)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28707),X28703))
      | hAPP(hAPP(X28704,X28702),X28703) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28708,X28707,X28706),X28702),X28705),X28703) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).

fof(i_0_7300,plain,
    ! [X17973,X17974,X17975,X17976,X17977,X17978] :
      ( ~ c_Finite__Set_Ofun__left__comm(X17978,X17977,X17976)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17978),X17975))
      | ~ hBOOL(hAPP(hAPP(c_member(X17978),X17974),X17975))
      | hAPP(hAPP(c_Finite__Set_Ofold(X17978,X17977,X17976),X17973),X17975) = hAPP(hAPP(X17976,X17974),hAPP(hAPP(c_Finite__Set_Ofold(X17978,X17977,X17976),X17973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17978,tc_HOL_Obool)),X17975),hAPP(hAPP(c_Set_Oinsert(X17978),X17974),c_Orderings_Obot__class_Obot(tc_fun(X17978,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).

fof(i_0_7301,plain,
    ! [X28355,X28356,X28357,X28358,X28359,X28360] : hAPP(c_Set_Ovimage(X28360,X28359,hAPP(c_Fun_Ocomp(X28358,X28359,X28360,X28357),X28356)),X28355) = hAPP(c_Set_Ovimage(X28360,X28358,X28356),hAPP(c_Set_Ovimage(X28358,X28359,X28357),X28355)),
    inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).

fof(i_0_7302,plain,
    ! [X28498,X28499,X28500,X28501,X28502,X28503] : hAPP(c_Set_Oimage(X28503,X28502,hAPP(c_Fun_Ocomp(X28501,X28502,X28503,X28500),X28499)),X28498) = hAPP(c_Set_Oimage(X28501,X28502,X28500),hAPP(c_Set_Oimage(X28503,X28501,X28499),X28498)),
    inference(variable_rename,[status(thm)],[fact_image__compose]) ).

fof(i_0_7303,plain,
    ! [X29311,X29312,X29313,X29315,X29316,X29317,X29318] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29313,X29313)),X29312),c_Transitive__Closure_Ortrancl(X29313,X29311)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29313,X29313)),X29312),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29313,X29313),tc_HOL_Obool),esk345_3(X29311,X29312,X29313)),X29311))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29317,X29317)),X29316),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29317,X29317),tc_HOL_Obool),X29318),X29315)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29317,X29317)),X29316),c_Transitive__Closure_Ortrancl(X29317,X29315))) ) ),
    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_rtrancl__power])])])])]) ).

fof(i_0_7304,plain,
    ! [X28828,X28829,X28830,X28831,X28832,X28833,X28834] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28834,X28833,X28832,X28831),X28830),X28829),X28828) = hAPP(hAPP(X28829,hAPP(c_Product__Type_Ofst(X28833,X28832),hAPP(X28830,X28828))),hAPP(c_Product__Type_Osnd(X28833,X28832),hAPP(X28830,X28828))),
    inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).

fof(i_0_7305,plain,
    ! [X26550,X26551,X26552,X26553,X26554] :
      ( ( hAPP(c_Relation_OImage(X26554,X26554,X26552),hAPP(hAPP(c_Set_Oinsert(X26554),X26551),c_Orderings_Obot__class_Obot(tc_fun(X26554,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26554,X26554,X26552),hAPP(hAPP(c_Set_Oinsert(X26554),X26550),c_Orderings_Obot__class_Obot(tc_fun(X26554,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26554,X26554)),hAPP(hAPP(c_Product__Type_OPair(X26554,X26554),X26551),X26550)),X26552))
        | ~ c_Equiv__Relations_Oequiv(X26554,X26553,X26552) )
      & ( hBOOL(hAPP(hAPP(c_member(X26554),X26551),X26553))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26554,X26554)),hAPP(hAPP(c_Product__Type_OPair(X26554,X26554),X26551),X26550)),X26552))
        | ~ c_Equiv__Relations_Oequiv(X26554,X26553,X26552) )
      & ( hBOOL(hAPP(hAPP(c_member(X26554),X26550),X26553))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26554,X26554)),hAPP(hAPP(c_Product__Type_OPair(X26554,X26554),X26551),X26550)),X26552))
        | ~ c_Equiv__Relations_Oequiv(X26554,X26553,X26552) )
      & ( hAPP(c_Relation_OImage(X26554,X26554,X26552),hAPP(hAPP(c_Set_Oinsert(X26554),X26551),c_Orderings_Obot__class_Obot(tc_fun(X26554,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26554,X26554,X26552),hAPP(hAPP(c_Set_Oinsert(X26554),X26550),c_Orderings_Obot__class_Obot(tc_fun(X26554,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X26554),X26551),X26553))
        | ~ hBOOL(hAPP(hAPP(c_member(X26554),X26550),X26553))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26554,X26554)),hAPP(hAPP(c_Product__Type_OPair(X26554,X26554),X26551),X26550)),X26552))
        | ~ c_Equiv__Relations_Oequiv(X26554,X26553,X26552) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).

fof(i_0_7306,plain,
    ! [X22210,X22211,X22212] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),c_Groups_Ozero__class_Ozero(X22212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22211),X22211)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22210),X22210))))
        | X22211 != c_Groups_Ozero__class_Ozero(X22212)
        | X22210 != c_Groups_Ozero__class_Ozero(X22212)
        | ~ class_Rings_Olinordered__ring__strict(X22212) )
      & ( X22211 = c_Groups_Ozero__class_Ozero(X22212)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),c_Groups_Ozero__class_Ozero(X22212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22211),X22211)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22210),X22210))))
        | ~ class_Rings_Olinordered__ring__strict(X22212) )
      & ( X22210 = c_Groups_Ozero__class_Ozero(X22212)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),c_Groups_Ozero__class_Ozero(X22212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22211),X22211)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22212),X22210),X22210))))
        | ~ class_Rings_Olinordered__ring__strict(X22212) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).

fof(i_0_7307,plain,
    ! [X29379,X29380] : c_Transitive__Closure_Ortrancl(X29380,X29379) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X29380,X29380),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X29380,X29380),tc_HOL_Obool),tc_fun(tc_prod(X29380,X29380),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X29380,X29380),tc_HOL_Obool)),X29379)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(i_0_7308,plain,
    ! [X32515,X32516,X32517,X32518] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32518),esk461_4(X32515,X32516,X32517,X32518)),hAPP(c_List_Oset(X32518),X32517)))
        | c_List_OtakeWhile(X32518,X32516,hAPP(hAPP(c_List_Oappend(X32518),X32517),X32515)) = hAPP(hAPP(c_List_Oappend(X32518),X32517),c_List_OtakeWhile(X32518,X32516,X32515)) )
      & ( ~ hBOOL(hAPP(X32516,esk461_4(X32515,X32516,X32517,X32518)))
        | c_List_OtakeWhile(X32518,X32516,hAPP(hAPP(c_List_Oappend(X32518),X32517),X32515)) = hAPP(hAPP(c_List_Oappend(X32518),X32517),c_List_OtakeWhile(X32518,X32516,X32515)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])]) ).

fof(i_0_7309,plain,
    ! [X28492,X28493,X28494,X28495,X28496,X28497] :
      ( ~ c_Fun_Oinj__on(X28497,X28496,hAPP(c_Fun_Ocomp(X28495,X28496,X28497,X28494),X28493),X28492)
      | c_Fun_Oinj__on(X28495,X28496,X28494,hAPP(c_Set_Oimage(X28497,X28495,X28493),X28492)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).

fof(i_0_7310,plain,
    ! [X22655,X22656,X22657,X22659,X22660] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22657),esk127_3(X22655,X22656,X22657)),X22656))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) )
      & ( hAPP(X22655,esk127_3(X22655,X22656,X22657)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22657),X22659),X22656))
        | esk127_3(X22655,X22656,X22657) = X22659
        | hAPP(X22655,X22659) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22657),esk128_4(X22655,X22656,X22657,X22660)),X22656))
        | ~ hBOOL(hAPP(hAPP(c_member(X22657),X22660),X22656))
        | hAPP(X22655,X22660) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) )
      & ( X22660 != esk128_4(X22655,X22656,X22657,X22660)
        | ~ hBOOL(hAPP(hAPP(c_member(X22657),X22660),X22656))
        | hAPP(X22655,X22660) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) )
      & ( hAPP(X22655,esk128_4(X22655,X22656,X22657,X22660)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X22657),X22660),X22656))
        | hAPP(X22655,X22660) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22657,tc_Nat_Onat),X22655),X22656) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22657),X22656)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff])])])])]) ).

fof(i_0_7311,plain,
    ! [X32014,X32015,X32016] :
      ( ~ class_Orderings_Olinorder(X32016)
      | ~ c_List_Olinorder__class_Osorted(X32016,X32015)
      | c_List_Olinorder__class_Osorted(X32016,c_List_Olinorder__class_Oinsort__insert__key(X32016,X32016,c_COMBI(X32016),X32014,X32015)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).

fof(i_0_7312,plain,
    ! [X25051,X25052,X25053,X25054,X25055] :
      ( ~ class_Rings_Olinordered__idom(X25055)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25055),hAPP(c_Groups_Oabs__class_Oabs(X25055),X25054)),X25053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25055),hAPP(c_Groups_Oabs__class_Oabs(X25055),X25052)),X25051))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25055),hAPP(c_Groups_Oabs__class_Oabs(X25055),X25054)),hAPP(c_Groups_Oabs__class_Oabs(X25055),X25052))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25055),X25053),X25051))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).

fof(i_0_7313,plain,
    ! [X17987,X17988,X17989,X17990,X17991,X17992] :
      ( ~ c_Finite__Set_Ofun__left__comm(X17992,X17991,X17990)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17992),X17989))
      | hAPP(hAPP(c_Finite__Set_Ofold(X17992,X17991,X17990),X17988),hAPP(hAPP(c_Set_Oinsert(X17992),X17987),X17989)) = hAPP(hAPP(X17990,X17987),hAPP(hAPP(c_Finite__Set_Ofold(X17992,X17991,X17990),X17988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17992,tc_HOL_Obool)),X17989),hAPP(hAPP(c_Set_Oinsert(X17992),X17987),c_Orderings_Obot__class_Obot(tc_fun(X17992,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])]) ).

fof(i_0_7314,plain,
    ! [X32269,X32270,X32271,X32272,X32273] : c_List_OtakeWhile(X32273,X32272,hAPP(hAPP(c_List_Omap(X32271,X32273),X32270),X32269)) = hAPP(hAPP(c_List_Omap(X32271,X32273),X32270),c_List_OtakeWhile(X32271,hAPP(c_Fun_Ocomp(X32273,tc_HOL_Obool,X32271,X32272),X32270),X32269)),
    inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).

fof(i_0_7315,plain,
    ! [X17482,X17483,X17484,X17485,X17486,X17487] :
      ( ( X17487 != X17486
        | hAPP(c_Fun_Ofun__upd(X17485,X17484,X17483,X17486,X17482),X17487) = X17482 )
      & ( X17487 = X17486
        | hAPP(c_Fun_Ofun__upd(X17485,X17484,X17483,X17486,X17482),X17487) = hAPP(X17483,X17487) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).

fof(i_0_7316,plain,
    ! [X17466,X17467,X17468,X17469,X17470,X17471] :
      ( X17471 = X17470
      | hAPP(c_Fun_Ofun__upd(X17469,X17468,X17467,X17470,X17466),X17471) = hAPP(X17467,X17471) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).

fof(i_0_7317,plain,
    ! [X17453,X17454,X17455,X17456,X17457,X17458] :
      ( ( X17458 != X17457
        | hAPP(c_Fun_Ofun__upd(X17456,X17455,X17454,X17457,X17453),X17458) = X17453 )
      & ( X17458 = X17457
        | hAPP(c_Fun_Ofun__upd(X17456,X17455,X17454,X17457,X17453),X17458) = hAPP(X17454,X17458) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).

fof(i_0_7318,plain,
    ! [X22662,X22663,X22664,X22666,X22667] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22664),esk129_3(X22662,X22663,X22664)),X22663))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) )
      & ( hAPP(X22662,esk129_3(X22662,X22663,X22664)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22664),X22666),X22663))
        | esk129_3(X22662,X22663,X22664) = X22666
        | hAPP(X22662,X22666) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22664),esk130_4(X22662,X22663,X22664,X22667)),X22663))
        | ~ hBOOL(hAPP(hAPP(c_member(X22664),X22667),X22663))
        | hAPP(X22662,X22667) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) )
      & ( X22667 != esk130_4(X22662,X22663,X22664,X22667)
        | ~ hBOOL(hAPP(hAPP(c_member(X22664),X22667),X22663))
        | hAPP(X22662,X22667) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) )
      & ( hAPP(X22662,esk130_4(X22662,X22663,X22664,X22667)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X22664),X22667),X22663))
        | hAPP(X22662,X22667) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22664,tc_Nat_Onat),X22662),X22663) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22664),X22663)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff])])])])]) ).

fof(i_0_7319,plain,
    ! [X29179,X29180,X29181] :
      ( ~ c_Relation_Orefl__on(X29181,X29180,X29179)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29181,X29181),tc_HOL_Obool)),X29179),hAPP(hAPP(c_Relation_Orel__comp(X29181,X29181,X29181),hAPP(c_Relation_Oconverse(X29181,X29181),X29179)),X29179))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).

fof(i_0_7320,plain,
    ! [X17448,X17449,X17450,X17451,X17452] : hAPP(c_Fun_Ofun__upd(X17452,X17451,X17450,X17449,X17448),X17449) = X17448,
    inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).

fof(i_0_7321,plain,
    ! [X28486,X28487,X28488,X28489,X28490,X28491] :
      ( ~ c_Fun_Oinj__on(X28491,X28490,X28489,X28488)
      | ~ c_Fun_Oinj__on(X28490,X28487,X28486,hAPP(c_Set_Oimage(X28491,X28490,X28489),X28488))
      | c_Fun_Oinj__on(X28491,X28487,hAPP(c_Fun_Ocomp(X28490,X28487,X28491,X28486),X28489),X28488) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on])]) ).

fof(i_0_7322,plain,
    ! [X31423,X31424,X31425,X31426,X31427] : c_Enum_Oproduct(X31427,X31426,hAPP(hAPP(c_List_Olist_OCons(X31427),X31425),X31424),X31423) = hAPP(hAPP(c_List_Oappend(tc_prod(X31427,X31426)),hAPP(hAPP(c_List_Omap(X31426,tc_prod(X31427,X31426)),hAPP(c_Product__Type_OPair(X31427,X31426),X31425)),X31423)),c_Enum_Oproduct(X31427,X31426,X31424,X31423)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J]) ).

cnf(i_0_7323,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Wellfounded_Omeasure(X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5566]) ).

cnf(i_0_7324,plain,
    c_Wellfounded_Omeasure(X1) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[i_0_5567]) ).

fof(i_0_7325,plain,
    ! [X30879,X30880] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30880),hAPP(c_List_Oset(tc_Nat_Onat),X30879)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30880),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30879))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).

fof(i_0_7326,plain,
    ! [X26453,X26454,X26455,X26456,X26457,X26458] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26458),X26457),X26456))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26458,X26455)),hAPP(hAPP(c_Product__Type_OPair(X26458,X26455),X26457),X26454)),X26453))
      | hBOOL(hAPP(hAPP(c_member(X26455),X26454),hAPP(c_Relation_OImage(X26458,X26455,X26453),X26456))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).

fof(i_0_7327,plain,
    ! [X31196,X31197,X31198,X31199,X31200,X31201] : hAPP(hAPP(c_List_Omap(X31201,X31200),X31199),hAPP(hAPP(c_List_Omap(X31198,X31201),X31197),X31196)) = hAPP(hAPP(c_List_Omap(X31198,X31200),hAPP(c_Fun_Ocomp(X31201,X31200,X31198,X31199),X31197)),X31196),
    inference(variable_rename,[status(thm)],[fact_map__map]) ).

fof(i_0_7328,plain,
    ! [X31190,X31191,X31192,X31193,X31194,X31195] : hAPP(hAPP(c_List_Omap(X31195,X31194),X31193),hAPP(hAPP(c_List_Omap(X31192,X31195),X31191),X31190)) = hAPP(hAPP(c_List_Omap(X31192,X31194),hAPP(c_Fun_Ocomp(X31195,X31194,X31192,X31193),X31191)),X31190),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(i_0_7329,plain,
    ! [X30287,X30288,X30289,X30290] : hAPP(hAPP(c_List_Otake(X30290),X30289),hAPP(hAPP(c_List_Olist_OCons(X30290),X30288),X30287)) = c_Nat_Onat_Onat__case(tc_List_Olist(X30290),c_List_Olist_ONil(X30290),hAPP(hAPP(c_COMBB(tc_List_Olist(X30290),tc_List_Olist(X30290),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X30290),X30288)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X30290),tc_List_Olist(X30290)),c_List_Otake(X30290)),X30287)),X30289),
    inference(variable_rename,[status(thm)],[fact_take__Cons]) ).

fof(i_0_7330,plain,
    ! [X25543,X25544,X25545,X25546,X25547] : hAPP(c_Relation_OImage(X25547,X25546,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X25547,X25546),tc_HOL_Obool)),X25545),X25544)),X25543) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25546,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25547,X25546,X25545),X25543)),hAPP(c_Relation_OImage(X25547,X25546,X25544),X25543)),
    inference(variable_rename,[status(thm)],[fact_Un__Image]) ).

fof(i_0_7331,plain,
    ! [X28934,X28935,X28936,X28937,X28938] :
      ( ( X28938 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28937,X28936,X28938,X28935),X28934) = hAPP(c_Product__Type_OPair(X28937,X28936),X28934) )
      & ( X28938 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28937,X28936,X28938,X28935),X28934) = hAPP(hAPP(c_Product__Type_Oscomp(X28936,X28937,X28936,tc_prod(X28937,X28936)),hAPP(X28935,X28934)),c_Random_Oiterate(X28937,X28936,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28938),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X28935)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).

fof(i_0_7332,plain,
    ! [X26515,X26516,X26517,X26518,X26519] :
      ( ~ c_Equiv__Relations_Oequiv(X26519,X26518,X26517)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26519,X26519)),hAPP(hAPP(c_Product__Type_OPair(X26519,X26519),X26516),X26515)),X26517))
      | hAPP(c_Relation_OImage(X26519,X26519,X26517),hAPP(hAPP(c_Set_Oinsert(X26519),X26516),c_Orderings_Obot__class_Obot(tc_fun(X26519,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26519,X26519,X26517),hAPP(hAPP(c_Set_Oinsert(X26519),X26515),c_Orderings_Obot__class_Obot(tc_fun(X26519,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).

fof(i_0_7333,plain,
    ! [X27929,X27930,X27931,X27932,X27933,X27934] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27934),X27932),X27930))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27934,X27933)),hAPP(hAPP(c_Product__Type_OPair(X27934,X27933),X27932),X27931)),hAPP(hAPP(c_Product__Type_OSigma(X27934,X27933),X27930),X27929))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27933),X27931),hAPP(X27929,X27932)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27934,X27933)),hAPP(hAPP(c_Product__Type_OPair(X27934,X27933),X27932),X27931)),hAPP(hAPP(c_Product__Type_OSigma(X27934,X27933),X27930),X27929))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5568])])]) ).

fof(i_0_7334,plain,
    ! [X27911,X27912,X27913,X27914,X27915,X27916] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27916),X27914),X27912))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27916,X27915)),hAPP(hAPP(c_Product__Type_OPair(X27916,X27915),X27914),X27913)),hAPP(hAPP(c_Product__Type_OSigma(X27916,X27915),X27912),X27911))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27915),X27913),hAPP(X27911,X27914)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27916,X27915)),hAPP(hAPP(c_Product__Type_OPair(X27916,X27915),X27914),X27913)),hAPP(hAPP(c_Product__Type_OSigma(X27916,X27915),X27912),X27911))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27916),X27914),X27912))
        | ~ hBOOL(hAPP(hAPP(c_member(X27915),X27913),hAPP(X27911,X27914)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27916,X27915)),hAPP(hAPP(c_Product__Type_OPair(X27916,X27915),X27914),X27913)),hAPP(hAPP(c_Product__Type_OSigma(X27916,X27915),X27912),X27911))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).

fof(i_0_7335,plain,
    ! [X27923,X27924,X27925,X27926,X27927,X27928] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27928,X27927)),hAPP(hAPP(c_Product__Type_OPair(X27928,X27927),X27926),X27925)),hAPP(hAPP(c_Product__Type_OSigma(X27928,X27927),X27924),X27923)))
      | hBOOL(hAPP(hAPP(c_member(X27927),X27925),hAPP(X27923,X27926))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).

fof(i_0_7336,plain,
    ! [X29663,X29664,X29665] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29665,X29665),tc_HOL_Obool)),X29664),X29663))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29665),tc_List_Olist(X29665)),tc_HOL_Obool)),c_List_Olistrel(X29665,X29664)),c_List_Olistrel(X29665,X29663))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).

fof(i_0_7337,plain,
    ! [X29612,X29613,X29614] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29614,X29614),tc_HOL_Obool)),X29613),X29612))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29614),tc_List_Olist(X29614)),tc_HOL_Obool)),c_List_Olistrel1(X29614,X29613)),c_List_Olistrel1(X29614,X29612))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).

fof(i_0_7338,plain,
    ! [X33804,X33805,X33806] :
      ( ( c_Fun_Oinj__on(X33806,X33805,X33804,c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool)))
        | ~ c_Fun_Obij__betw(X33806,X33805,X33804,c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33805,tc_HOL_Obool))) )
      & ( hAPP(c_Set_Oimage(X33806,X33805,X33804),c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33805,tc_HOL_Obool))
        | ~ c_Fun_Obij__betw(X33806,X33805,X33804,c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33805,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X33806,X33805,X33804,c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(X33806,X33805,X33804),c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33805,tc_HOL_Obool))
        | c_Fun_Obij__betw(X33806,X33805,X33804,c_Orderings_Otop__class_Otop(tc_fun(X33806,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33805,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__def])])]) ).

fof(i_0_7339,plain,
    ! [X33754,X33755,X33756] :
      ( ~ c_Fun_Obij__betw(X33756,X33755,X33754,c_Orderings_Otop__class_Otop(tc_fun(X33756,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33755,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X33756,X33755,X33754,c_Orderings_Otop__class_Otop(tc_fun(X33756,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__is__inj])]) ).

cnf(i_0_7340,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oconcat(X1,X4)) = c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_5569]) ).

fof(i_0_7341,plain,
    ! [X28873,X28874,X28875,X28876,X28877,X28878,X28879] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28879,X28878,X28877,X28876),X28875),X28874),X28873) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28878,X28877,X28876),X28874),hAPP(X28875,X28873)),
    inference(variable_rename,[status(thm)],[fact_scomp__def]) ).

fof(i_0_7342,plain,
    ! [X28866,X28867,X28868,X28869,X28870,X28871,X28872] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28872,X28871,X28870,X28869),X28868),X28867),X28866) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28871,X28870,X28869),X28867),hAPP(X28868,X28866)),
    inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).

fof(i_0_7343,plain,
    ! [X19615,X19616,X19617,X19618] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19618,tc_HOL_Obool)),X19617),X19616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19618,tc_HOL_Obool)),X19615),X19616))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19618,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19618,tc_HOL_Obool)),X19617),X19615)),X19616)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).

fof(i_0_7344,plain,
    ! [X21042,X21043,X21044,X21045,X21046] :
      ( ~ c_Finite__Set_Ofolding__one(X21046,X21045,X21044)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21046),X21043))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21046),X21042))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21046,tc_HOL_Obool)),X21043),X21042) = c_Orderings_Obot__class_Obot(tc_fun(X21046,tc_HOL_Obool))
      | hAPP(hAPP(X21045,hAPP(X21044,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21046,tc_HOL_Obool)),X21043),X21042))),hAPP(X21044,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21046,tc_HOL_Obool)),X21043),X21042))) = hAPP(hAPP(X21045,hAPP(X21044,X21043)),hAPP(X21044,X21042)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).

fof(i_0_7345,plain,
    ! [X17777,X17778,X17779,X17780,X17781] :
      ( ~ c_Fun_Oinj__on(X17781,X17780,X17779,X17778)
      | ~ hBOOL(hAPP(hAPP(c_member(X17780),X17777),hAPP(c_Set_Oimage(X17781,X17780,X17779),X17778)))
      | hAPP(X17779,hAPP(c_Fun_Othe__inv__into(X17781,X17780,X17778,X17779),X17777)) = X17777 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).

cnf(i_0_7346,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5570]) ).

cnf(i_0_7347,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5571]) ).

fof(i_0_7348,plain,
    ! [X25173,X25174,X25175,X25176] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X25176,tc_HOL_Obool),tc_fun(X25175,tc_HOL_Obool)),X25174),hAPP(hAPP(c_COMBC(tc_fun(X25176,tc_HOL_Obool),tc_fun(X25176,tc_fun(X25175,tc_HOL_Obool)),tc_fun(X25175,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25176,tc_fun(X25175,tc_HOL_Obool))),X25173)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25176,tc_fun(X25175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25176,tc_HOL_Obool),X25174)),X25173),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(i_0_7349,plain,
    ! [X25014,X25015,X25016,X25017] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25017,tc_HOL_Obool),tc_fun(X25016,tc_HOL_Obool)),X25015),hAPP(hAPP(c_COMBC(tc_fun(X25017,tc_HOL_Obool),tc_fun(X25017,tc_fun(X25016,tc_HOL_Obool)),tc_fun(X25016,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25017,tc_fun(X25016,tc_HOL_Obool))),X25014)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25017,tc_fun(X25016,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25017,tc_HOL_Obool),X25015)),X25014),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(i_0_7350,plain,
    ! [X25169,X25170,X25171,X25172] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25172,tc_fun(X25171,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25172,tc_HOL_Obool),X25170)),X25169) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X25172,tc_HOL_Obool),tc_fun(X25171,tc_HOL_Obool)),X25170),hAPP(hAPP(c_COMBC(tc_fun(X25172,tc_HOL_Obool),tc_fun(X25172,tc_fun(X25171,tc_HOL_Obool)),tc_fun(X25171,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X25172,tc_fun(X25171,tc_HOL_Obool))),X25169)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(i_0_7351,plain,
    ! [X25018,X25019,X25020,X25021] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25021,tc_fun(X25020,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25021,tc_HOL_Obool),X25019)),X25018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25021,tc_HOL_Obool),tc_fun(X25020,tc_HOL_Obool)),X25019),hAPP(hAPP(c_COMBC(tc_fun(X25021,tc_HOL_Obool),tc_fun(X25021,tc_fun(X25020,tc_HOL_Obool)),tc_fun(X25020,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25021,tc_fun(X25020,tc_HOL_Obool))),X25018)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(i_0_7352,plain,
    ! [X17672,X17673,X17674,X17675,X17676,X17677,X17678,X17679,X17680,X17681] :
      ( ( ~ c_Fun_Oinj__on(X17675,X17674,X17673,X17672)
        | ~ hBOOL(hAPP(hAPP(c_member(X17675),X17676),X17672))
        | ~ hBOOL(hAPP(hAPP(c_member(X17675),X17677),X17672))
        | hAPP(X17673,X17676) != hAPP(X17673,X17677)
        | X17676 = X17677 )
      & ( hBOOL(hAPP(hAPP(c_member(X17681),esk20_4(X17678,X17679,X17680,X17681)),X17678))
        | c_Fun_Oinj__on(X17681,X17680,X17679,X17678) )
      & ( hBOOL(hAPP(hAPP(c_member(X17681),esk21_4(X17678,X17679,X17680,X17681)),X17678))
        | c_Fun_Oinj__on(X17681,X17680,X17679,X17678) )
      & ( hAPP(X17679,esk20_4(X17678,X17679,X17680,X17681)) = hAPP(X17679,esk21_4(X17678,X17679,X17680,X17681))
        | c_Fun_Oinj__on(X17681,X17680,X17679,X17678) )
      & ( esk20_4(X17678,X17679,X17680,X17681) != esk21_4(X17678,X17679,X17680,X17681)
        | c_Fun_Oinj__on(X17681,X17680,X17679,X17678) ) ),
    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_inj__on__def])])])])])]) ).

fof(i_0_7353,plain,
    ! [X28976,X28977,X28978] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28978,X28978),tc_HOL_Obool)),X28977),X28976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28978,X28978),tc_HOL_Obool)),X28976),c_Transitive__Closure_Ortrancl(X28978,X28977)))
      | c_Transitive__Closure_Ortrancl(X28978,X28976) = c_Transitive__Closure_Ortrancl(X28978,X28977) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).

fof(i_0_7354,plain,
    ! [X26540,X26541,X26542,X26543,X26544] :
      ( hAPP(c_Relation_OImage(X26544,X26544,X26543),hAPP(hAPP(c_Set_Oinsert(X26544),X26542),c_Orderings_Obot__class_Obot(tc_fun(X26544,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26544,X26544,X26543),hAPP(hAPP(c_Set_Oinsert(X26544),X26541),c_Orderings_Obot__class_Obot(tc_fun(X26544,tc_HOL_Obool))))
      | ~ c_Equiv__Relations_Oequiv(X26544,X26540,X26543)
      | ~ hBOOL(hAPP(hAPP(c_member(X26544),X26541),X26540))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X26544,X26544)),hAPP(hAPP(c_Product__Type_OPair(X26544,X26544),X26542),X26541)),X26543)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).

fof(i_0_7355,plain,
    ! [X27917,X27918,X27919,X27920,X27921,X27922] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27922,X27921)),hAPP(hAPP(c_Product__Type_OPair(X27922,X27921),X27920),X27919)),hAPP(hAPP(c_Product__Type_OSigma(X27922,X27921),X27918),X27917)))
      | hBOOL(hAPP(hAPP(c_member(X27922),X27920),X27918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).

fof(i_0_7356,plain,
    ! [X22441,X22442,X22443,X22444,X22446] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22443),esk121_4(X22441,X22442,X22443,X22444)),X22442))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22443,X22444),X22441),X22442) != c_Groups_Ozero__class_Ozero(X22444)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22443),X22442))
        | ~ class_Rings_Ocomm__semiring__1(X22444)
        | ~ class_Rings_Ono__zero__divisors(X22444) )
      & ( hAPP(X22441,esk121_4(X22441,X22442,X22443,X22444)) = c_Groups_Ozero__class_Ozero(X22444)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22443,X22444),X22441),X22442) != c_Groups_Ozero__class_Ozero(X22444)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22443),X22442))
        | ~ class_Rings_Ocomm__semiring__1(X22444)
        | ~ class_Rings_Ono__zero__divisors(X22444) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22443),X22446),X22442))
        | hAPP(X22441,X22446) != c_Groups_Ozero__class_Ozero(X22444)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22443,X22444),X22441),X22442) = c_Groups_Ozero__class_Ozero(X22444)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22443),X22442))
        | ~ class_Rings_Ocomm__semiring__1(X22444)
        | ~ class_Rings_Ono__zero__divisors(X22444) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff])])])])]) ).

fof(i_0_7357,plain,
    ! [X19687,X19688,X19689,X19690] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19690),X19689))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19688),hAPP(c_Set_Oimage(X19690,X19688,X19687),X19689))),hAPP(c_Finite__Set_Ocard(X19690),X19689))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_7358,plain,
    ! [X30938,X30939,X30940,X30941,X30942] :
      ( ~ class_Orderings_Olinorder(X30942)
      | hBOOL(hAPP(hAPP(c_member(X30942),hAPP(X30941,X30940)),hAPP(c_Set_Oimage(X30939,X30942,X30941),hAPP(c_List_Oset(X30939),X30938))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30939,X30942,X30941,X30940,X30938) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30939,X30942,X30941),X30940),X30938) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5572])]) ).

cnf(i_0_7359,plain,
    ( c_Relation_Ototal__on(X1,X2,X3)
    | ~ c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5573]) ).

fof(i_0_7360,plain,
    ! [X21649,X21650,X21651,X21652,X21653,X21654,X21655,X21656,X21657] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21652,tc_fun(X21651,tc_HOL_Obool)),X21650),X21649) != c_Orderings_Otop__class_Otop(tc_fun(X21651,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X21652),X21653),X21650))
        | hAPP(X21649,X21653) = c_Orderings_Otop__class_Otop(tc_fun(X21651,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21657),esk108_4(X21654,X21655,X21656,X21657)),X21655))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21657,tc_fun(X21656,tc_HOL_Obool)),X21655),X21654) = c_Orderings_Otop__class_Otop(tc_fun(X21656,tc_HOL_Obool)) )
      & ( hAPP(X21654,esk108_4(X21654,X21655,X21656,X21657)) != c_Orderings_Otop__class_Otop(tc_fun(X21656,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21657,tc_fun(X21656,tc_HOL_Obool)),X21655),X21654) = c_Orderings_Otop__class_Otop(tc_fun(X21656,tc_HOL_Obool)) ) ),
    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_INTER__UNIV__conv_I2_J])])])])])]) ).

fof(i_0_7361,plain,
    ! [X21247,X21248,X21249,X21250,X21251,X21252,X21253,X21254,X21255] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21250,tc_fun(X21249,tc_HOL_Obool)),X21248),X21247) != c_Orderings_Obot__class_Obot(tc_fun(X21249,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X21250),X21251),X21248))
        | hAPP(X21247,X21251) = c_Orderings_Obot__class_Obot(tc_fun(X21249,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21255),esk98_4(X21252,X21253,X21254,X21255)),X21253))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21255,tc_fun(X21254,tc_HOL_Obool)),X21253),X21252) = c_Orderings_Obot__class_Obot(tc_fun(X21254,tc_HOL_Obool)) )
      & ( hAPP(X21252,esk98_4(X21252,X21253,X21254,X21255)) != c_Orderings_Obot__class_Obot(tc_fun(X21254,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21255,tc_fun(X21254,tc_HOL_Obool)),X21253),X21252) = c_Orderings_Obot__class_Obot(tc_fun(X21254,tc_HOL_Obool)) ) ),
    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_UNION__empty__conv_I2_J])])])])])]) ).

fof(i_0_7362,plain,
    ! [X21659,X21660,X21661,X21662,X21663,X21664,X21665,X21666,X21667] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(X21662,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21661,tc_fun(X21662,tc_HOL_Obool)),X21660),X21659)
        | ~ hBOOL(hAPP(hAPP(c_member(X21661),X21663),X21660))
        | hAPP(X21659,X21663) = c_Orderings_Otop__class_Otop(tc_fun(X21662,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21666),esk109_4(X21664,X21665,X21666,X21667)),X21665))
        | c_Orderings_Otop__class_Otop(tc_fun(X21667,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21666,tc_fun(X21667,tc_HOL_Obool)),X21665),X21664) )
      & ( hAPP(X21664,esk109_4(X21664,X21665,X21666,X21667)) != c_Orderings_Otop__class_Otop(tc_fun(X21667,tc_HOL_Obool))
        | c_Orderings_Otop__class_Otop(tc_fun(X21667,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21666,tc_fun(X21667,tc_HOL_Obool)),X21665),X21664) ) ),
    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_INTER__UNIV__conv_I1_J])])])])])]) ).

fof(i_0_7363,plain,
    ! [X21264,X21265,X21266,X21267,X21268,X21269,X21270,X21271,X21272] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X21267,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21266,tc_fun(X21267,tc_HOL_Obool)),X21265),X21264)
        | ~ hBOOL(hAPP(hAPP(c_member(X21266),X21268),X21265))
        | hAPP(X21264,X21268) = c_Orderings_Obot__class_Obot(tc_fun(X21267,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21271),esk99_4(X21269,X21270,X21271,X21272)),X21270))
        | c_Orderings_Obot__class_Obot(tc_fun(X21272,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21271,tc_fun(X21272,tc_HOL_Obool)),X21270),X21269) )
      & ( hAPP(X21269,esk99_4(X21269,X21270,X21271,X21272)) != c_Orderings_Obot__class_Obot(tc_fun(X21272,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X21272,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21271,tc_fun(X21272,tc_HOL_Obool)),X21270),X21269) ) ),
    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_UNION__empty__conv_I1_J])])])])])]) ).

fof(i_0_7364,plain,
    ! [X25555,X25556,X25557,X25558] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25558),esk248_4(X25555,X25556,X25557,X25558)),X25556))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25558,tc_Nat_Onat),X25557),X25556) != hAPP(c_Nat_OSuc,X25555) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X25557,esk248_4(X25555,X25556,X25557,X25558))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25558,tc_Nat_Onat),X25557),X25556) != hAPP(c_Nat_OSuc,X25555) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).

fof(i_0_7365,plain,
    ! [X22006,X22007,X22008] :
      ( ~ class_Lattices_Olattice(X22008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22008),X22007))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22008),X22006))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22008,tc_HOL_Obool)),X22007),X22006) = c_Orderings_Obot__class_Obot(tc_fun(X22008,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22008),c_Big__Operators_Olattice__class_OInf__fin(X22008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22008,tc_HOL_Obool)),X22007),X22006))),c_Big__Operators_Olattice__class_OInf__fin(X22008,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22008,tc_HOL_Obool)),X22007),X22006))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22008),c_Big__Operators_Olattice__class_OInf__fin(X22008,X22007)),c_Big__Operators_Olattice__class_OInf__fin(X22008,X22006)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).

fof(i_0_7366,plain,
    ! [X21101,X21102,X21103] :
      ( ~ class_Lattices_Olattice(X21103)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21103),X21102))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21103),X21101))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21103,tc_HOL_Obool)),X21102),X21101) = c_Orderings_Obot__class_Obot(tc_fun(X21103,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21103),c_Big__Operators_Olattice__class_OSup__fin(X21103,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21103,tc_HOL_Obool)),X21102),X21101))),c_Big__Operators_Olattice__class_OSup__fin(X21103,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21103,tc_HOL_Obool)),X21102),X21101))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21103),c_Big__Operators_Olattice__class_OSup__fin(X21103,X21102)),c_Big__Operators_Olattice__class_OSup__fin(X21103,X21101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).

fof(i_0_7367,plain,
    ! [X21113,X21114,X21115] :
      ( ~ class_Orderings_Olinorder(X21115)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21115),X21114))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21115),X21113))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21115,tc_HOL_Obool)),X21114),X21113) = c_Orderings_Obot__class_Obot(tc_fun(X21115,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X21115),c_Big__Operators_Olinorder__class_OMax(X21115,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21115,tc_HOL_Obool)),X21114),X21113))),c_Big__Operators_Olinorder__class_OMax(X21115,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21115,tc_HOL_Obool)),X21114),X21113))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X21115),c_Big__Operators_Olinorder__class_OMax(X21115,X21114)),c_Big__Operators_Olinorder__class_OMax(X21115,X21113)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).

fof(i_0_7368,plain,
    ! [X21107,X21108,X21109] :
      ( ~ class_Orderings_Olinorder(X21109)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21109),X21108))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21109),X21107))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21109,tc_HOL_Obool)),X21108),X21107) = c_Orderings_Obot__class_Obot(tc_fun(X21109,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21109),c_Big__Operators_Olinorder__class_OMin(X21109,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21109,tc_HOL_Obool)),X21108),X21107))),c_Big__Operators_Olinorder__class_OMin(X21109,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21109,tc_HOL_Obool)),X21108),X21107))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21109),c_Big__Operators_Olinorder__class_OMin(X21109,X21108)),c_Big__Operators_Olinorder__class_OMin(X21109,X21107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).

fof(i_0_7369,plain,
    ! [X32396,X32397,X32400,X32401,X32402] :
      ( ( X32396 = hAPP(hAPP(c_List_Olist_OCons(X32397),esk450_2(X32396,X32397)),esk449_2(X32396,X32397))
        | X32396 = c_List_Olist_ONil(X32397)
        | ~ c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32397),X32400),hAPP(c_List_Oset(X32397),esk449_2(X32396,X32397))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32397),esk450_2(X32396,X32397)),X32400))
        | X32396 = c_List_Olist_ONil(X32397)
        | ~ c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) )
      & ( c_List_Olinorder__class_Osorted(X32397,esk449_2(X32396,X32397))
        | X32396 = c_List_Olist_ONil(X32397)
        | ~ c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) )
      & ( X32396 != c_List_Olist_ONil(X32397)
        | c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) )
      & ( hBOOL(hAPP(hAPP(c_member(X32397),esk451_4(X32396,X32397,X32401,X32402)),hAPP(c_List_Oset(X32397),X32401)))
        | X32396 != hAPP(hAPP(c_List_Olist_OCons(X32397),X32402),X32401)
        | ~ c_List_Olinorder__class_Osorted(X32397,X32401)
        | c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32397),X32402),esk451_4(X32396,X32397,X32401,X32402)))
        | X32396 != hAPP(hAPP(c_List_Olist_OCons(X32397),X32402),X32401)
        | ~ c_List_Olinorder__class_Osorted(X32397,X32401)
        | c_List_Olinorder__class_Osorted(X32397,X32396)
        | ~ class_Orderings_Olinorder(X32397) ) ),
    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_sorted_Osimps])])])])])]) ).

fof(i_0_7370,plain,
    ! [X27437,X27438,X27439,X27440,X27441,X27442,X27443] :
      ( ( hAPP(X27440,X27438) != hAPP(X27440,X27437)
        | X27438 = X27437
        | ~ hBOOL(hAPP(hAPP(c_member(X27442),X27437),X27439))
        | ~ hBOOL(hAPP(hAPP(c_member(X27442),X27438),X27439))
        | ~ c_Typedef_Otype__definition(X27443,X27442,X27441,X27440,X27439) )
      & ( X27438 != X27437
        | hAPP(X27440,X27438) = hAPP(X27440,X27437)
        | ~ hBOOL(hAPP(hAPP(c_member(X27442),X27437),X27439))
        | ~ hBOOL(hAPP(hAPP(c_member(X27442),X27438),X27439))
        | ~ c_Typedef_Otype__definition(X27443,X27442,X27441,X27440,X27439) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).

fof(i_0_7371,plain,
    ! [X32808,X32809] :
      ( ( ~ c_Wellfounded_Oacyclic(X32809,hAPP(c_Set_OCollect(tc_prod(X32809,X32809)),hAPP(c_Product__Type_Oprod_Oprod__case(X32809,X32809,tc_HOL_Obool),c_Predicate_Oconversep(X32809,X32809,X32808))))
        | c_Wellfounded_Oacyclic(X32809,hAPP(c_Set_OCollect(tc_prod(X32809,X32809)),hAPP(c_Product__Type_Oprod_Oprod__case(X32809,X32809,tc_HOL_Obool),X32808))) )
      & ( ~ c_Wellfounded_Oacyclic(X32809,hAPP(c_Set_OCollect(tc_prod(X32809,X32809)),hAPP(c_Product__Type_Oprod_Oprod__case(X32809,X32809,tc_HOL_Obool),X32808)))
        | c_Wellfounded_Oacyclic(X32809,hAPP(c_Set_OCollect(tc_prod(X32809,X32809)),hAPP(c_Product__Type_Oprod_Oprod__case(X32809,X32809,tc_HOL_Obool),c_Predicate_Oconversep(X32809,X32809,X32808)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])]) ).

cnf(i_0_7372,plain,
    ( hAPP(c_List_OremoveAll(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(c_List_OremoveAll(X3,X1),X4)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_5510]) ).

fof(i_0_7373,plain,
    ! [X27240,X27241,X27242,X27243] : hAPP(c_Relation_OField(X27243),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27243,X27243)),hAPP(hAPP(c_Product__Type_OPair(X27243,X27243),X27242),X27241)),X27240)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27243,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27243),X27242),hAPP(hAPP(c_Set_Oinsert(X27243),X27241),c_Orderings_Obot__class_Obot(tc_fun(X27243,tc_HOL_Obool))))),hAPP(c_Relation_OField(X27243),X27240)),
    inference(variable_rename,[status(thm)],[fact_Field__insert]) ).

fof(i_0_7374,plain,
    ! [X30815,X30816,X30817] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30817),X30816))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30817),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30816),X30815))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])]) ).

cnf(i_0_7375,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5574]) ).

fof(i_0_7376,plain,
    ! [X33060,X33061,X33062,X33063,X33064,X33065] : c_Nitpick_Opair__box_Opair__box__size(X33065,X33064,X33063,X33062,c_Nitpick_Opair__box_OPairBox(X33065,X33064,X33061,X33060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33063,X33061)),hAPP(X33062,X33060))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I1_J]) ).

fof(i_0_7377,plain,
    ! [X25226,X25227,X25228] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk230_3(X25226,X25227,X25228)),X25227))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk229_3(X25226,X25227,X25228)),X25227))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk231_3(X25226,X25227,X25228)),X25227))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk229_3(X25226,X25227,X25228)),X25227))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( esk230_3(X25226,X25227,X25228) != esk231_3(X25226,X25227,X25228)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk229_3(X25226,X25227,X25228)),X25227))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25228,tc_HOL_Obool)),esk230_3(X25226,X25227,X25228)),esk231_3(X25226,X25227,X25228)) != c_Orderings_Obot__class_Obot(tc_fun(X25228,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk229_3(X25226,X25227,X25228)),X25227))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk230_3(X25226,X25227,X25228)),X25227))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hAPP(c_Finite__Set_Ocard(X25228),esk229_3(X25226,X25227,X25228)) != X25226
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25228,tc_HOL_Obool)),esk231_3(X25226,X25227,X25228)),X25227))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hAPP(c_Finite__Set_Ocard(X25228),esk229_3(X25226,X25227,X25228)) != X25226
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( esk230_3(X25226,X25227,X25228) != esk231_3(X25226,X25227,X25228)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hAPP(c_Finite__Set_Ocard(X25228),esk229_3(X25226,X25227,X25228)) != X25226
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25228,tc_HOL_Obool)),esk230_3(X25226,X25227,X25228)),esk231_3(X25226,X25227,X25228)) != c_Orderings_Obot__class_Obot(tc_fun(X25228,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25226),hAPP(c_Finite__Set_Ocard(tc_fun(X25228,tc_HOL_Obool)),X25227)) = hAPP(c_Finite__Set_Ocard(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227))
        | hAPP(c_Finite__Set_Ocard(X25228),esk229_3(X25226,X25227,X25228)) != X25226
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25228),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25228,tc_HOL_Obool),X25227)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25228,tc_HOL_Obool)),X25227)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__partition])])])]) ).

fof(i_0_7378,plain,
    ! [X33733,X33734,X33735] :
      ( ~ c_Fun_Obij__betw(X33735,X33734,X33733,c_Orderings_Otop__class_Otop(tc_fun(X33735,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33734,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33735,X33734,X33733),c_Orderings_Otop__class_Otop(tc_fun(X33735,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33734,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__is__surj])]) ).

fof(i_0_7379,plain,
    ! [X32078,X32079,X32080] :
      ( ~ class_Orderings_Olinorder(X32080)
      | c_List_Olinorder__class_Osorted(X32080,hAPP(c_List_Ofilter(X32080,hAPP(hAPP(c_COMBC(X32080,X32080,tc_HOL_Obool),c_fequal),hAPP(X32079,X32078))),X32078)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).

fof(i_0_7380,plain,
    ! [X28470,X28471,X28472,X28473,X28474] :
      ( ~ c_Fun_Oinj__on(X28474,X28473,X28472,c_Orderings_Otop__class_Otop(tc_fun(X28474,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X28471,X28474,X28470,c_Orderings_Otop__class_Otop(tc_fun(X28471,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X28471,X28473,hAPP(c_Fun_Ocomp(X28474,X28473,X28471,X28472),X28470),c_Orderings_Otop__class_Otop(tc_fun(X28471,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).

fof(i_0_7381,plain,
    ! [X30078,X30079,X30080,X30081] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30081,tc_HOL_Obool)),hAPP(c_List_Oset(X30081),hAPP(hAPP(c_List_Olist__update(X30081,X30080),X30079),X30078))),hAPP(hAPP(c_Set_Oinsert(X30081),X30078),hAPP(c_List_Oset(X30081),X30080)))),
    inference(variable_rename,[status(thm)],[fact_set__update__subset__insert]) ).

cnf(i_0_7382,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2),
    inference(split_conjunct,[status(thm)],[i_0_5575]) ).

fof(i_0_7383,plain,
    ! [X19199,X19200,X19201] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19201,tc_HOL_Obool)),X19200),hAPP(hAPP(c_Set_Oinsert(X19201),X19199),c_Orderings_Obot__class_Obot(tc_fun(X19201,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19201,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X19201,c_Orderings_Oord__class_Omin(X19201),X19200) = X19199
        | ~ hBOOL(hAPP(hAPP(c_member(X19201),X19199),X19200))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19201),X19200))
        | ~ class_Orderings_Olinorder(X19201) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19201,tc_HOL_Obool)),X19200),hAPP(hAPP(c_Set_Oinsert(X19201),X19199),c_Orderings_Obot__class_Obot(tc_fun(X19201,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19201,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X19201,c_Orderings_Oord__class_Omin(X19201),X19200) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19201),X19199),c_Big__Operators_Olattice_OInf__fin(X19201,c_Orderings_Oord__class_Omin(X19201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19201,tc_HOL_Obool)),X19200),hAPP(hAPP(c_Set_Oinsert(X19201),X19199),c_Orderings_Obot__class_Obot(tc_fun(X19201,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X19201),X19199),X19200))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19201),X19200))
        | ~ class_Orderings_Olinorder(X19201) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove])])]) ).

fof(i_0_7384,plain,
    ! [X19196,X19197,X19198] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19198,tc_HOL_Obool)),X19197),hAPP(hAPP(c_Set_Oinsert(X19198),X19196),c_Orderings_Obot__class_Obot(tc_fun(X19198,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19198,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X19198,c_Orderings_Oord__class_Omax(X19198),X19197) = X19196
        | ~ hBOOL(hAPP(hAPP(c_member(X19198),X19196),X19197))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19198),X19197))
        | ~ class_Orderings_Olinorder(X19198) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19198,tc_HOL_Obool)),X19197),hAPP(hAPP(c_Set_Oinsert(X19198),X19196),c_Orderings_Obot__class_Obot(tc_fun(X19198,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19198,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X19198,c_Orderings_Oord__class_Omax(X19198),X19197) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19198),X19196),c_Big__Operators_Olattice_OSup__fin(X19198,c_Orderings_Oord__class_Omax(X19198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19198,tc_HOL_Obool)),X19197),hAPP(hAPP(c_Set_Oinsert(X19198),X19196),c_Orderings_Obot__class_Obot(tc_fun(X19198,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X19198),X19196),X19197))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19198),X19197))
        | ~ class_Orderings_Olinorder(X19198) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove])])]) ).

fof(i_0_7385,plain,
    ! [X23737,X23738,X23739] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23739,tc_Nat_Onat),X23738),X23737) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23739,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X23739),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23738)),X23737)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(i_0_7386,plain,
    ! [X23730,X23731,X23732] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23732,tc_Nat_Onat),X23731),X23730) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23732,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X23732),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23731)),X23730)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(i_0_7387,plain,
    ! [X20932,X20933,X20934,X20935,X20936] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20936),X20935),hAPP(c_Set_Ovimage(X20936,X20934,X20933),hAPP(hAPP(c_Set_Oinsert(X20934),X20932),c_Orderings_Obot__class_Obot(tc_fun(X20934,tc_HOL_Obool))))))
        | hAPP(X20933,X20935) = X20932 )
      & ( hAPP(X20933,X20935) != X20932
        | hBOOL(hAPP(hAPP(c_member(X20936),X20935),hAPP(c_Set_Ovimage(X20936,X20934,X20933),hAPP(hAPP(c_Set_Oinsert(X20934),X20932),c_Orderings_Obot__class_Obot(tc_fun(X20934,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])]) ).

cnf(i_0_7388,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5576]) ).

fof(i_0_7389,plain,
    ! [X28464,X28465,X28466,X28467,X28468,X28469] :
      ( ~ c_Fun_Oinj__on(X28469,X28468,hAPP(c_Fun_Ocomp(X28467,X28468,X28469,X28466),X28465),X28464)
      | c_Fun_Oinj__on(X28469,X28467,X28465,X28464) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2])]) ).

cnf(i_0_7390,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_Osucc(X2))),
    inference(split_conjunct,[status(thm)],[i_0_5577]) ).

fof(i_0_7391,plain,
    ! [X17364,X17365,X17366,X17367] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17367,tc_HOL_Obool)),X17366),hAPP(hAPP(c_Set_Oinsert(X17367),X17365),X17364))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17367,tc_HOL_Obool)),X17366),X17364))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17367,tc_HOL_Obool)),X17366),X17364)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17367,tc_HOL_Obool)),X17366),hAPP(hAPP(c_Set_Oinsert(X17367),X17365),X17364)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).

fof(i_0_7392,plain,
    ! [X25351,X25352,X25353] : hAPP(hAPP(c_Set_Oinsert(X25353),X25352),X25351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25353,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25353),hAPP(hAPP(c_COMBC(X25353,X25353,tc_HOL_Obool),c_fequal),X25352))),X25351),
    inference(variable_rename,[status(thm)],[fact_insert__def]) ).

cnf(i_0_7393,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5578]) ).

cnf(i_0_7394,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5579]) ).

cnf(i_0_7395,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5580]) ).

cnf(i_0_7396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5581]) ).

cnf(i_0_7397,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5515]) ).

cnf(i_0_7398,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5516]) ).

cnf(i_0_7399,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5517]) ).

cnf(i_0_7400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5518]) ).

fof(i_0_7401,plain,
    ! [X18545,X18546,X18547,X18548,X18549,X18550] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),X18549),X18548)),X18547) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),X18546),X18548)),X18545)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18550),X18549),X18546)),X18548)),X18547) = X18545
        | ~ class_Rings_Oring(X18550) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18550),X18549),X18546)),X18548)),X18547) != X18545
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),X18549),X18548)),X18547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18550),X18546),X18548)),X18545)
        | ~ class_Rings_Oring(X18550) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).

fof(i_0_7402,plain,
    ! [X18539,X18540,X18541,X18542,X18543,X18544] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),X18543),X18542)),X18541) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),X18540),X18542)),X18539)
        | X18541 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18544),X18540),X18543)),X18542)),X18539)
        | ~ class_Rings_Oring(X18544) )
      & ( X18541 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18544),X18540),X18543)),X18542)),X18539)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),X18543),X18542)),X18541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18544),X18540),X18542)),X18539)
        | ~ class_Rings_Oring(X18544) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).

fof(i_0_7403,plain,
    ! [X29190,X29191,X29192,X29193,X29194,X29195] :
      ( ~ c_Relation_Osingle__valued(X29195,X29194,hAPP(c_Relation_Oconverse(X29194,X29195),X29193))
      | X29192 = c_Orderings_Obot__class_Obot(tc_fun(X29191,tc_HOL_Obool))
      | hAPP(c_Relation_OImage(X29194,X29195,X29193),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29191,tc_fun(X29194,tc_HOL_Obool)),X29192),X29190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29191,tc_fun(X29195,tc_HOL_Obool)),X29192),hAPP(hAPP(c_COMBB(tc_fun(X29194,tc_HOL_Obool),tc_fun(X29195,tc_HOL_Obool),X29191),c_Relation_OImage(X29194,X29195,X29193)),X29190)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).

fof(i_0_7404,plain,
    ! [X31823,X31824,X31825] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X31825),tc_List_Olist(X31825)),c_List_Opartition(X31825,X31824,X31823)) = hAPP(c_List_Ofilter(X31825,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31825,c_fNot),X31824)),X31823),
    inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).

cnf(i_0_7405,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5582]) ).

fof(i_0_7406,plain,
    ! [X33562,X33563,X33564,X33565,X33566] :
      ( ~ c_Fun_Oinj__on(X33566,X33565,X33564,X33563)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33566,tc_HOL_Obool)),X33562),X33563))
      | hAPP(c_Set_Oimage(X33565,X33566,c_Hilbert__Choice_Oinv__into(X33566,X33565,X33563,X33564)),hAPP(c_Set_Oimage(X33566,X33565,X33564),X33562)) = X33562 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_7407,plain,
    ! [X20736,X20737,X20738,X20739,X20740] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20740,tc_HOL_Obool)),X20739),X20738))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20737,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20737,X20740,X20736),X20739)),hAPP(c_Set_Ovimage(X20737,X20740,X20736),X20738))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).

fof(i_0_7408,plain,
    ! [X17815,X17816,X17817,X17818,X17819] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17819,tc_HOL_Obool)),X17818),X17817))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17816,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17819,X17816,X17815),X17818)),hAPP(c_Set_Oimage(X17819,X17816,X17815),X17817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_7409,plain,
    ! [X25845,X25846,X25847,X25848,X25849,X25850] :
      ( ~ c_Equiv__Relations_Oequiv(X25850,X25849,X25848)
      | ~ c_Equiv__Relations_Ocongruent(X25850,tc_fun(X25847,tc_HOL_Obool),X25848,X25846)
      | ~ hBOOL(hAPP(hAPP(c_member(X25850),X25845),X25849))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25850,tc_fun(X25847,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25850,X25850,X25848),hAPP(hAPP(c_Set_Oinsert(X25850),X25845),c_Orderings_Obot__class_Obot(tc_fun(X25850,tc_HOL_Obool))))),X25846) = hAPP(X25846,X25845) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).

fof(i_0_7410,plain,
    ! [X19253,X19254,X19255] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19255,tc_HOL_Obool)),X19254),hAPP(hAPP(c_Set_Oinsert(X19255),X19253),c_Orderings_Obot__class_Obot(tc_fun(X19255,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19255,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X19255,c_Orderings_Oord__class_Omin(X19255),hAPP(hAPP(c_Set_Oinsert(X19255),X19253),X19254)) = X19253
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19255),X19254))
        | ~ class_Orderings_Olinorder(X19255) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19255,tc_HOL_Obool)),X19254),hAPP(hAPP(c_Set_Oinsert(X19255),X19253),c_Orderings_Obot__class_Obot(tc_fun(X19255,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19255,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X19255,c_Orderings_Oord__class_Omin(X19255),hAPP(hAPP(c_Set_Oinsert(X19255),X19253),X19254)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19255),X19253),c_Big__Operators_Olattice_OInf__fin(X19255,c_Orderings_Oord__class_Omin(X19255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19255,tc_HOL_Obool)),X19254),hAPP(hAPP(c_Set_Oinsert(X19255),X19253),c_Orderings_Obot__class_Obot(tc_fun(X19255,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19255),X19254))
        | ~ class_Orderings_Olinorder(X19255) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])]) ).

fof(i_0_7411,plain,
    ! [X19256,X19257,X19258] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19258,tc_HOL_Obool)),X19257),hAPP(hAPP(c_Set_Oinsert(X19258),X19256),c_Orderings_Obot__class_Obot(tc_fun(X19258,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19258,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X19258,c_Orderings_Oord__class_Omax(X19258),hAPP(hAPP(c_Set_Oinsert(X19258),X19256),X19257)) = X19256
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19258),X19257))
        | ~ class_Orderings_Olinorder(X19258) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19258,tc_HOL_Obool)),X19257),hAPP(hAPP(c_Set_Oinsert(X19258),X19256),c_Orderings_Obot__class_Obot(tc_fun(X19258,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19258,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X19258,c_Orderings_Oord__class_Omax(X19258),hAPP(hAPP(c_Set_Oinsert(X19258),X19256),X19257)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19258),X19256),c_Big__Operators_Olattice_OSup__fin(X19258,c_Orderings_Oord__class_Omax(X19258),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19258,tc_HOL_Obool)),X19257),hAPP(hAPP(c_Set_Oinsert(X19258),X19256),c_Orderings_Obot__class_Obot(tc_fun(X19258,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19258),X19257))
        | ~ class_Orderings_Olinorder(X19258) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])]) ).

fof(i_0_7412,plain,
    ! [X28398,X28399,X28400,X28401,X28402,X28403,X28404,X28405,X28406,X28407,X28408] :
      ( hAPP(X28408,hAPP(X28407,X28406)) != hAPP(X28405,hAPP(X28404,X28403))
      | hAPP(hAPP(c_Fun_Ocomp(X28402,X28401,X28400,X28408),X28407),X28406) = hAPP(hAPP(c_Fun_Ocomp(X28399,X28401,X28398,X28405),X28404),X28403) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).

cnf(i_0_7413,plain,
    ( c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = c_List_OdropWhile(X3,X1,X4)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5583]) ).

fof(i_0_7414,plain,
    ! [X33472,X33473,X33474] :
      ( ~ c_Fun_Oinj__on(X33474,X33473,X33472,c_Orderings_Otop__class_Otop(tc_fun(X33474,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33473,X33474,X33474,c_Hilbert__Choice_Oinv__into(X33474,X33473,c_Orderings_Otop__class_Otop(tc_fun(X33474,tc_HOL_Obool)),X33472)),X33472) = c_Fun_Oid(X33474) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__o__cancel])]) ).

fof(i_0_7415,plain,
    ! [X33736,X33737,X33738,X33739] :
      ( ~ c_Fun_Obij__betw(X33739,X33738,X33737,X33736,c_Orderings_Otop__class_Otop(tc_fun(X33738,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33739,X33738,X33737),c_Orderings_Otop__class_Otop(tc_fun(X33739,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33738,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__surj])]) ).

fof(i_0_7416,plain,
    ! [X17267,X17268,X17269,X17270,X17271] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17271,tc_HOL_Obool)),X17268),hAPP(hAPP(c_Set_Oinsert(X17271),X17267),c_Orderings_Obot__class_Obot(tc_fun(X17271,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X17271,tc_HOL_Obool))
        | hAPP(X17269,X17268) = X17267
        | ~ hBOOL(hAPP(hAPP(c_member(X17271),X17267),X17268))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17271),X17268))
        | ~ c_Finite__Set_Ofolding__one(X17271,X17270,X17269) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17271,tc_HOL_Obool)),X17268),hAPP(hAPP(c_Set_Oinsert(X17271),X17267),c_Orderings_Obot__class_Obot(tc_fun(X17271,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X17271,tc_HOL_Obool))
        | hAPP(X17269,X17268) = hAPP(hAPP(X17270,X17267),hAPP(X17269,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17271,tc_HOL_Obool)),X17268),hAPP(hAPP(c_Set_Oinsert(X17271),X17267),c_Orderings_Obot__class_Obot(tc_fun(X17271,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X17271),X17267),X17268))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17271),X17268))
        | ~ c_Finite__Set_Ofolding__one(X17271,X17270,X17269) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).

fof(i_0_7417,plain,
    ! [X21027,X21028,X21029] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21029),X21028))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21029),X21027))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21029),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21029,tc_HOL_Obool)),X21028),X21027))),hAPP(c_Finite__Set_Ocard(X21029),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21029,tc_HOL_Obool)),X21028),X21027))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21029),X21028)),hAPP(c_Finite__Set_Ocard(X21029),X21027)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).

fof(i_0_7418,plain,
    ! [X21030,X21031,X21032] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21032),X21031))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21032),X21030))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21032),X21031)),hAPP(c_Finite__Set_Ocard(X21032),X21030)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21032),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21032,tc_HOL_Obool)),X21031),X21030))),hAPP(c_Finite__Set_Ocard(X21032),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21032,tc_HOL_Obool)),X21031),X21030))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).

fof(i_0_7419,plain,
    ! [X27618,X27619,X27620,X27621] :
      ( ( hBOOL(hAPP(X27621,esk293_4(X27618,X27619,X27620,X27621)))
        | c_Wellfounded_Owf(tc_prod(X27618,X27620),c_Recdef_Osame__fst(X27618,X27620,X27621,X27619)) )
      & ( ~ c_Wellfounded_Owf(X27620,hAPP(X27619,esk293_4(X27618,X27619,X27620,X27621)))
        | c_Wellfounded_Owf(tc_prod(X27618,X27620),c_Recdef_Osame__fst(X27618,X27620,X27621,X27619)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__same__fst])])])]) ).

fof(i_0_7420,plain,
    ! [X26766,X26767,X26768,X26769,X26770] :
      ( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X26770,X26769,X26768),X26767),X26766))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26770,X26769)),hAPP(hAPP(c_Product__Type_OPair(X26770,X26769),X26767),X26766)),X26768)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26770,X26769)),hAPP(hAPP(c_Product__Type_OPair(X26770,X26769),X26767),X26766)),X26768))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X26770,X26769,X26768),X26767),X26766)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

fof(i_0_7421,plain,
    ! [X33749,X33750,X33751,X33752,X33753] :
      ( ~ c_Fun_Obij__betw(X33753,X33752,X33751,X33750,X33749)
      | c_Fun_Oinj__on(X33753,X33752,X33751,X33750) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__inj__on])]) ).

fof(i_0_7422,plain,
    ! [X33740,X33741,X33742,X33743,X33744] :
      ( ( c_Fun_Oinj__on(X33744,X33743,X33742,X33741)
        | ~ c_Fun_Obij__betw(X33744,X33743,X33742,X33741,X33740) )
      & ( hAPP(c_Set_Oimage(X33744,X33743,X33742),X33741) = X33740
        | ~ c_Fun_Obij__betw(X33744,X33743,X33742,X33741,X33740) )
      & ( ~ c_Fun_Oinj__on(X33744,X33743,X33742,X33741)
        | hAPP(c_Set_Oimage(X33744,X33743,X33742),X33741) != X33740
        | c_Fun_Obij__betw(X33744,X33743,X33742,X33741,X33740) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__def])])]) ).

cnf(i_0_7423,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5584]) ).

fof(i_0_7424,plain,
    ! [X28988,X28989,X28990] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28990,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28990,X28990,X28989),X28988)),X28988))
      | hAPP(c_Relation_OImage(X28990,X28990,c_Transitive__Closure_Ortrancl(X28990,X28989)),X28988) = X28988 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).

cnf(i_0_7425,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5585]) ).

fof(i_0_7426,plain,
    ! [X29046,X29047,X29048,X29049] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29049,X29049)),hAPP(hAPP(c_Product__Type_OPair(X29049,X29049),X29048),X29047)),c_Transitive__Closure_Ortrancl(X29049,X29046)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29049),X29047),c_Wellfounded_Oacc(X29049,X29046)))
      | hBOOL(hAPP(hAPP(c_member(X29049),X29048),c_Wellfounded_Oacc(X29049,X29046))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).

fof(i_0_7427,plain,
    ! [X29042,X29043,X29044,X29045] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29045),X29044),c_Wellfounded_Oacc(X29045,X29043)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29045,X29045)),hAPP(hAPP(c_Product__Type_OPair(X29045,X29045),X29042),X29044)),c_Transitive__Closure_Ortrancl(X29045,X29043)))
      | hBOOL(hAPP(hAPP(c_member(X29045),X29042),c_Wellfounded_Oacc(X29045,X29043))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).

fof(i_0_7428,plain,
    ! [X20201,X20202,X20203,X20204] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20204),X20203))
      | ~ hBOOL(hAPP(hAPP(c_member(X20204),X20202),X20203))
      | hBOOL(hAPP(hAPP(c_member(X20204),X20202),X20201))
      | hAPP(c_Finite__Set_Ocard(X20204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20204,tc_HOL_Obool)),X20203),hAPP(hAPP(c_Set_Oinsert(X20204),X20202),X20201))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X20204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20204,tc_HOL_Obool)),X20203),X20201))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5586])]) ).

cnf(i_0_7429,plain,
    hAPP(c_List_Orev(X1),c_List_Oconcat(X1,X2)) = c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_5587]) ).

fof(i_0_7430,plain,
    ! [X21919,X21920,X21921,X21922,X21923] :
      ( ( X21923 != c_Orderings_Obot__class_Obot(tc_fun(X21922,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21922,tc_fun(X21921,tc_HOL_Obool)),X21923),hAPP(hAPP(c_COMBB(tc_fun(X21921,tc_HOL_Obool),tc_fun(X21921,tc_HOL_Obool),X21922),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21921,tc_HOL_Obool)),X21920)),X21919)) = c_Orderings_Otop__class_Otop(tc_fun(X21921,tc_HOL_Obool)) )
      & ( X21923 = c_Orderings_Obot__class_Obot(tc_fun(X21922,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21922,tc_fun(X21921,tc_HOL_Obool)),X21923),hAPP(hAPP(c_COMBB(tc_fun(X21921,tc_HOL_Obool),tc_fun(X21921,tc_HOL_Obool),X21922),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21921,tc_HOL_Obool)),X21920)),X21919)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21921,tc_HOL_Obool)),X21920),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21922,tc_fun(X21921,tc_HOL_Obool)),X21923),X21919)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).

fof(i_0_7431,plain,
    ! [X21961,X21962,X21963,X21964,X21965] :
      ( ( X21965 != c_Orderings_Obot__class_Obot(tc_fun(X21964,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21964,tc_fun(X21963,tc_HOL_Obool)),X21965),hAPP(hAPP(c_COMBB(tc_fun(X21963,tc_HOL_Obool),tc_fun(X21963,tc_HOL_Obool),X21964),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21963,tc_HOL_Obool)),X21962)),X21961)) = c_Orderings_Otop__class_Otop(tc_fun(X21963,tc_HOL_Obool)) )
      & ( X21965 = c_Orderings_Obot__class_Obot(tc_fun(X21964,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21964,tc_fun(X21963,tc_HOL_Obool)),X21965),hAPP(hAPP(c_COMBB(tc_fun(X21963,tc_HOL_Obool),tc_fun(X21963,tc_HOL_Obool),X21964),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21963,tc_HOL_Obool)),X21962)),X21961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21963,tc_HOL_Obool)),X21962),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21964,tc_fun(X21963,tc_HOL_Obool)),X21965),X21961)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).

fof(i_0_7432,plain,
    ! [X21168,X21169,X21170,X21171,X21172] :
      ( ( X21172 != c_Orderings_Obot__class_Obot(tc_fun(X21171,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21171,tc_fun(X21170,tc_HOL_Obool)),X21172),hAPP(hAPP(c_COMBB(tc_fun(X21170,tc_HOL_Obool),tc_fun(X21170,tc_HOL_Obool),X21171),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21170,tc_HOL_Obool)),X21169)),X21168)) = c_Orderings_Obot__class_Obot(tc_fun(X21170,tc_HOL_Obool)) )
      & ( X21172 = c_Orderings_Obot__class_Obot(tc_fun(X21171,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21171,tc_fun(X21170,tc_HOL_Obool)),X21172),hAPP(hAPP(c_COMBB(tc_fun(X21170,tc_HOL_Obool),tc_fun(X21170,tc_HOL_Obool),X21171),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21170,tc_HOL_Obool)),X21169)),X21168)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21170,tc_HOL_Obool)),X21169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21171,tc_fun(X21170,tc_HOL_Obool)),X21172),X21168)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).

fof(i_0_7433,plain,
    ! [X21859,X21860,X21861,X21862,X21863] :
      ( ( X21863 != c_Orderings_Obot__class_Obot(tc_fun(X21862,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21861,tc_HOL_Obool)),X21860),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21862,tc_fun(X21861,tc_HOL_Obool)),X21863),X21859)) = X21860 )
      & ( X21863 = c_Orderings_Obot__class_Obot(tc_fun(X21862,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21861,tc_HOL_Obool)),X21860),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21862,tc_fun(X21861,tc_HOL_Obool)),X21863),X21859)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21862,tc_fun(X21861,tc_HOL_Obool)),X21863),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool),X21862),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21861,tc_HOL_Obool)),X21860)),X21859)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).

fof(i_0_7434,plain,
    ! [X21421,X21422,X21423,X21424,X21425] :
      ( ( X21425 != c_Orderings_Obot__class_Obot(tc_fun(X21424,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21423,tc_HOL_Obool)),X21422),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21424,tc_fun(X21423,tc_HOL_Obool)),X21425),X21421)) = X21422 )
      & ( X21425 = c_Orderings_Obot__class_Obot(tc_fun(X21424,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21423,tc_HOL_Obool)),X21422),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21424,tc_fun(X21423,tc_HOL_Obool)),X21425),X21421)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21424,tc_fun(X21423,tc_HOL_Obool)),X21425),hAPP(hAPP(c_COMBB(tc_fun(X21423,tc_HOL_Obool),tc_fun(X21423,tc_HOL_Obool),X21424),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21423,tc_HOL_Obool)),X21422)),X21421)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).

fof(i_0_7435,plain,
    ! [X21937,X21938,X21939,X21940,X21941] :
      ( ( X21941 != c_Orderings_Obot__class_Obot(tc_fun(X21940,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21939,tc_HOL_Obool)),X21938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21940,tc_fun(X21939,tc_HOL_Obool)),X21941),X21937)) = X21938 )
      & ( X21941 = c_Orderings_Obot__class_Obot(tc_fun(X21940,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21939,tc_HOL_Obool)),X21938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21940,tc_fun(X21939,tc_HOL_Obool)),X21941),X21937)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21940,tc_fun(X21939,tc_HOL_Obool)),X21941),hAPP(hAPP(c_COMBB(tc_fun(X21939,tc_HOL_Obool),tc_fun(X21939,tc_HOL_Obool),X21940),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21939,tc_HOL_Obool)),X21938)),X21937)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).

fof(i_0_7436,plain,
    ! [X17388,X17389,X17390,X17391,X17392] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17392,tc_HOL_Obool)),X17389),hAPP(hAPP(c_Set_Oinsert(X17392),X17388),c_Orderings_Obot__class_Obot(tc_fun(X17392,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X17392,tc_HOL_Obool))
        | hAPP(X17390,hAPP(hAPP(c_Set_Oinsert(X17392),X17388),X17389)) = X17388
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17392),X17389))
        | ~ c_Finite__Set_Ofolding__one(X17392,X17391,X17390) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17392,tc_HOL_Obool)),X17389),hAPP(hAPP(c_Set_Oinsert(X17392),X17388),c_Orderings_Obot__class_Obot(tc_fun(X17392,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X17392,tc_HOL_Obool))
        | hAPP(X17390,hAPP(hAPP(c_Set_Oinsert(X17392),X17388),X17389)) = hAPP(hAPP(X17391,X17388),hAPP(X17390,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17392,tc_HOL_Obool)),X17389),hAPP(hAPP(c_Set_Oinsert(X17392),X17388),c_Orderings_Obot__class_Obot(tc_fun(X17392,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17392),X17389))
        | ~ c_Finite__Set_Ofolding__one(X17392,X17391,X17390) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).

fof(i_0_7437,plain,
    ! [X21449,X21450,X21451] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21451,tc_HOL_Obool)),X21450),hAPP(hAPP(c_Set_Oinsert(X21451),X21449),c_Orderings_Obot__class_Obot(tc_fun(X21451,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X21451,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X21451,X21450) = X21449
        | ~ hBOOL(hAPP(hAPP(c_member(X21451),X21449),X21450))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21451),X21450))
        | ~ class_Lattices_Olattice(X21451) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21451,tc_HOL_Obool)),X21450),hAPP(hAPP(c_Set_Oinsert(X21451),X21449),c_Orderings_Obot__class_Obot(tc_fun(X21451,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21451,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X21451,X21450) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21451),X21449),c_Big__Operators_Olattice__class_OInf__fin(X21451,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21451,tc_HOL_Obool)),X21450),hAPP(hAPP(c_Set_Oinsert(X21451),X21449),c_Orderings_Obot__class_Obot(tc_fun(X21451,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X21451),X21449),X21450))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21451),X21450))
        | ~ class_Lattices_Olattice(X21451) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).

fof(i_0_7438,plain,
    ! [X20312,X20313,X20314] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20314,tc_HOL_Obool)),X20313),hAPP(hAPP(c_Set_Oinsert(X20314),X20312),c_Orderings_Obot__class_Obot(tc_fun(X20314,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20314,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20314,X20313) = X20312
        | ~ hBOOL(hAPP(hAPP(c_member(X20314),X20312),X20313))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20314),X20313))
        | ~ class_Lattices_Olattice(X20314) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20314,tc_HOL_Obool)),X20313),hAPP(hAPP(c_Set_Oinsert(X20314),X20312),c_Orderings_Obot__class_Obot(tc_fun(X20314,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20314,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20314,X20313) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20314),X20312),c_Big__Operators_Olattice__class_OSup__fin(X20314,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20314,tc_HOL_Obool)),X20313),hAPP(hAPP(c_Set_Oinsert(X20314),X20312),c_Orderings_Obot__class_Obot(tc_fun(X20314,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20314),X20312),X20313))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20314),X20313))
        | ~ class_Lattices_Olattice(X20314) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).

fof(i_0_7439,plain,
    ! [X18649,X18650,X18651] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18651,tc_HOL_Obool)),X18650),hAPP(hAPP(c_Set_Oinsert(X18651),X18649),c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X18651,X18650) = X18649
        | ~ hBOOL(hAPP(hAPP(c_member(X18651),X18649),X18650))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18651),X18650))
        | ~ class_Orderings_Olinorder(X18651) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18651,tc_HOL_Obool)),X18650),hAPP(hAPP(c_Set_Oinsert(X18651),X18649),c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X18651,X18650) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18651),X18649),c_Big__Operators_Olinorder__class_OMin(X18651,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18651,tc_HOL_Obool)),X18650),hAPP(hAPP(c_Set_Oinsert(X18651),X18649),c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X18651),X18649),X18650))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18651),X18650))
        | ~ class_Orderings_Olinorder(X18651) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).

fof(i_0_7440,plain,
    ! [X18652,X18653,X18654] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18654,tc_HOL_Obool)),X18653),hAPP(hAPP(c_Set_Oinsert(X18654),X18652),c_Orderings_Obot__class_Obot(tc_fun(X18654,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X18654,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X18654,X18653) = X18652
        | ~ hBOOL(hAPP(hAPP(c_member(X18654),X18652),X18653))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18654),X18653))
        | ~ class_Orderings_Olinorder(X18654) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18654,tc_HOL_Obool)),X18653),hAPP(hAPP(c_Set_Oinsert(X18654),X18652),c_Orderings_Obot__class_Obot(tc_fun(X18654,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X18654,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X18654,X18653) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18654),X18652),c_Big__Operators_Olinorder__class_OMax(X18654,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18654,tc_HOL_Obool)),X18653),hAPP(hAPP(c_Set_Oinsert(X18654),X18652),c_Orderings_Obot__class_Obot(tc_fun(X18654,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X18654),X18652),X18653))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18654),X18653))
        | ~ class_Orderings_Olinorder(X18654) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).

fof(i_0_7441,plain,
    ! [X27457,X27458,X27459,X27460,X27461,X27462] :
      ( ~ c_Typedef_Otype__definition(X27462,X27461,X27460,X27459,X27458)
      | hBOOL(hAPP(hAPP(c_member(X27461),hAPP(X27460,X27457)),X27458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).

fof(i_0_7442,plain,
    ! [X27463,X27464,X27465,X27466,X27467,X27468] :
      ( ~ c_Typedef_Otype__definition(X27468,X27467,X27466,X27465,X27464)
      | ~ hBOOL(hAPP(hAPP(c_member(X27467),X27463),X27464))
      | hAPP(X27466,hAPP(X27465,X27463)) = X27463 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).

fof(i_0_7443,plain,
    ! [X32063,X32064,X32065,X32066,X32067] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32067,hAPP(hAPP(c_List_Omap(X32066,X32067),X32065),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32066,X32067,X32065),X32064),X32063)))
        | c_List_Olinorder__class_Osorted(X32067,hAPP(hAPP(c_List_Omap(X32066,X32067),X32065),X32063))
        | ~ class_Orderings_Olinorder(X32067) )
      & ( ~ c_List_Olinorder__class_Osorted(X32067,hAPP(hAPP(c_List_Omap(X32066,X32067),X32065),X32063))
        | c_List_Olinorder__class_Osorted(X32067,hAPP(hAPP(c_List_Omap(X32066,X32067),X32065),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32066,X32067,X32065),X32064),X32063)))
        | ~ class_Orderings_Olinorder(X32067) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).

fof(i_0_7444,plain,
    ! [X25619,X25620,X25621] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk252_3(X25619,X25620,X25621)),X25621))
        | ~ hBOOL(hAPP(X25620,X25619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25619),X25621))
        | hBOOL(hAPP(X25620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X25620,esk252_3(X25619,X25620,X25621)))
        | ~ hBOOL(hAPP(X25620,X25619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25619),X25621))
        | hBOOL(hAPP(X25620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(X25620,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk252_3(X25619,X25620,X25621)),X25621)))
        | ~ hBOOL(hAPP(X25620,X25619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25619),X25621))
        | hBOOL(hAPP(X25620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__induct__0])])])]) ).

fof(i_0_7445,plain,
    ! [X33807,X33808,X33809] :
      ( ~ c_Fun_Oinj__on(X33809,X33808,X33807,c_Orderings_Otop__class_Otop(tc_fun(X33809,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33809,X33808,X33807),c_Orderings_Otop__class_Otop(tc_fun(X33809,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33808,tc_HOL_Obool))
      | c_Fun_Obij__betw(X33809,X33808,X33807,c_Orderings_Otop__class_Otop(tc_fun(X33809,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33808,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bijI])]) ).

fof(i_0_7446,plain,
    ! [X24787,X24788,X24789] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24789),X24788)),X24787) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24789),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24788),X24787))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24789),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24788,X24787))),X24787)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(i_0_7447,plain,
    ! [X24901,X24902,X24903] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24903),X24902)),X24901) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24903),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24902),X24901))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24903),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24902,X24901))),X24901)),
    inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).

fof(i_0_7448,plain,
    ! [X20225,X20226,X20227,X20228,X20229] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20228),X20227)),X20226) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20229),X20227)),X20225)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20228),X20229)),X20227)),X20226) = X20225
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20229),X20228)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20228),X20229)),X20227)),X20226) != X20225
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20228),X20227)),X20226) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20229),X20227)),X20225)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20229),X20228)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).

fof(i_0_7449,plain,
    ! [X20240,X20241,X20242,X20243,X20244] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20244),X20242)),X20241) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20243),X20242)),X20240)
        | X20241 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20243),X20244)),X20242)),X20240)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20244),X20243)) )
      & ( X20241 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20243),X20244)),X20242)),X20240)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20244),X20242)),X20241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20243),X20242)),X20240)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20244),X20243)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).

fof(i_0_7450,plain,
    ! [X19319,X19320,X19321,X19322,X19323,X19324] :
      ( ~ class_Groups_Oab__semigroup__mult(X19324)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19323),X19322))
      | hBOOL(hAPP(hAPP(c_member(X19323),X19321),X19322))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19324,X19323,c_Groups_Otimes__class_Otimes(X19324)),X19320),X19319),hAPP(hAPP(c_Set_Oinsert(X19323),X19321),X19322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19324),hAPP(X19320,X19321)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19324,X19323,c_Groups_Otimes__class_Otimes(X19324)),X19320),X19319),X19322)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5588])]) ).

cnf(i_0_7451,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Oconcat(X1,X3)) = c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_5589]) ).

fof(i_0_7452,plain,
    ! [X20897,X20898,X20899,X20900] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20900,tc_HOL_Obool)),X20899),X20898)),X20897) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20900,tc_HOL_Obool)),X20899),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20900,tc_HOL_Obool)),X20898),X20897))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20900,tc_HOL_Obool)),X20897),X20899)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20900,tc_HOL_Obool)),X20897),X20899))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20900,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20900,tc_HOL_Obool)),X20899),X20898)),X20897) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20900,tc_HOL_Obool)),X20899),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20900,tc_HOL_Obool)),X20898),X20897)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).

fof(i_0_7453,plain,
    ! [X21708,X21709,X21710,X21711,X21712] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21712,tc_fun(X21711,tc_HOL_Obool)),X21710),hAPP(hAPP(c_COMBB(tc_fun(X21711,tc_HOL_Obool),tc_fun(X21711,tc_HOL_Obool),X21712),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21711,tc_HOL_Obool)),X21709)),X21708)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21711,tc_HOL_Obool)),X21709),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21712,tc_fun(X21711,tc_HOL_Obool)),X21710),X21708)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(i_0_7454,plain,
    ! [X21314,X21315,X21316,X21317,X21318] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21318,tc_fun(X21317,tc_HOL_Obool)),X21316),hAPP(hAPP(c_COMBB(tc_fun(X21317,tc_HOL_Obool),tc_fun(X21317,tc_HOL_Obool),X21318),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21317,tc_HOL_Obool)),X21315)),X21314)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21317,tc_HOL_Obool)),X21315),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21318,tc_fun(X21317,tc_HOL_Obool)),X21316),X21314)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(i_0_7455,plain,
    ! [X21875,X21876,X21877,X21878,X21879] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21879,tc_fun(X21878,tc_HOL_Obool)),X21877),hAPP(hAPP(c_COMBB(tc_fun(X21878,tc_HOL_Obool),tc_fun(X21878,tc_HOL_Obool),X21879),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21878,tc_HOL_Obool)),X21876)),X21875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21878,tc_HOL_Obool)),X21876),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21879,tc_fun(X21878,tc_HOL_Obool)),X21877),X21875)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(i_0_7456,plain,
    ! [X21329,X21330,X21331,X21332,X21333] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21333,tc_HOL_Obool)),X21332),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21331,tc_fun(X21333,tc_HOL_Obool)),X21330),X21329)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21331,tc_fun(X21333,tc_HOL_Obool)),X21330),hAPP(hAPP(c_COMBB(tc_fun(X21333,tc_HOL_Obool),tc_fun(X21333,tc_HOL_Obool),X21331),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21333,tc_HOL_Obool)),X21332)),X21329)),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).

fof(i_0_7457,plain,
    ! [X21324,X21325,X21326,X21327,X21328] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21328,tc_HOL_Obool)),X21327),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21326,tc_fun(X21328,tc_HOL_Obool)),X21325),X21324)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21326,tc_fun(X21328,tc_HOL_Obool)),X21325),hAPP(hAPP(c_COMBB(tc_fun(X21328,tc_HOL_Obool),tc_fun(X21328,tc_HOL_Obool),X21326),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21328,tc_HOL_Obool)),X21327)),X21324)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(i_0_7458,plain,
    ! [X21698,X21699,X21700,X21701,X21702] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21702,tc_HOL_Obool)),X21701),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21700,tc_fun(X21702,tc_HOL_Obool)),X21699),X21698)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21700,tc_fun(X21702,tc_HOL_Obool)),X21699),hAPP(hAPP(c_COMBB(tc_fun(X21702,tc_HOL_Obool),tc_fun(X21702,tc_HOL_Obool),X21700),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21702,tc_HOL_Obool)),X21701)),X21698)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(i_0_7459,plain,
    ! [X21693,X21694,X21695,X21696,X21697] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21697,tc_HOL_Obool)),X21696),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21695,tc_fun(X21697,tc_HOL_Obool)),X21694),X21693)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21695,tc_fun(X21697,tc_HOL_Obool)),X21694),hAPP(hAPP(c_COMBB(tc_fun(X21697,tc_HOL_Obool),tc_fun(X21697,tc_HOL_Obool),X21695),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21697,tc_HOL_Obool)),X21696)),X21693)),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).

fof(i_0_7460,plain,
    ! [X21880,X21881,X21882,X21883,X21884] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21884,tc_HOL_Obool)),X21883),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21882,tc_fun(X21884,tc_HOL_Obool)),X21881),X21880)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21882,tc_fun(X21884,tc_HOL_Obool)),X21881),hAPP(hAPP(c_COMBB(tc_fun(X21884,tc_HOL_Obool),tc_fun(X21884,tc_HOL_Obool),X21882),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21884,tc_HOL_Obool)),X21883)),X21880)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(i_0_7461,plain,
    ! [X27402,X27403,X27404,X27405] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27405,X27405,X27405),X27404),X27403) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27405,X27405),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27405,X27405,X27405),X27404),X27402) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27405,X27405),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27405,X27405,X27405),X27404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27405,X27405),tc_HOL_Obool)),X27403),X27402)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27405,X27405),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR])]) ).

cnf(i_0_7462,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5541]) ).

cnf(i_0_7463,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5542]) ).

fof(i_0_7464,plain,
    ! [X33775,X33776,X33777,X33778,X33779] :
      ( ( ~ c_Fun_Obij__betw(X33778,X33776,X33779,X33777,X33775)
        | hAPP(c_Finite__Set_Ocard(X33778),X33777) = hAPP(c_Finite__Set_Ocard(X33776),X33775)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33776),X33775))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33778),X33777)) )
      & ( hAPP(c_Finite__Set_Ocard(X33778),X33777) != hAPP(c_Finite__Set_Ocard(X33776),X33775)
        | c_Fun_Obij__betw(X33778,X33776,esk537_4(X33775,X33776,X33777,X33778),X33777,X33775)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33776),X33775))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33778),X33777)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BIJ])])])])]) ).

fof(i_0_7465,plain,
    ! [X27432,X27433,X27434,X27435,X27436] :
      ( ~ c_Typedef_Otype__definition(X27436,X27435,X27434,X27433,X27432)
      | hAPP(c_Set_Oimage(X27436,X27435,X27434),c_Orderings_Otop__class_Otop(tc_fun(X27436,tc_HOL_Obool))) = X27432 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).

fof(i_0_7466,plain,
    ! [X25493,X25494,X25495] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X25495),hAPP(hAPP(c_Set_Oinsert(X25495),X25494),c_Orderings_Obot__class_Obot(tc_fun(X25495,tc_HOL_Obool)))),X25493) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X25495,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25495,X25495,X25493),hAPP(hAPP(c_Set_Oinsert(X25495),X25494),c_Orderings_Obot__class_Obot(tc_fun(X25495,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25495,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).

fof(i_0_7467,plain,
    ! [X26425,X26426,X26427,X26428,X26429,X26430] :
      ( ~ c_Equiv__Relations_Ocongruent(X26430,X26429,X26428,X26427)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26430,X26430)),hAPP(hAPP(c_Product__Type_OPair(X26430,X26430),X26426),X26425)),X26428))
      | hAPP(X26427,X26426) = hAPP(X26427,X26425) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).

fof(i_0_7468,plain,
    ! [X28973,X28974,X28975] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28975,X28975),tc_HOL_Obool)),X28974),c_Transitive__Closure_Ortrancl(X28975,X28973)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28975,X28975),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28975,X28974)),c_Transitive__Closure_Ortrancl(X28975,X28973))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).

cnf(i_0_7469,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5533]) ).

cnf(i_0_7470,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5529]) ).

fof(i_0_7471,plain,
    ! [X29307,X29308,X29309,X29310] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29310,X29310)),X29309),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29310,X29310),tc_HOL_Obool),X29308),X29307)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29310,X29310)),X29309),c_Transitive__Closure_Ortrancl(X29310,X29307))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).

fof(i_0_7472,plain,
    ! [X27417,X27418,X27419,X27420] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27420),X27419),c_Wellfounded_Oacc(X27420,X27418)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27420,X27420)),hAPP(hAPP(c_Product__Type_OPair(X27420,X27420),X27417),X27419)),X27418))
      | hBOOL(hAPP(hAPP(c_member(X27420),X27417),c_Wellfounded_Oacc(X27420,X27418))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).

fof(i_0_7473,plain,
    ! [X32452,X32453,X32454] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32454,X32454)),hAPP(hAPP(c_Product__Type_OPair(X32454,X32454),X32453),X32452)),c_List_Omeasures(X32454,c_List_Olist_ONil(tc_fun(X32454,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[i_0_5590]) ).

fof(i_0_7474,plain,
    ! [X22003,X22004,X22005] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22005,tc_HOL_Obool)),X22004),hAPP(hAPP(c_Set_Oinsert(X22005),X22003),c_Orderings_Obot__class_Obot(tc_fun(X22005,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X22005,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X22005,hAPP(hAPP(c_Set_Oinsert(X22005),X22003),X22004)) = X22003
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22005),X22004))
        | ~ class_Lattices_Olattice(X22005) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22005,tc_HOL_Obool)),X22004),hAPP(hAPP(c_Set_Oinsert(X22005),X22003),c_Orderings_Obot__class_Obot(tc_fun(X22005,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X22005,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X22005,hAPP(hAPP(c_Set_Oinsert(X22005),X22003),X22004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22005),X22003),c_Big__Operators_Olattice__class_OInf__fin(X22005,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22005,tc_HOL_Obool)),X22004),hAPP(hAPP(c_Set_Oinsert(X22005),X22003),c_Orderings_Obot__class_Obot(tc_fun(X22005,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22005),X22004))
        | ~ class_Lattices_Olattice(X22005) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).

fof(i_0_7475,plain,
    ! [X20357,X20358,X20359] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20359,tc_HOL_Obool)),X20358),hAPP(hAPP(c_Set_Oinsert(X20359),X20357),c_Orderings_Obot__class_Obot(tc_fun(X20359,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20359,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20359,hAPP(hAPP(c_Set_Oinsert(X20359),X20357),X20358)) = X20357
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20359),X20358))
        | ~ class_Lattices_Olattice(X20359) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20359,tc_HOL_Obool)),X20358),hAPP(hAPP(c_Set_Oinsert(X20359),X20357),c_Orderings_Obot__class_Obot(tc_fun(X20359,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20359,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20359,hAPP(hAPP(c_Set_Oinsert(X20359),X20357),X20358)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20359),X20357),c_Big__Operators_Olattice__class_OSup__fin(X20359,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20359,tc_HOL_Obool)),X20358),hAPP(hAPP(c_Set_Oinsert(X20359),X20357),c_Orderings_Obot__class_Obot(tc_fun(X20359,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20359),X20358))
        | ~ class_Lattices_Olattice(X20359) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).

fof(i_0_7476,plain,
    ! [X19167,X19168,X19169] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19169,tc_HOL_Obool)),X19168),hAPP(hAPP(c_Set_Oinsert(X19169),X19167),c_Orderings_Obot__class_Obot(tc_fun(X19169,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19169,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X19169,hAPP(hAPP(c_Set_Oinsert(X19169),X19167),X19168)) = X19167
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19169),X19168))
        | ~ class_Orderings_Olinorder(X19169) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19169,tc_HOL_Obool)),X19168),hAPP(hAPP(c_Set_Oinsert(X19169),X19167),c_Orderings_Obot__class_Obot(tc_fun(X19169,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19169,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X19169,hAPP(hAPP(c_Set_Oinsert(X19169),X19167),X19168)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19169),X19167),c_Big__Operators_Olinorder__class_OMin(X19169,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19169,tc_HOL_Obool)),X19168),hAPP(hAPP(c_Set_Oinsert(X19169),X19167),c_Orderings_Obot__class_Obot(tc_fun(X19169,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19169),X19168))
        | ~ class_Orderings_Olinorder(X19169) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).

fof(i_0_7477,plain,
    ! [X19164,X19165,X19166] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19166,tc_HOL_Obool)),X19165),hAPP(hAPP(c_Set_Oinsert(X19166),X19164),c_Orderings_Obot__class_Obot(tc_fun(X19166,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X19166,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X19166,hAPP(hAPP(c_Set_Oinsert(X19166),X19164),X19165)) = X19164
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19166),X19165))
        | ~ class_Orderings_Olinorder(X19166) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19166,tc_HOL_Obool)),X19165),hAPP(hAPP(c_Set_Oinsert(X19166),X19164),c_Orderings_Obot__class_Obot(tc_fun(X19166,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19166,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X19166,hAPP(hAPP(c_Set_Oinsert(X19166),X19164),X19165)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19166),X19164),c_Big__Operators_Olinorder__class_OMax(X19166,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19166,tc_HOL_Obool)),X19165),hAPP(hAPP(c_Set_Oinsert(X19166),X19164),c_Orderings_Obot__class_Obot(tc_fun(X19166,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19166),X19165))
        | ~ class_Orderings_Olinorder(X19166) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).

fof(i_0_7478,plain,
    ! [X27427,X27428,X27429,X27430,X27431] :
      ( ~ c_Typedef_Otype__definition(X27431,X27430,X27429,X27428,X27427)
      | hAPP(c_Set_Oimage(X27430,X27431,X27428),X27427) = c_Orderings_Otop__class_Otop(tc_fun(X27431,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).

fof(i_0_7479,plain,
    ! [X31240,X31241,X31242,X31243] :
      ( ~ c_Fun_Oinj__on(X31243,X31242,X31241,c_Complete__Lattice_OSup__class_OSup(tc_fun(X31243,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X31243),tc_fun(X31243,tc_HOL_Obool),c_List_Oset(X31243)),X31240)))
      | c_Fun_Oinj__on(tc_List_Olist(X31243),tc_List_Olist(X31242),hAPP(c_List_Omap(X31243,X31242),X31241),X31240) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).

fof(i_0_7480,plain,
    ! [X23876,X23877,X23878,X23879] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)),X23878))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)),X23878))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)),X23878))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23877),c_Groups_Ozero__class_Ozero(X23879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)),X23878))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),c_Groups_Ozero__class_Ozero(X23879)),X23876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)),X23878))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),X23878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23879),X23876),X23877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23879),X23878),X23877)),X23876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23879) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5591])])]) ).

fof(i_0_7481,plain,
    ! [X23757,X23758,X23759,X23760] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)),X23759))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23757))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23757))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)),X23759))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23757))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)),X23759))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23758))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23757))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23760),X23758),c_Groups_Ozero__class_Ozero(X23760)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)),X23759))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),c_Groups_Ozero__class_Ozero(X23760)),X23757))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)),X23759))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),X23759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23760),X23757),X23758)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23760),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23760),X23759),X23758)),X23757))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23760) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5592])])]) ).

fof(i_0_7482,plain,
    ! [X33555,X33556,X33557,X33558] :
      ( ~ c_Fun_Oinj__on(X33558,X33557,X33556,c_Orderings_Otop__class_Otop(tc_fun(X33558,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33557,X33558,c_Hilbert__Choice_Oinv__into(X33558,X33557,c_Orderings_Otop__class_Otop(tc_fun(X33558,tc_HOL_Obool)),X33556)),hAPP(c_Set_Oimage(X33558,X33557,X33556),X33555)) = X33555 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_7483,plain,
    ! [X33551,X33552,X33553,X33554] :
      ( ~ c_Fun_Oinj__on(X33554,X33553,X33552,c_Orderings_Otop__class_Otop(tc_fun(X33554,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33553,X33554,c_Hilbert__Choice_Oinv__into(X33554,X33553,c_Orderings_Otop__class_Otop(tc_fun(X33554,tc_HOL_Obool)),X33552)),hAPP(c_Set_Oimage(X33554,X33553,X33552),X33551)) = X33551 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_7484,plain,
    ! [X30039,X30040,X30041,X30042,X30043,X30044] : hAPP(hAPP(c_List_Olist__update(tc_prod(X30044,X30043),hAPP(hAPP(c_List_Ozip(X30044,X30043),X30042),X30041)),X30040),X30039) = hAPP(hAPP(c_List_Ozip(X30044,X30043),hAPP(hAPP(c_List_Olist__update(X30044,X30042),X30040),hAPP(c_Product__Type_Ofst(X30044,X30043),X30039))),hAPP(hAPP(c_List_Olist__update(X30043,X30041),X30040),hAPP(c_Product__Type_Osnd(X30044,X30043),X30039))),
    inference(variable_rename,[status(thm)],[fact_update__zip]) ).

cnf(i_0_7485,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5535]) ).

cnf(i_0_7486,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5536]) ).

cnf(i_0_7487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5538]) ).

cnf(i_0_7488,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5537]) ).

cnf(i_0_7489,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5539]) ).

cnf(i_0_7490,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X3))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5593]) ).

fof(i_0_7491,plain,
    ! [X25273] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25273)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(i_0_7492,plain,
    ! [X25274] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X25274)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(i_0_7493,plain,
    ! [X27391,X27392,X27393,X27394,X27395,X27396,X27397] : hAPP(hAPP(c_Relation_Orel__comp(X27397,X27396,X27395),hAPP(hAPP(c_Relation_Orel__comp(X27397,X27394,X27396),X27393),X27392)),X27391) = hAPP(hAPP(c_Relation_Orel__comp(X27397,X27394,X27395),X27393),hAPP(hAPP(c_Relation_Orel__comp(X27394,X27396,X27395),X27392),X27391)),
    inference(variable_rename,[status(thm)],[fact_O__assoc]) ).

fof(i_0_7494,plain,
    ! [X18661,X18662,X18663,X18664,X18665] :
      ( ~ class_Groups_Ocomm__monoid__mult(X18665)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18664),X18663))
      | ~ hBOOL(hAPP(hAPP(c_member(X18664),X18662),X18663))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X18664,X18665),X18661),X18663) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18665),hAPP(X18661,X18662)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X18664,X18665),X18661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18664,tc_HOL_Obool)),X18663),hAPP(hAPP(c_Set_Oinsert(X18664),X18662),c_Orderings_Obot__class_Obot(tc_fun(X18664,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).

fof(i_0_7495,plain,
    ! [X18174,X18175,X18176,X18177,X18178] :
      ( ~ class_Groups_Ocomm__monoid__add(X18178)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18177),X18176))
      | ~ hBOOL(hAPP(hAPP(c_member(X18177),X18175),X18176))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18177,X18178),X18174),X18176) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18178),hAPP(X18174,X18175)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18177,X18178),X18174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18177,tc_HOL_Obool)),X18176),hAPP(hAPP(c_Set_Oinsert(X18177),X18175),c_Orderings_Obot__class_Obot(tc_fun(X18177,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).

fof(i_0_7496,plain,
    ! [X18034,X18035,X18036,X18037,X18038] :
      ( ~ class_Groups_Ocomm__monoid__add(X18038)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18037),X18036))
      | ~ hBOOL(hAPP(hAPP(c_member(X18037),X18035),X18036))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18037,X18038),X18034),X18036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18038),hAPP(X18034,X18035)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18037,X18038),X18034),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18037,tc_HOL_Obool)),X18036),hAPP(hAPP(c_Set_Oinsert(X18037),X18035),c_Orderings_Obot__class_Obot(tc_fun(X18037,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).

fof(i_0_7497,plain,
    ! [X24513,X24514,X24515,X24516] : hAPP(c_Set_OPow(X24516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X24515,tc_fun(X24516,tc_HOL_Obool)),X24514),X24513)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X24515,tc_fun(tc_fun(X24516,tc_HOL_Obool),tc_HOL_Obool)),X24514),hAPP(hAPP(c_COMBB(tc_fun(X24516,tc_HOL_Obool),tc_fun(tc_fun(X24516,tc_HOL_Obool),tc_HOL_Obool),X24515),c_Set_OPow(X24516)),X24513)),
    inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).

fof(i_0_7498,plain,
    ! [X23209,X23210,X23211] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23211),X23210)),X23209)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23209),X23211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23211))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23210)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).

fof(i_0_7499,plain,
    ! [X33781,X33782,X33783,X33784,X33785] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33785),X33782))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33784),X33781))
        | ~ c_Fun_Obij__betw(X33785,X33784,X33783,X33782,X33781) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33784),X33781))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33785),X33782))
        | ~ c_Fun_Obij__betw(X33785,X33784,X33783,X33782,X33781) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__finite])])]) ).

fof(i_0_7500,plain,
    ! [X33771,X33772,X33773,X33774] :
      ( ~ c_Fun_Obij__betw(X33774,X33773,X33772,c_Orderings_Obot__class_Obot(tc_fun(X33774,tc_HOL_Obool)),X33771)
      | X33771 = c_Orderings_Obot__class_Obot(tc_fun(X33773,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty1])]) ).

fof(i_0_7501,plain,
    ! [X33767,X33768,X33769,X33770] :
      ( ~ c_Fun_Obij__betw(X33770,X33769,X33768,X33767,c_Orderings_Obot__class_Obot(tc_fun(X33769,tc_HOL_Obool)))
      | X33767 = c_Orderings_Obot__class_Obot(tc_fun(X33770,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty2])]) ).

fof(i_0_7502,plain,
    ! [X24265,X24266,X24267] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24267,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24266)),X24265) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24267,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24267,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X24266)),X24265)),hAPP(X24265,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(i_0_7503,plain,
    ! [X21033,X21034,X21035] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21035,tc_HOL_Obool)),X21034),X21033)))
      | hAPP(c_Finite__Set_Ocard(X21035),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21035,tc_HOL_Obool)),X21034),X21033)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21035),X21034)),hAPP(c_Finite__Set_Ocard(X21035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21035,tc_HOL_Obool)),X21034),X21033))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])]) ).

cnf(i_0_7504,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[fact_pair__leq__def]) ).

fof(i_0_7505,plain,
    ! [X21869,X21870,X21871,X21872,X21873] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21873,tc_fun(X21872,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21873,tc_HOL_Obool)),X21871),X21870)),X21869) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21872,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21873,tc_fun(X21872,tc_HOL_Obool)),X21871),X21869)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21873,tc_fun(X21872,tc_HOL_Obool)),X21870),X21869)),
    inference(variable_rename,[status(thm)],[fact_INT__Un]) ).

fof(i_0_7506,plain,
    ! [X21309,X21310,X21311,X21312,X21313] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21313,tc_fun(X21312,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21313,tc_HOL_Obool)),X21311),X21310)),X21309) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21312,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21313,tc_fun(X21312,tc_HOL_Obool)),X21311),X21309)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21313,tc_fun(X21312,tc_HOL_Obool)),X21310),X21309)),
    inference(variable_rename,[status(thm)],[fact_UN__Un]) ).

cnf(i_0_7507,plain,
    ( ~ c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))
    | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5594]) ).

fof(i_0_7508,plain,
    ! [X29038,X29039,X29040,X29041] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29041,X29041)),hAPP(hAPP(c_Product__Type_OPair(X29041,X29041),X29040),X29038)),c_Transitive__Closure_Ortrancl(X29041,X29039)))
        | X29040 = X29038
        | hBOOL(hAPP(hAPP(c_member(X29041),X29040),hAPP(c_Relation_ODomain(X29041,X29041),X29039))) )
      & ( X29040 != X29038
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29041,X29041)),hAPP(hAPP(c_Product__Type_OPair(X29041,X29041),X29040),X29038)),c_Transitive__Closure_Ortrancl(X29041,X29039)))
        | hBOOL(hAPP(hAPP(c_member(X29041),X29040),hAPP(c_Relation_ODomain(X29041,X29041),X29039))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5595])])]) ).

cnf(i_0_7509,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5596]) ).

fof(i_0_7510,plain,
    ! [X18234,X18235,X18236,X18237,X18238,X18239,X18240] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(X18240,X18239,X18238,X18237,X18236)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18239),X18235))
      | hAPP(hAPP(X18236,X18234),X18235) = X18237 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5597])]) ).

fof(i_0_7511,plain,
    ! [X19024,X19025,X19026] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19026,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19026,tc_HOL_Obool)),X19025)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19026,tc_HOL_Obool)),X19024)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19026,tc_HOL_Obool)),X19024),X19025)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19026,tc_HOL_Obool)),X19024),X19025))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19026,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19026,tc_HOL_Obool)),X19025)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19026,tc_HOL_Obool)),X19024))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).

fof(i_0_7512,plain,
    ! [X21820,X21821,X21822,X21823,X21824] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21824),X21823),X21822))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21821,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21824,tc_fun(X21821,tc_HOL_Obool)),X21822),X21820)),hAPP(X21820,X21823))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).

fof(i_0_7513,plain,
    ! [X28979,X28980,X28981] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28981,X28981),tc_HOL_Obool)),X28980),X28979))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28981,X28981),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28981,X28980)),c_Transitive__Closure_Ortrancl(X28981,X28979))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).

fof(i_0_7514,plain,
    ! [X25523,X25524,X25525,X25526,X25527,X25528] : hAPP(c_Relation_OImage(X25528,X25527,X25526),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25525,tc_fun(X25528,tc_HOL_Obool)),X25524),X25523)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25525,tc_fun(X25527,tc_HOL_Obool)),X25524),hAPP(hAPP(c_COMBB(tc_fun(X25528,tc_HOL_Obool),tc_fun(X25527,tc_HOL_Obool),X25525),c_Relation_OImage(X25528,X25527,X25526)),X25523)),
    inference(variable_rename,[status(thm)],[fact_Image__UN]) ).

fof(i_0_7515,plain,
    ! [X21734,X21735,X21736,X21737,X21738,X21739] : hAPP(c_Set_Ovimage(X21739,X21738,X21737),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21736,tc_fun(X21738,tc_HOL_Obool)),X21735),X21734)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21736,tc_fun(X21739,tc_HOL_Obool)),X21735),hAPP(hAPP(c_COMBB(tc_fun(X21738,tc_HOL_Obool),tc_fun(X21739,tc_HOL_Obool),X21736),c_Set_Ovimage(X21739,X21738,X21737)),X21734)),
    inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).

fof(i_0_7516,plain,
    ! [X21368,X21369,X21370,X21371,X21372,X21373] : hAPP(c_Set_Ovimage(X21373,X21372,X21371),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21370,tc_fun(X21372,tc_HOL_Obool)),X21369),X21368)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21370,tc_fun(X21373,tc_HOL_Obool)),X21369),hAPP(hAPP(c_COMBB(tc_fun(X21372,tc_HOL_Obool),tc_fun(X21373,tc_HOL_Obool),X21370),c_Set_Ovimage(X21373,X21372,X21371)),X21368)),
    inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).

fof(i_0_7517,plain,
    ! [X21292,X21293,X21294,X21295,X21296,X21297] : hAPP(c_Set_Oimage(X21297,X21296,X21295),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21294,tc_fun(X21297,tc_HOL_Obool)),X21293),X21292)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21294,tc_fun(X21296,tc_HOL_Obool)),X21293),hAPP(hAPP(c_COMBB(tc_fun(X21297,tc_HOL_Obool),tc_fun(X21296,tc_HOL_Obool),X21294),c_Set_Oimage(X21297,X21296,X21295)),X21292)),
    inference(variable_rename,[status(thm)],[fact_image__UN]) ).

fof(i_0_7518,plain,
    ! [X23912,X23913,X23914,X23915,X23916] :
      ( ~ class_Fields_Ofield(X23916)
      | X23915 = c_Groups_Ozero__class_Ozero(X23916)
      | X23914 = c_Groups_Ozero__class_Ozero(X23916)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23916),X23913),X23915)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23916),X23912),X23914)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23916),X23913),X23914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23916),X23912),X23915))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23916),X23915),X23914)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).

fof(i_0_7519,plain,
    ! [X23933,X23934,X23935,X23936,X23937] :
      ( ~ class_Fields_Ofield(X23937)
      | X23936 = c_Groups_Ozero__class_Ozero(X23937)
      | X23935 = c_Groups_Ozero__class_Ozero(X23937)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23937),X23934),X23936)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23937),X23933),X23935)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23937),X23934),X23935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23937),X23933),X23936))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23937),X23936),X23935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).

fof(i_0_7520,plain,
    ! [X25354,X25355] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25355,tc_HOL_Obool)),X25354) = hAPP(c_Set_OCollect(X25355),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25355),c_fNot),hAPP(hAPP(c_COMBC(X25355,tc_fun(X25355,tc_HOL_Obool),tc_HOL_Obool),c_member(X25355)),X25354))),
    inference(variable_rename,[status(thm)],[fact_Compl__eq]) ).

cnf(i_0_7521,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5598]) ).

fof(i_0_7522,plain,
    ! [X31490,X31491,X31492,X31493,X31494] :
      ( ~ c_List_Olist__all2(X31494,X31493,X31492,X31491,X31490)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31494)),X31491) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31493)),X31490) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])]) ).

fof(i_0_7523,plain,
    ! [X21817,X21818,X21819] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21819)),X21818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21819)),X21817)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21818),X21817)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21818),X21817))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21819)),X21818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21819)),X21817))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).

fof(i_0_7524,plain,
    ! [X21844,X21845,X21846] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21846)),X21845)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21846)),X21844)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21845),X21844)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21845),X21844))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21846)),X21845)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21846)),X21844))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).

fof(i_0_7525,plain,
    ! [X24574,X24575,X24576,X24577,X24578] :
      ( ( ~ hBOOL(hAPP(hAPP(X24575,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24574),X24576)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24574,X24576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24578),X24576))
        | X24574 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24576),X24577)),X24578)
        | hBOOL(hAPP(hAPP(X24575,X24577),X24578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk211_3(X24574,X24575,X24576)))
        | hBOOL(hAPP(hAPP(X24575,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24574),X24576)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24574,X24576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk211_3(X24574,X24575,X24576)),X24576))
        | hBOOL(hAPP(hAPP(X24575,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24574),X24576)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24574,X24576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576)) )
      & ( X24574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24576),esk210_3(X24574,X24575,X24576))),esk211_3(X24574,X24575,X24576))
        | hBOOL(hAPP(hAPP(X24575,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24574),X24576)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24574,X24576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576)) )
      & ( ~ hBOOL(hAPP(hAPP(X24575,esk210_3(X24574,X24575,X24576)),esk211_3(X24574,X24575,X24576)))
        | hBOOL(hAPP(hAPP(X24575,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24574),X24576)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24574,X24576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])]) ).

fof(i_0_7526,plain,
    ! [X30933,X30934,X30935,X30936,X30937] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30936),X30934),hAPP(c_List_Oset(X30936),X30933)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30936),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30936,X30937,X30935),X30934),X30933)))
        | ~ class_Orderings_Olinorder(X30937) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30936),X30933))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30936),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30936,X30937,X30935),X30934),X30933)))
        | ~ class_Orderings_Olinorder(X30937) )
      & ( hBOOL(hAPP(hAPP(c_member(X30936),X30934),hAPP(c_List_Oset(X30936),X30933)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30936),X30933))
        | hBOOL(hAPP(c_List_Odistinct(X30936),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30936,X30937,X30935),X30934),X30933)))
        | ~ class_Orderings_Olinorder(X30937) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5599])])]) ).

fof(i_0_7527,plain,
    ! [X33567,X33568,X33569,X33570,X33571] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33571,tc_HOL_Obool)),X33570),hAPP(c_Set_Oimage(X33569,X33571,X33568),X33567)))
      | c_Fun_Oinj__on(X33571,X33569,c_Hilbert__Choice_Oinv__into(X33569,X33571,X33567,X33568),X33570) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_7528,plain,
    ! [X28631,X28632,X28633,X28634,X28635,X28636] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28636,tc_fun(X28635,tc_HOL_Obool)),X28634),hAPP(c_Fun_Ocomp(X28633,tc_fun(X28635,tc_HOL_Obool),X28636,X28632),X28631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28633,tc_fun(X28635,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28636,X28633,X28631),X28634)),X28632),
    inference(variable_rename,[status(thm)],[fact_UN__o]) ).

fof(i_0_7529,plain,
    ! [X19147,X19148,X19149,X19150,X19151] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19151)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19150),X19149))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19150,X19151),X19148),hAPP(hAPP(c_Set_Oinsert(X19150),X19147),X19149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19151),hAPP(X19148,X19147)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19150,X19151),X19148),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19150,tc_HOL_Obool)),X19149),hAPP(hAPP(c_Set_Oinsert(X19150),X19147),c_Orderings_Obot__class_Obot(tc_fun(X19150,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).

fof(i_0_7530,plain,
    ! [X18164,X18165,X18166,X18167,X18168] :
      ( ~ class_Groups_Ocomm__monoid__add(X18168)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18167),X18166))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18167,X18168),X18165),hAPP(hAPP(c_Set_Oinsert(X18167),X18164),X18166)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18168),hAPP(X18165,X18164)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18167,X18168),X18165),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18167,tc_HOL_Obool)),X18166),hAPP(hAPP(c_Set_Oinsert(X18167),X18164),c_Orderings_Obot__class_Obot(tc_fun(X18167,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).

fof(i_0_7531,plain,
    ! [X33500,X33501,X33502,X33503,X33504] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33504),X33503),hAPP(c_Set_Oimage(X33502,X33504,X33501),X33500)))
      | hAPP(X33501,hAPP(c_Hilbert__Choice_Oinv__into(X33502,X33504,X33500,X33501),X33503)) = X33503 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

fof(i_0_7532,plain,
    ! [X24581,X24582,X24583,X24584,X24585] :
      ( ( ~ hBOOL(hAPP(hAPP(X24582,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24581),X24583)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24581,X24583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),X24585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24585),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X24581 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24583),X24584)),X24585)
        | hBOOL(hAPP(hAPP(X24582,X24584),X24585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),esk213_3(X24581,X24582,X24583)))
        | hBOOL(hAPP(hAPP(X24582,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24581),X24583)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24581,X24583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk213_3(X24581,X24582,X24583)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X24582,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24581),X24583)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24581,X24583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X24581 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24583),esk212_3(X24581,X24582,X24583))),esk213_3(X24581,X24582,X24583))
        | hBOOL(hAPP(hAPP(X24582,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24581),X24583)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24581,X24583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(X24582,esk212_3(X24581,X24582,X24583)),esk213_3(X24581,X24582,X24583)))
        | hBOOL(hAPP(hAPP(X24582,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24581),X24583)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24581,X24583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__neg__lemma])])])])]) ).

fof(i_0_7533,plain,
    ! [X31071,X31072] : hAPP(hAPP(c_List_Ozip(X31072,X31072),X31071),X31071) = hAPP(hAPP(c_List_Omap(X31072,tc_prod(X31072,X31072)),hAPP(hAPP(c_COMBS(X31072,X31072,tc_prod(X31072,X31072)),c_Product__Type_OPair(X31072,X31072)),c_COMBI(X31072))),X31071),
    inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).

fof(i_0_7534,plain,
    ! [X23659,X23660] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23660),X23659) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23660)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23659))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(i_0_7535,plain,
    ! [X23726,X23727] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23727),X23726) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23727)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23726))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(i_0_7536,plain,
    ! [X33579,X33580,X33581] :
      ( ( hAPP(c_Set_Oimage(X33581,X33580,X33579),c_Orderings_Otop__class_Otop(tc_fun(X33581,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33580,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(X33581,X33580,X33580,X33579),c_Hilbert__Choice_Oinv__into(X33581,X33580,c_Orderings_Otop__class_Otop(tc_fun(X33581,tc_HOL_Obool)),X33579)) = c_Fun_Oid(X33580) )
      & ( hAPP(c_Fun_Ocomp(X33581,X33580,X33580,X33579),c_Hilbert__Choice_Oinv__into(X33581,X33580,c_Orderings_Otop__class_Otop(tc_fun(X33581,tc_HOL_Obool)),X33579)) != c_Fun_Oid(X33580)
        | hAPP(c_Set_Oimage(X33581,X33580,X33579),c_Orderings_Otop__class_Otop(tc_fun(X33581,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33580,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff])]) ).

fof(i_0_7537,plain,
    ! [X22690,X22691,X22692] :
      ( ~ class_Rings_Olinordered__semidom(X22692)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22692),c_Groups_Ozero__class_Ozero(X22692)),X22691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22692),X22691),c_Groups_Oone__class_Oone(X22692)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22692),X22691),hAPP(hAPP(c_Power_Opower__class_Opower(X22692),X22691),X22690))),hAPP(hAPP(c_Power_Opower__class_Opower(X22692),X22691),X22690))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).

fof(i_0_7538,plain,
    ! [X27444,X27445,X27446,X27447,X27448,X27449,X27450] :
      ( ( hAPP(X27448,X27445) != hAPP(X27448,X27444)
        | X27445 = X27444
        | ~ c_Typedef_Otype__definition(X27450,X27449,X27448,X27447,X27446) )
      & ( X27445 != X27444
        | hAPP(X27448,X27445) = hAPP(X27448,X27444)
        | ~ c_Typedef_Otype__definition(X27450,X27449,X27448,X27447,X27446) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).

fof(i_0_7539,plain,
    ! [X27955,X27956,X27957,X27958] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27958,X27957)),hAPP(hAPP(c_Product__Type_OSigma(X27958,X27957),X27956),hAPP(c_COMBK(tc_fun(X27957,tc_HOL_Obool),X27958),X27955))))
      | X27956 = c_Orderings_Obot__class_Obot(tc_fun(X27958,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27957),X27955)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).

fof(i_0_7540,plain,
    ! [X27951,X27952,X27953,X27954] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27954,X27953)),hAPP(hAPP(c_Product__Type_OSigma(X27954,X27953),X27952),hAPP(c_COMBK(tc_fun(X27953,tc_HOL_Obool),X27954),X27951))))
      | X27951 = c_Orderings_Obot__class_Obot(tc_fun(X27953,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27954),X27952)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).

fof(i_0_7541,plain,
    ! [X27451,X27452,X27453,X27454,X27455,X27456] :
      ( ~ c_Typedef_Otype__definition(X27456,X27455,X27454,X27453,X27452)
      | hAPP(X27453,hAPP(X27454,X27451)) = X27451 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])]) ).

fof(i_0_7542,plain,
    ! [X33762,X33763,X33764,X33765,X33766] :
      ( ~ c_Fun_Obij__betw(X33766,X33765,X33764,X33763,X33762)
      | hAPP(c_Finite__Set_Ocard(X33766),X33763) = hAPP(c_Finite__Set_Ocard(X33765),X33762) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__same__card])]) ).

cnf(i_0_7543,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5600]) ).

fof(i_0_7544,plain,
    ! [X25059,X25060,X25061] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25061)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25061),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25061),hAPP(c_Groups_Oabs__class_Oabs(X25061),X25060)),hAPP(c_Groups_Oabs__class_Oabs(X25061),X25059))),hAPP(c_Groups_Oabs__class_Oabs(X25061),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25061),X25060),X25059)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).

fof(i_0_7545,plain,
    ! [X25056,X25057,X25058] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25058)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25058),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25058),hAPP(c_Groups_Oabs__class_Oabs(X25058),X25057)),hAPP(c_Groups_Oabs__class_Oabs(X25058),X25056))),hAPP(c_Groups_Oabs__class_Oabs(X25058),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25058),X25056),X25057)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).

cnf(i_0_7546,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5601]) ).

fof(i_0_7547,plain,
    ! [X20944,X20945,X20946,X20947,X20948] : hAPP(c_Set_Ovimage(X20948,X20947,X20946),hAPP(hAPP(c_Set_Oinsert(X20947),X20945),X20944)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20948,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20948,X20947,X20946),hAPP(hAPP(c_Set_Oinsert(X20947),X20945),c_Orderings_Obot__class_Obot(tc_fun(X20947,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X20948,X20947,X20946),X20944)),
    inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).

fof(i_0_7548,plain,
    ! [X17437,X17438,X17439,X17440,X17441] :
      ( ( c_Fun_Ofun__upd(X17441,X17440,X17439,X17438,X17437) != X17439
        | hAPP(X17439,X17438) = X17437 )
      & ( hAPP(X17439,X17438) != X17437
        | c_Fun_Ofun__upd(X17441,X17440,X17439,X17438,X17437) = X17439 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).

fof(i_0_7549,plain,
    ! [X31495,X31496,X31497,X31498] :
      ( ( ~ c_List_Olist__all2(X31498,X31497,X31496,c_List_Olist_ONil(X31498),X31495)
        | X31495 = c_List_Olist_ONil(X31497) )
      & ( X31495 != c_List_Olist_ONil(X31497)
        | c_List_Olist__all2(X31498,X31497,X31496,c_List_Olist_ONil(X31498),X31495) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])]) ).

fof(i_0_7550,plain,
    ! [X31499,X31500,X31501,X31502] :
      ( ( ~ c_List_Olist__all2(X31502,X31501,X31500,X31499,c_List_Olist_ONil(X31501))
        | X31499 = c_List_Olist_ONil(X31502) )
      & ( X31499 != c_List_Olist_ONil(X31502)
        | c_List_Olist__all2(X31502,X31501,X31500,X31499,c_List_Olist_ONil(X31501)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])]) ).

fof(i_0_7551,plain,
    ! [X33786,X33787,X33788] :
      ( ( ~ c_Fun_Obij__betw(X33788,X33788,c_Fun_Oid(X33788),X33787,X33786)
        | X33787 = X33786 )
      & ( X33787 != X33786
        | c_Fun_Obij__betw(X33788,X33788,c_Fun_Oid(X33788),X33787,X33786) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__id__iff])]) ).

fof(i_0_7552,plain,
    ! [X27708,X27709,X27710,X27711,X27712] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27712,X27711)),hAPP(hAPP(c_Product__Type_OPair(X27712,X27711),X27710),X27709)),X27708))
      | hBOOL(hAPP(hAPP(c_member(X27712),X27710),hAPP(c_Relation_ODomain(X27712,X27711),X27708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).

fof(i_0_7553,plain,
    ! [X27627,X27628,X27629,X27630,X27631] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27631,X27630)),hAPP(hAPP(c_Product__Type_OPair(X27631,X27630),X27629),X27628)),X27627))
      | hBOOL(hAPP(hAPP(c_member(X27630),X27628),hAPP(c_Relation_ORange(X27631,X27630),X27627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).

fof(i_0_7554,plain,
    ! [X30642,X30643,X30644,X30645] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30645),X30644))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30643,tc_HOL_Obool)),hAPP(c_List_Oset(X30643),hAPP(hAPP(c_List_Odrop(X30643),X30644),X30642))),hAPP(c_List_Oset(X30643),hAPP(hAPP(c_List_Odrop(X30643),X30645),X30642)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).

fof(i_0_7555,plain,
    ! [X29817,X29818,X29819,X29820] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29820),X29819))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29818,tc_HOL_Obool)),hAPP(c_List_Oset(X29818),hAPP(hAPP(c_List_Otake(X29818),X29820),X29817))),hAPP(c_List_Oset(X29818),hAPP(hAPP(c_List_Otake(X29818),X29819),X29817)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).

fof(i_0_7556,plain,
    ! [X31487,X31488,X31489] :
      ( ( X31489 != X31488
        | c_List_Olist__all2(X31487,X31487,c_fequal,X31489,X31488) )
      & ( ~ c_List_Olist__all2(X31487,X31487,c_fequal,X31489,X31488)
        | X31489 = X31488 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])]) ).

fof(i_0_7557,plain,
    ! [X30881,X30882,X30883] :
      ( ~ class_Orderings_Olinorder(X30883)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30883),X30882))
      | c_List_Olinorder__class_Osorted__list__of__set(X30883,hAPP(hAPP(c_Set_Oinsert(X30883),X30881),X30882)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30883,X30883,c_COMBI(X30883)),X30881),c_List_Olinorder__class_Osorted__list__of__set(X30883,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30883,tc_HOL_Obool)),X30882),hAPP(hAPP(c_Set_Oinsert(X30883),X30881),c_Orderings_Obot__class_Obot(tc_fun(X30883,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).

fof(i_0_7558,plain,
    ! [X22607,X22608,X22609,X22610] :
      ( ~ class_Rings_Olinordered__semidom(X22610)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22610),hAPP(hAPP(c_Power_Opower__class_Opower(X22610),X22609),hAPP(c_Nat_OSuc,X22608))),hAPP(hAPP(c_Power_Opower__class_Opower(X22610),X22607),hAPP(c_Nat_OSuc,X22608))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22610),c_Groups_Ozero__class_Ozero(X22610)),X22607))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22610),X22609),X22607)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).

cnf(i_0_7559,plain,
    c_List_Oconcat(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_5602]) ).

fof(i_0_7560,plain,
    ! [X19837,X19838,X19839,X19840] :
      ( ~ class_Lattices_Osemilattice__sup(X19840)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19840),X19839))
      | ~ hBOOL(hAPP(hAPP(c_member(X19840),X19838),X19839))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19840),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19840),X19838),X19837)),hAPP(hAPP(c_Finite__Set_Ofold(X19840,X19840,c_Lattices_Osemilattice__sup__class_Osup(X19840)),X19837),X19839))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).

fof(i_0_7561,plain,
    ! [X19121,X19122,X19123,X19124] :
      ( ~ class_Orderings_Olinorder(X19124)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19124),X19123))
      | ~ hBOOL(hAPP(hAPP(c_member(X19124),X19122),X19123))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19124),X19122),X19121)),hAPP(hAPP(c_Finite__Set_Ofold(X19124,X19124,c_Orderings_Oord__class_Omax(X19124)),X19121),X19123))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).

fof(i_0_7562,plain,
    ! [X27720,X27721,X27722,X27723] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27723,X27722),tc_HOL_Obool)),X27721),X27720))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27723,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27723,X27722),X27721)),hAPP(c_Relation_ODomain(X27723,X27722),X27720))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).

fof(i_0_7563,plain,
    ! [X33548,X33549,X33550] :
      ( ~ c_Fun_Oinj__on(X33550,X33549,X33548,c_Orderings_Otop__class_Otop(tc_fun(X33550,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33549,X33550,c_Hilbert__Choice_Oinv__into(X33550,X33549,c_Orderings_Otop__class_Otop(tc_fun(X33550,tc_HOL_Obool)),X33548)),c_Orderings_Otop__class_Otop(tc_fun(X33549,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33550,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

cnf(i_0_7564,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5603]) ).

fof(i_0_7565,plain,
    ! [X23946,X23947,X23948] :
      ( ~ class_Fields_Olinordered__field(X23948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23948),X23947),X23946))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23948),X23947),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23948),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23948),X23947),X23946)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23948),c_Groups_Oone__class_Oone(X23948)),c_Groups_Oone__class_Oone(X23948))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

fof(i_0_7566,plain,
    ! [X23974,X23975] :
      ( ~ c_Nat__Transfer_Onat__set(X23975)
      | ~ c_Nat__Transfer_Onat__set(X23974)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23975),X23974) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23975)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23974))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])]) ).

fof(i_0_7567,plain,
    ! [X23976,X23977] :
      ( ~ c_Nat__Transfer_Onat__set(X23977)
      | ~ c_Nat__Transfer_Onat__set(X23976)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23977),X23976) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23977)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23976))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])]) ).

fof(i_0_7568,plain,
    ! [X24206,X24207,X24208,X24209,X24210] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24209),X24208))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24208),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24209),X24208))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24210),X24207),X24209))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24210),X24208),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24209),X24208))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24209),X24208))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24206))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24210),X24207),X24209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24208),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24206))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24210),X24208),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24209))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24208),X24206))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24210),X24207),X24206))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24210,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24209,X24208)),c_SetInterval_Oord__class_OatLeastAtMost(X24210,X24207,X24206)))
        | ~ class_Orderings_Oorder(X24210) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5604])])]) ).

fof(i_0_7569,plain,
    ! [X18634,X18635,X18636,X18637,X18638] :
      ( ~ class_Rings_Osemiring(X18638)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18638),X18637),X18636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18638),X18635),X18636)),X18634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18638),X18637),X18635)),X18636)),X18634) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_7570,plain,
    ! [X27882,X27883] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27883,X27883),tc_HOL_Obool)),c_Relation_OId__on(X27883,X27882)),hAPP(hAPP(c_Product__Type_OSigma(X27883,X27883),X27882),hAPP(c_COMBK(tc_fun(X27883,tc_HOL_Obool),X27883),X27882)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(i_0_7571,plain,
    ! [X31718,X31719] :
      ( ~ class_Orderings_Olinorder(X31719)
      | c_List_Olinorder__class_Osort__key(X31719,X31719,c_COMBI(X31719),X31718) = hAPP(c_List_Ofoldl(tc_List_Olist(X31719),X31719,hAPP(c_COMBC(X31719,tc_List_Olist(X31719),tc_List_Olist(X31719)),c_List_Olinorder__class_Oinsort__key(X31719,X31719,c_COMBI(X31719))),c_List_Olist_ONil(X31719)),X31718) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])]) ).

fof(i_0_7572,plain,
    ! [X27624,X27625,X27626] : hAPP(c_Relation_ORange(X27626,X27625),hAPP(c_Set_OCollect(tc_prod(X27626,X27625)),hAPP(c_Product__Type_Oprod_Oprod__case(X27626,X27625,tc_HOL_Obool),X27624))) = hAPP(c_Set_OCollect(X27625),hAPP(hAPP(c_COMBB(tc_fun(X27626,tc_HOL_Obool),tc_HOL_Obool,X27625),c_HOL_OEx(X27626)),hAPP(c_COMBC(X27626,X27625,tc_HOL_Obool),X27624))),
    inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).

fof(i_0_7573,plain,
    ! [X33745,X33746,X33747,X33748] :
      ( ~ c_Fun_Oinj__on(X33748,X33747,X33746,X33745)
      | c_Fun_Obij__betw(X33748,X33747,X33746,X33745,hAPP(c_Set_Oimage(X33748,X33747,X33746),X33745)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imp__bij__betw])]) ).

fof(i_0_7574,plain,
    ! [X27864,X27865,X27866] :
      ( ~ c_Equiv__Relations_Oequiv(X27866,X27865,X27864)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27866,X27866),tc_HOL_Obool)),X27864),hAPP(hAPP(c_Product__Type_OSigma(X27866,X27866),X27865),hAPP(c_COMBK(tc_fun(X27866,tc_HOL_Obool),X27866),X27865)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).

fof(i_0_7575,plain,
    ! [X31185,X31186,X31187,X31188,X31189] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31189),tc_List_Olist(X31188),tc_List_Olist(X31187),hAPP(c_List_Omap(X31189,X31188),X31186)),hAPP(c_List_Omap(X31187,X31189),X31185)) = hAPP(c_List_Omap(X31187,X31188),hAPP(c_Fun_Ocomp(X31189,X31188,X31187,X31186),X31185)),
    inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).

fof(i_0_7576,plain,
    ! [X31180,X31181,X31182,X31183,X31184] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31184),tc_List_Olist(X31183),tc_List_Olist(X31182),hAPP(c_List_Omap(X31184,X31183),X31181)),hAPP(c_List_Omap(X31182,X31184),X31180)) = hAPP(c_List_Omap(X31182,X31183),hAPP(c_Fun_Ocomp(X31184,X31183,X31182,X31181),X31180)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(i_0_7577,plain,
    ! [X28205,X28206,X28207,X28208,X28209] :
      ( ~ c_Relation_Orefl__on(X28209,X28208,X28207)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28209,X28209)),hAPP(hAPP(c_Product__Type_OPair(X28209,X28209),X28206),X28205)),X28207))
      | hBOOL(hAPP(hAPP(c_member(X28209),X28206),X28208)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).

fof(i_0_7578,plain,
    ! [X28210,X28211,X28212,X28213,X28214] :
      ( ~ c_Relation_Orefl__on(X28214,X28213,X28212)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28214,X28214)),hAPP(hAPP(c_Product__Type_OPair(X28214,X28214),X28211),X28210)),X28212))
      | hBOOL(hAPP(hAPP(c_member(X28214),X28210),X28213)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).

cnf(i_0_7579,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5605]) ).

fof(i_0_7580,plain,
    ! [X30276,X30277] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30277),tc_List_Olist(X30277))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30277),tc_List_Olist(X30277)),c_List_Olist_ONil(X30277)),c_List_Olist_ONil(X30277))),c_List_Olistrel(X30277,X30276))),
    inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).

fof(i_0_7581,plain,
    ! [X25008,X25009,X25010] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25010,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25010,tc_HOL_Obool),X25009)),X25008) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25010,tc_HOL_Obool),tc_fun(X25010,tc_HOL_Obool)),X25009),hAPP(hAPP(c_COMBC(tc_fun(X25010,tc_HOL_Obool),tc_fun(X25010,tc_HOL_Obool),tc_fun(X25010,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25010,tc_HOL_Obool))),X25008)),
    inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).

fof(i_0_7582,plain,
    ! [X27269,X27270,X27271,X27272] :
      ( ( X27271 = X27270
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27272,X27272)),hAPP(hAPP(c_Product__Type_OPair(X27272,X27272),X27271),X27270)),c_Relation_OId__on(X27272,X27269))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27272),X27271),X27269))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27272,X27272)),hAPP(hAPP(c_Product__Type_OPair(X27272,X27272),X27271),X27270)),c_Relation_OId__on(X27272,X27269))) )
      & ( X27271 != X27270
        | ~ hBOOL(hAPP(hAPP(c_member(X27272),X27271),X27269))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27272,X27272)),hAPP(hAPP(c_Product__Type_OPair(X27272,X27272),X27271),X27270)),c_Relation_OId__on(X27272,X27269))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).

fof(i_0_7583,plain,
    ! [X23519,X23520,X23521,X23522] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23522),X23520))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23522,X23521)),c_Sum__Type_OPlus(X23522,X23521,X23520,X23519))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23521),X23519))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23522,X23521)),c_Sum__Type_OPlus(X23522,X23521,X23520,X23519))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23522),X23520))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23521),X23519))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23522,X23521)),c_Sum__Type_OPlus(X23522,X23521,X23520,X23519))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_7584,plain,
    ! [X23527,X23528,X23529,X23530] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23530,X23529)),c_Sum__Type_OPlus(X23530,X23529,X23528,X23527)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23530),X23528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_7585,plain,
    ! [X23531,X23532,X23533,X23534] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23534,X23533)),c_Sum__Type_OPlus(X23534,X23533,X23532,X23531)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23533),X23531)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_7586,plain,
    ! [X27785,X27786,X27787,X27788,X27789,X27790] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27790),X27789),X27788))
      | ~ hBOOL(hAPP(hAPP(c_member(X27787),X27786),hAPP(X27785,X27789)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27790,X27787)),hAPP(hAPP(c_Product__Type_OPair(X27790,X27787),X27789),X27786)),hAPP(hAPP(c_Product__Type_OSigma(X27790,X27787),X27788),X27785))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).

fof(i_0_7587,plain,
    ! [X25221,X25222,X25223] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),esk227_3(X25221,X25222,X25223)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25223,tc_HOL_Obool)),X25222),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25223,tc_HOL_Obool),X25221)) = c_Orderings_Obot__class_Obot(tc_fun(X25223,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),esk228_3(X25221,X25222,X25223)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25223,tc_HOL_Obool)),X25222),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25223,tc_HOL_Obool),X25221)) = c_Orderings_Obot__class_Obot(tc_fun(X25223,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)) )
      & ( esk227_3(X25221,X25222,X25223) != esk228_3(X25221,X25222,X25223)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25223,tc_HOL_Obool)),X25222),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25223,tc_HOL_Obool),X25221)) = c_Orderings_Obot__class_Obot(tc_fun(X25223,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25223,tc_HOL_Obool)),esk227_3(X25221,X25222,X25223)),esk228_3(X25221,X25222,X25223)) != c_Orderings_Obot__class_Obot(tc_fun(X25223,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25223,tc_HOL_Obool)),X25222),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25223,tc_HOL_Obool),X25221)) = c_Orderings_Obot__class_Obot(tc_fun(X25223,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25223,tc_HOL_Obool)),X25222),X25221)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5606])])])]) ).

fof(i_0_7588,plain,
    ! [X30818,X30819,X30820,X30821] :
      ( ~ class_Groups_Osemigroup__add(X30821)
      | hAPP(c_List_Ofoldl(X30821,X30821,c_Groups_Oplus__class_Oplus(X30821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30821),X30820),X30819)),X30818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30821),X30820),hAPP(c_List_Ofoldl(X30821,X30821,c_Groups_Oplus__class_Oplus(X30821),X30819),X30818)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).

fof(i_0_7589,plain,
    ! [X29333,X29334,X29335] : hBOOL(hAPP(hAPP(c_member(tc_prod(X29335,X29335)),hAPP(hAPP(c_Product__Type_OPair(X29335,X29335),X29334),X29334)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29335,X29335),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29333))),
    inference(variable_rename,[status(thm)],[fact_rel__pow__0__I]) ).

cnf(i_0_7590,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),c_Relation_OId(X1)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5607]) ).

fof(i_0_7591,plain,
    ! [X30526,X30527,X30528,X30529,X30530] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30529)),X30528)))
        | hAPP(hAPP(c_List_Olist__update(X30529,hAPP(hAPP(c_List_Oappend(X30529),X30528),X30527)),X30530),X30526) = hAPP(hAPP(c_List_Oappend(X30529),hAPP(hAPP(c_List_Olist__update(X30529,X30528),X30530),X30526)),X30527) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30529)),X30528)))
        | hAPP(hAPP(c_List_Olist__update(X30529,hAPP(hAPP(c_List_Oappend(X30529),X30528),X30527)),X30530),X30526) = hAPP(hAPP(c_List_Oappend(X30529),X30528),hAPP(hAPP(c_List_Olist__update(X30529,X30527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30529)),X30528))),X30526)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5608])]) ).

fof(i_0_7592,plain,
    ! [X25645,X25646,X25647,X25648,X25649] :
      ( ~ c_Equiv__Relations_Oequiv(X25649,X25648,X25647)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25649,tc_HOL_Obool)),X25646),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25649),X25648),X25647)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25649,tc_HOL_Obool)),X25645),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25649),X25648),X25647)))
      | X25646 = X25645
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25649,tc_HOL_Obool)),X25646),X25645) = c_Orderings_Obot__class_Obot(tc_fun(X25649,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).

fof(i_0_7593,plain,
    ! [X31267,X31268,X31269] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31268)),X31267)))
      | hAPP(c_Random_Opick(X31268,hAPP(hAPP(c_List_Omap(X31268,tc_prod(tc_Code__Numeral_Ocode__numeral,X31268)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X31268),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X31267)),hAPP(c_Code__Numeral_Oof__nat,X31269)) = hAPP(hAPP(c_List_Onth(X31268),X31267),X31269) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).

fof(i_0_7594,plain,
    ! [X23872,X23873,X23874,X23875] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),c_Groups_Ozero__class_Ozero(X23875)),X23872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),c_Groups_Ozero__class_Ozero(X23875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23872),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),c_Groups_Ozero__class_Ozero(X23875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23875),X23874),X23872)),X23873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23875),X23874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23875),X23873),X23872)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23875) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5609])])]) ).

fof(i_0_7595,plain,
    ! [X23753,X23754,X23755,X23756] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),c_Groups_Ozero__class_Ozero(X23756)),X23753))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),c_Groups_Ozero__class_Ozero(X23756)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23756),X23753),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),c_Groups_Ozero__class_Ozero(X23756)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23756),X23755),X23753)),X23754))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23756),X23755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23756),X23754),X23753)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23756) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5610])])]) ).

fof(i_0_7596,plain,
    ! [X23103,X23104] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23104),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23103),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23104)))))
      | X23104 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23103),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23104))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_7597,plain,
    ! [X20275,X20276,X20277,X20278,X20279] :
      ( ( hBOOL(hAPP(hAPP(X20277,X20276),X20278))
        | ~ hBOOL(hAPP(hAPP(c_member(X20279),X20278),c_SetInterval_Oord_OgreaterThanLessThan(X20279,X20277,X20276,X20275))) )
      & ( hBOOL(hAPP(hAPP(X20277,X20278),X20275))
        | ~ hBOOL(hAPP(hAPP(c_member(X20279),X20278),c_SetInterval_Oord_OgreaterThanLessThan(X20279,X20277,X20276,X20275))) )
      & ( ~ hBOOL(hAPP(hAPP(X20277,X20276),X20278))
        | ~ hBOOL(hAPP(hAPP(X20277,X20278),X20275))
        | hBOOL(hAPP(hAPP(c_member(X20279),X20278),c_SetInterval_Oord_OgreaterThanLessThan(X20279,X20277,X20276,X20275))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).

fof(i_0_7598,plain,
    ! [X20270,X20271,X20272,X20273,X20274] :
      ( ( hBOOL(hAPP(hAPP(X20272,X20271),X20273))
        | ~ hBOOL(hAPP(hAPP(c_member(X20274),X20273),c_SetInterval_Oord_OatLeastAtMost(X20274,X20272,X20271,X20270))) )
      & ( hBOOL(hAPP(hAPP(X20272,X20273),X20270))
        | ~ hBOOL(hAPP(hAPP(c_member(X20274),X20273),c_SetInterval_Oord_OatLeastAtMost(X20274,X20272,X20271,X20270))) )
      & ( ~ hBOOL(hAPP(hAPP(X20272,X20271),X20273))
        | ~ hBOOL(hAPP(hAPP(X20272,X20273),X20270))
        | hBOOL(hAPP(hAPP(c_member(X20274),X20273),c_SetInterval_Oord_OatLeastAtMost(X20274,X20272,X20271,X20270))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).

cnf(i_0_7599,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_5611]) ).

cnf(i_0_7600,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5) = c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5612]) ).

fof(i_0_7601,plain,
    ! [X30305,X30306] : c_List_Oset__Cons(X30306,X30305,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30306)),c_List_Olist_ONil(X30306)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30306),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X30306,tc_List_Olist(X30306),hAPP(hAPP(c_COMBC(X30306,tc_List_Olist(X30306),tc_List_Olist(X30306)),c_List_Olist_OCons(X30306)),c_List_Olist_ONil(X30306))),X30305),
    inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(i_0_7602,plain,
    ! [X21809,X21810,X21811,X21812,X21813,X21814] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21814),X21813),X21812))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21814,tc_fun(X21811,tc_HOL_Obool)),X21812),hAPP(hAPP(c_COMBB(tc_fun(X21811,tc_HOL_Obool),tc_fun(X21811,tc_HOL_Obool),X21814),hAPP(c_Set_Oinsert(X21811),X21810)),X21809)) = hAPP(hAPP(c_Set_Oinsert(X21811),X21810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21814,tc_fun(X21811,tc_HOL_Obool)),X21812),X21809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).

fof(i_0_7603,plain,
    ! [X21374,X21375,X21376,X21377,X21378,X21379] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21379),X21378),X21377))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21379,tc_fun(X21376,tc_HOL_Obool)),X21377),hAPP(hAPP(c_COMBB(tc_fun(X21376,tc_HOL_Obool),tc_fun(X21376,tc_HOL_Obool),X21379),hAPP(c_Set_Oinsert(X21376),X21375)),X21374)) = hAPP(hAPP(c_Set_Oinsert(X21376),X21375),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21379,tc_fun(X21376,tc_HOL_Obool)),X21377),X21374)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).

fof(i_0_7604,plain,
    ! [X25462,X25463,X25466,X25467,X25468,X25469] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25463),X25462))
        | X25462 = hAPP(c_Set_Oimage(tc_Nat_Onat,X25463,esk243_2(X25462,X25463)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk242_2(X25462,X25463)))) )
      & ( X25466 != hAPP(c_Set_Oimage(tc_Nat_Onat,X25467,X25469),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25468)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25466)) ) ),
    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_finite__conv__nat__seg__image])])])])]) ).

fof(i_0_7605,plain,
    ! [X25378,X25379,X25380,X25381] :
      ( X25381 != hAPP(c_Set_Oimage(tc_Nat_Onat,X25380,X25379),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X25378)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X25380),X25381)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).

fof(i_0_7606,plain,
    ! [X30707,X30708,X30709] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30709),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30708)),X30707)))
      | hAPP(hAPP(c_List_Oappend(X30708),hAPP(hAPP(c_List_Otake(X30708),X30709),X30707)),hAPP(hAPP(c_List_Olist_OCons(X30708),hAPP(c_List_Ohd(X30708),hAPP(hAPP(c_List_Odrop(X30708),X30709),X30707))),c_List_Olist_ONil(X30708))) = hAPP(hAPP(c_List_Otake(X30708),hAPP(c_Nat_OSuc,X30709)),X30707) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).

fof(i_0_7607,plain,
    ! [X17356,X17357,X17358,X17359] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17359,tc_HOL_Obool)),X17358),hAPP(hAPP(c_Set_Oinsert(X17359),X17357),X17356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17359,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17359,tc_HOL_Obool)),X17358),hAPP(hAPP(c_Set_Oinsert(X17359),X17357),c_Orderings_Obot__class_Obot(tc_fun(X17359,tc_HOL_Obool))))),X17356),
    inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).

fof(i_0_7608,plain,
    ! [X29660,X29661,X29662] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29662),tc_List_Olist(X29662))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29662),tc_List_Olist(X29662)),X29661),X29661)),c_List_Olistrel(X29662,c_Transitive__Closure_Ortrancl(X29662,X29660)))),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).

cnf(i_0_7609,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5613]) ).

fof(i_0_7610,plain,
    ! [X25205,X25206,X25207] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25207,tc_HOL_Obool)),esk223_3(X25205,X25206,X25207)),X25206))
        | X25206 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25207,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25207,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X25207,tc_HOL_Obool),X25206)),X25205)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25207,tc_HOL_Obool)),esk223_3(X25205,X25206,X25207)),X25205))
        | X25206 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25207,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25207,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X25207,tc_HOL_Obool),X25206)),X25205)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])]) ).

fof(i_0_7611,plain,
    ! [X24825,X24826,X24827] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24827))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24826,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24825),X24827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24825),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24826),X24825),X24827))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24826,X24825)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).

fof(i_0_7612,plain,
    ! [X20765,X20766,X20767,X20768] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20768,tc_HOL_Obool)),X20767),X20766))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20768,tc_HOL_Obool)),X20767),X20765))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20768,tc_HOL_Obool)),X20767),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20768,tc_HOL_Obool)),X20766),X20765))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).

fof(i_0_7613,plain,
    ! [X33154,X33155,X33156] :
      ( ( ~ c_List_Olist__ex(tc_Int_Oint,X33156,c_List_Oupto(X33155,X33154))
        | ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X33156),X33155,X33154) )
      & ( c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X33156),X33155,X33154)
        | c_List_Olist__ex(tc_Int_Oint,X33156,c_List_Oupto(X33155,X33154)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5614])]) ).

fof(i_0_7614,plain,
    ! [X24552,X24553] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X24553),hAPP(c_Nat_OSuc,X24552)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24552),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X24552)),X24553),
    inference(variable_rename,[status(thm)],[fact_max__Suc2]) ).

cnf(i_0_7615,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(c_Wellfounded_Omeasure(X4),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5566]) ).

fof(i_0_7616,plain,
    ! [X29322,X29323,X29324,X29325] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29325,X29325),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29324),X29323)),X29322) = hAPP(hAPP(c_Relation_Orel__comp(X29325,X29325,X29325),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29325,X29325),tc_HOL_Obool),X29324),X29322)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29325,X29325),tc_HOL_Obool),X29323),X29322)),
    inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).

fof(i_0_7617,plain,
    ! [X25103,X25104,X25105] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25105,tc_HOL_Obool),tc_HOL_Obool)),X25104),X25103))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25105,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25105,tc_HOL_Obool),X25104)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25105,tc_HOL_Obool),X25103))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).

fof(i_0_7618,plain,
    ! [X21599,X21600,X21601] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X21601,tc_HOL_Obool),tc_HOL_Obool)),X21600),X21599))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21601,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21601,tc_HOL_Obool),X21599)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21601,tc_HOL_Obool),X21600))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).

fof(i_0_7619,plain,
    ! [X25048,X25049,X25050] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25050)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25050),hAPP(c_Groups_Oabs__class_Oabs(X25050),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25050),X25049),X25048))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25050),hAPP(c_Groups_Oabs__class_Oabs(X25050),X25049)),hAPP(c_Groups_Oabs__class_Oabs(X25050),X25048)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).

fof(i_0_7620,plain,
    ! [X25136,X25137,X25138] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25138)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25138),hAPP(c_Groups_Oabs__class_Oabs(X25138),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25138),X25137),X25136))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25138),hAPP(c_Groups_Oabs__class_Oabs(X25138),X25137)),hAPP(c_Groups_Oabs__class_Oabs(X25138),X25136)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).

cnf(i_0_7621,plain,
    c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orotate(X1,X2)),c_List_Orotate(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_5615]) ).

fof(i_0_7622,plain,
    ! [X24154,X24155,X24156,X24157,X24158] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24155),X24157))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24157),X24156))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24158,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24157,X24156)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24155,X24154)))
        | ~ class_Orderings_Oorder(X24158) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24156),X24154))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24157),X24156))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24158,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24157,X24156)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24155,X24154)))
        | ~ class_Orderings_Oorder(X24158) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24157),X24156))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24158,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24157,X24156)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24155,X24154)))
        | ~ class_Orderings_Oorder(X24158) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24155),X24157))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24158),X24156),X24154))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24158,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24157,X24156)),c_SetInterval_Oord__class_OatLeastAtMost(X24158,X24155,X24154)))
        | ~ class_Orderings_Oorder(X24158) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5616])])]) ).

fof(i_0_7623,plain,
    ! [X24492,X24493] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X24493),hAPP(c_Nat_OSuc,X24492)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X24492)),X24493),
    inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).

fof(i_0_7624,plain,
    ! [X20198,X20199,X20200] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20200),X20199))
      | ~ hBOOL(hAPP(hAPP(c_member(X20200),X20198),X20199))
      | hAPP(c_Finite__Set_Ocard(X20200),X20199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X20200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20200,tc_HOL_Obool)),X20199),hAPP(hAPP(c_Set_Oinsert(X20200),X20198),c_Orderings_Obot__class_Obot(tc_fun(X20200,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).

fof(i_0_7625,plain,
    ! [X30032,X30033,X30034,X30035,X30036,X30037,X30038] : hAPP(hAPP(c_List_Ozip(X30038,X30037),hAPP(hAPP(c_List_Olist__update(X30038,X30036),X30035),X30034)),hAPP(hAPP(c_List_Olist__update(X30037,X30033),X30035),X30032)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X30038,X30037),hAPP(hAPP(c_List_Ozip(X30038,X30037),X30036),X30033)),X30035),hAPP(hAPP(c_Product__Type_OPair(X30038,X30037),X30034),X30032)),
    inference(variable_rename,[status(thm)],[fact_zip__update]) ).

fof(i_0_7626,plain,
    ! [X20972,X20973,X20974,X20975,X20976] :
      ( ~ c_Fun_Oinj__on(X20976,X20975,X20974,c_Orderings_Otop__class_Otop(tc_fun(X20976,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X20976,X20975,X20974),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20976,tc_HOL_Obool)),X20973),X20972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20975,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20976,X20975,X20974),X20973)),hAPP(c_Set_Oimage(X20976,X20975,X20974),X20972)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).

fof(i_0_7627,plain,
    ! [X19813,X19814,X19815,X19816,X19817] :
      ( ~ c_Fun_Oinj__on(X19817,X19816,X19815,c_Orderings_Otop__class_Otop(tc_fun(X19817,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19817,X19816,X19815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19817,tc_HOL_Obool)),X19814),X19813)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19816,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19817,X19816,X19815),X19814)),hAPP(c_Set_Oimage(X19817,X19816,X19815),X19813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).

fof(i_0_7628,plain,
    ! [X17697,X17698,X17699,X17700] :
      ( ~ c_Fun_Oinj__on(X17700,X17699,X17698,X17697)
      | hAPP(c_Set_Oimage(X17699,X17700,c_Fun_Othe__inv__into(X17700,X17699,X17697,X17698)),hAPP(c_Set_Oimage(X17700,X17699,X17698),X17697)) = X17697 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).

fof(i_0_7629,plain,
    ! [X33092,X33093,X33094,X33095,X33096,X33097] : c_Nitpick_Opair__box_Opair__box__rec(X33097,X33096,X33095,X33094,c_Nitpick_Opair__box_OPairBox(X33097,X33096,X33093,X33092)) = hAPP(hAPP(X33094,X33093),X33092),
    inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).

fof(i_0_7630,plain,
    ! [X33086,X33087,X33088,X33089,X33090,X33091] : c_Nitpick_Opair__box_Opair__box__case(X33091,X33090,X33089,X33088,c_Nitpick_Opair__box_OPairBox(X33091,X33090,X33087,X33086)) = hAPP(hAPP(X33088,X33087),X33086),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(i_0_7631,plain,
    ! [X33997,X33998,X33999,X34000,X34001] :
      ( ~ class_Groups_Ocomm__monoid__mult(X34001)
      | ~ class_Rings_Odvd(X34001)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34000),X33999))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X34000,tc_HOL_Obool)),X33998),X33999))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34001),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X34000,X34001),X33997),X33998)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X34000,X34001),X33997),X33999))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset])]) ).

fof(i_0_7632,plain,
    ! [X32264,X32265,X32266,X32267,X32268] : hAPP(hAPP(c_List_Ozip(X32268,X32267),c_List_OtakeWhile(X32268,X32266,X32265)),X32264) = c_List_OtakeWhile(tc_prod(X32268,X32267),hAPP(c_Fun_Ocomp(X32268,tc_HOL_Obool,tc_prod(X32268,X32267),X32266),c_Product__Type_Ofst(X32268,X32267)),hAPP(hAPP(c_List_Ozip(X32268,X32267),X32265),X32264)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst]) ).

cnf(i_0_7633,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5617]) ).

cnf(i_0_7634,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5618]) ).

cnf(i_0_7635,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk363_2(X2,X1)),esk363_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5619]) ).

cnf(i_0_7636,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5620]) ).

fof(i_0_7637,plain,
    ! [X22892,X22893,X22894] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22894),X22893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22892))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22892)),X22894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22892)),X22893))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).

cnf(i_0_7638,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId(X3)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_5556]) ).

cnf(i_0_7639,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5621]) ).

fof(i_0_7640,plain,
    ! [X20815,X20816,X20817,X20818] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20818,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20818,tc_HOL_Obool)),X20817),X20816)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20818,tc_HOL_Obool)),X20815),X20816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20818,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20818,tc_HOL_Obool)),X20817),X20816)),X20815),
    inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).

fof(i_0_7641,plain,
    ! [X20786,X20787,X20788,X20789] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20789,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20789,tc_HOL_Obool)),X20788),X20787)),X20786) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20789,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20789,tc_HOL_Obool)),X20788),X20786)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20789,tc_HOL_Obool)),X20787),X20786)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(i_0_7642,plain,
    ! [X20811,X20812,X20813,X20814] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20814,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20814,tc_HOL_Obool)),X20813),X20812)),X20811) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20814,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20814,tc_HOL_Obool)),X20813),X20811)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20814,tc_HOL_Obool)),X20812),X20811)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(i_0_7643,plain,
    ! [X20790,X20791,X20792,X20793] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20793,tc_HOL_Obool)),X20792),X20791)),X20790) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20793,tc_HOL_Obool)),X20792),X20790)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20793,tc_HOL_Obool)),X20791),X20790)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(i_0_7644,plain,
    ! [X19635,X19636,X19637,X19638] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19638,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19638,tc_HOL_Obool)),X19637),X19636)),X19635) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19638,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19638,tc_HOL_Obool)),X19637),X19635)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19638,tc_HOL_Obool)),X19636),X19635)),
    inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).

fof(i_0_7645,plain,
    ! [X24424,X24425,X24426] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_3(X24424,X24425,X24426)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24426)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),X24426) = X24425
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24424))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24426)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk188_3(X24424,X24425,X24426)),X24424))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),X24426) = X24425
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24424))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24426)) )
      & ( X24425 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk188_3(X24424,X24425,X24426)),esk187_3(X24424,X24425,X24426))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),X24426) = X24425
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24425),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24424))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24426)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I3_J])])])]) ).

fof(i_0_7646,plain,
    ! [X24419,X24420,X24421] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_3(X24419,X24420,X24421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24421)))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),X24421) = X24420
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24421)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_3(X24419,X24420,X24421)),X24419))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),X24421) = X24420
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24421)) )
      & ( X24420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk186_3(X24419,X24420,X24421)),esk185_3(X24419,X24420,X24421))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),X24421) = X24420
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24420),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24421)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I3_J])])])]) ).

fof(i_0_7647,plain,
    ! [X30688,X30689,X30690,X30691] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30691),X30690)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30689)),X30688)))
      | hAPP(hAPP(c_List_Otake(X30689),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30691),X30690)),X30688) = hAPP(hAPP(c_List_Oappend(X30689),hAPP(hAPP(c_List_Otake(X30689),X30691),X30688)),hAPP(hAPP(c_List_Otake(X30689),X30690),hAPP(hAPP(c_List_Odrop(X30689),X30691),X30688))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).

fof(i_0_7648,plain,
    ! [X22745,X22746,X22747] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22747),esk132_3(X22745,X22746,X22747)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22747,tc_HOL_Obool)),X22746),X22745)))
        | hAPP(c_Finite__Set_Ocard(X22747),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22747,tc_HOL_Obool)),X22746),X22745)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22747),X22746)),hAPP(c_Finite__Set_Ocard(X22747),X22745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22747),X22745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22747),X22746)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X22747),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22747,tc_HOL_Obool)),X22746),X22745)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22747),X22746)),hAPP(c_Finite__Set_Ocard(X22747),X22745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22747),X22745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22747),X22746)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral])])])]) ).

cnf(i_0_7649,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3) = hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_5622]) ).

cnf(i_0_7650,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5623]) ).

fof(i_0_7651,plain,
    ! [X21456,X21457,X21458] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21458),X21457))
      | ~ hBOOL(hAPP(hAPP(c_member(X21458),X21456),X21457))
      | hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21458,tc_HOL_Obool)),X21457),hAPP(hAPP(c_Set_Oinsert(X21458),X21456),c_Orderings_Obot__class_Obot(tc_fun(X21458,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X21458),X21457) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).

fof(i_0_7652,plain,
    ! [X28678,X28679,X28680,X28681,X28682,X28683] :
      ( ~ c_Finite__Set_Ofolding(X28683,X28682,X28681,X28680)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28683),X28679))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28683),X28678))
      | hAPP(c_Fun_Ocomp(X28682,X28682,X28682,hAPP(X28680,X28678)),hAPP(X28680,X28679)) = hAPP(c_Fun_Ocomp(X28682,X28682,X28682,hAPP(X28680,X28679)),hAPP(X28680,X28678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).

fof(i_0_7653,plain,
    ! [X32304,X32305] :
      ( X32305 = c_List_Olist_ONil(X32304)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32304),X32305))
      | c_List_OtakeWhile(X32304,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32304),c_fNot),hAPP(hAPP(c_COMBC(X32304,X32304,tc_HOL_Obool),c_fequal),c_List_Olast(X32304,X32305))),X32305) = c_List_Obutlast(X32304,X32305) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).

fof(i_0_7654,plain,
    ! [X21892,X21893,X21894,X21895] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21895,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21894,tc_fun(X21895,tc_HOL_Obool)),X21893),X21892)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21894,tc_fun(X21895,tc_HOL_Obool)),X21893),hAPP(hAPP(c_COMBB(tc_fun(X21895,tc_HOL_Obool),tc_fun(X21895,tc_HOL_Obool),X21894),c_Groups_Ouminus__class_Ouminus(tc_fun(X21895,tc_HOL_Obool))),X21892)),
    inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).

fof(i_0_7655,plain,
    ! [X21888,X21889,X21890,X21891] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21891,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21890,tc_fun(X21891,tc_HOL_Obool)),X21889),X21888)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21890,tc_fun(X21891,tc_HOL_Obool)),X21889),hAPP(hAPP(c_COMBB(tc_fun(X21891,tc_HOL_Obool),tc_fun(X21891,tc_HOL_Obool),X21890),c_Groups_Ouminus__class_Ouminus(tc_fun(X21891,tc_HOL_Obool))),X21888)),
    inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).

fof(i_0_7656,plain,
    ! [X18150,X18151,X18152,X18153] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18153,X18152,hAPP(hAPP(c_Set_Oinsert(X18153),X18151),c_Orderings_Obot__class_Obot(tc_fun(X18153,tc_HOL_Obool)))),X18150))
        | X18151 = X18150 )
      & ( X18151 != X18150
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18153,X18152,hAPP(hAPP(c_Set_Oinsert(X18153),X18151),c_Orderings_Obot__class_Obot(tc_fun(X18153,tc_HOL_Obool)))),X18150)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).

fof(i_0_7657,plain,
    ! [X30943,X30944,X30945] :
      ( ~ class_Orderings_Olinorder(X30945)
      | hBOOL(hAPP(hAPP(c_member(X30945),X30944),hAPP(c_List_Oset(X30945),X30943)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30945,X30945,c_COMBI(X30945),X30944,X30943) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30945,X30945,c_COMBI(X30945)),X30944),X30943) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5624])]) ).

fof(i_0_7658,plain,
    ! [X26936,X26937,X26938,X26939,X26940] :
      ( ( ~ c_Relation_Oirrefl(X26937,X26936)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26937,X26937)),hAPP(hAPP(c_Product__Type_OPair(X26937,X26937),X26938),X26938)),X26936)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X26940,X26940)),hAPP(hAPP(c_Product__Type_OPair(X26940,X26940),esk271_2(X26939,X26940)),esk271_2(X26939,X26940))),X26939))
        | c_Relation_Oirrefl(X26940,X26939) ) ),
    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_5625])])])])]) ).

fof(i_0_7659,plain,
    ! [X28600,X28601,X28602,X28603,X28604,X28605] :
      ( ~ c_Finite__Set_Ofolding(X28605,X28604,X28603,X28602)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28605),X28601))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28605),X28600))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28605,tc_HOL_Obool)),X28601),X28600) != c_Orderings_Obot__class_Obot(tc_fun(X28605,tc_HOL_Obool))
      | hAPP(X28602,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28605,tc_HOL_Obool)),X28601),X28600)) = hAPP(c_Fun_Ocomp(X28604,X28604,X28604,hAPP(X28602,X28601)),hAPP(X28602,X28600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).

fof(i_0_7660,plain,
    ! [X23537,X23538,X23539,X23541,X23542,X23543,X23544] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23537),esk156_3(X23537,X23538,X23539))),X23538))
        | X23537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23537),hAPP(c_Nat_OSuc,esk156_3(X23537,X23538,X23539)))))
        | X23537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( hBOOL(hAPP(X23539,esk156_3(X23537,X23538,X23539)))
        | X23537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23537),esk156_3(X23537,X23538,X23539))),X23538))
        | hBOOL(hAPP(X23539,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23537),hAPP(c_Nat_OSuc,esk156_3(X23537,X23538,X23539)))))
        | hBOOL(hAPP(X23539,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( hBOOL(hAPP(X23539,esk156_3(X23537,X23538,X23539)))
        | hBOOL(hAPP(X23539,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23538),X23537))) )
      & ( X23541 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23543,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23543,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23542),X23541))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23541),X23544)),X23542))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23541),hAPP(c_Nat_OSuc,X23544))))
        | ~ hBOOL(hAPP(X23543,X23544))
        | hBOOL(hAPP(X23543,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23542),X23541))) ) ),
    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_split__div_H])])])])])]) ).

fof(i_0_7661,plain,
    ! [X20195,X20196,X20197] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20197),X20196))
      | hAPP(c_Finite__Set_Ocard(X20197),hAPP(hAPP(c_Set_Oinsert(X20197),X20195),X20196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X20197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20197,tc_HOL_Obool)),X20196),hAPP(hAPP(c_Set_Oinsert(X20197),X20195),c_Orderings_Obot__class_Obot(tc_fun(X20197,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).

fof(i_0_7662,plain,
    ! [X28383,X28384,X28385,X28386,X28387,X28388,X28389,X28390,X28391] :
      ( hAPP(c_Fun_Ocomp(X28390,X28389,X28388,X28387),X28386) != hAPP(c_Fun_Ocomp(X28385,X28389,X28388,X28384),X28383)
      | hAPP(X28387,hAPP(X28386,X28391)) = hAPP(X28384,hAPP(X28383,X28391)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).

fof(i_0_7663,plain,
    ! [X28374,X28375,X28376,X28377,X28378,X28379,X28380,X28381,X28382] :
      ( hAPP(c_Fun_Ocomp(X28382,X28381,X28380,X28379),X28378) != hAPP(c_Fun_Ocomp(X28377,X28381,X28380,X28376),X28375)
      | hAPP(X28379,hAPP(X28378,X28374)) = hAPP(X28376,hAPP(X28375,X28374)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).

fof(i_0_7664,plain,
    ! [X30915,X30916,X30917,X30918] :
      ( ~ class_Orderings_Olinorder(X30918)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30918,X30918,c_COMBI(X30918)),X30917),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30918,X30918,c_COMBI(X30918)),X30916),X30915)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30918,X30918,c_COMBI(X30918)),X30916),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30918,X30918,c_COMBI(X30918)),X30917),X30915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).

fof(i_0_7665,plain,
    ! [X28337,X28338,X28339,X28340,X28341,X28342,X28343] :
      ( hAPP(c_Fun_Ocomp(X28343,X28342,X28341,X28340),X28339) != hAPP(c_Fun_Ocomp(X28342,X28342,X28341,c_Fun_Oid(X28342)),X28338)
      | hAPP(X28340,hAPP(X28339,X28337)) = hAPP(X28338,X28337) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).

fof(i_0_7666,plain,
    ! [X31682,X31683,X31684,X31685] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31684),c_List_Olinorder__class_Osort__key(X31684,X31685,X31683,X31682)))
        | hBOOL(hAPP(c_List_Odistinct(X31684),X31682))
        | ~ class_Orderings_Olinorder(X31685) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31684),X31682))
        | hBOOL(hAPP(c_List_Odistinct(X31684),c_List_Olinorder__class_Osort__key(X31684,X31685,X31683,X31682)))
        | ~ class_Orderings_Olinorder(X31685) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sort])])]) ).

fof(i_0_7667,plain,
    ! [X25838,X25839,X25840,X25841] :
      ( ~ c_Equiv__Relations_Oequiv(X25841,X25840,X25839)
      | ~ hBOOL(hAPP(hAPP(c_member(X25841),X25838),X25840))
      | hBOOL(hAPP(hAPP(c_member(X25841),X25838),hAPP(c_Relation_OImage(X25841,X25841,X25839),hAPP(hAPP(c_Set_Oinsert(X25841),X25838),c_Orderings_Obot__class_Obot(tc_fun(X25841,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).

fof(i_0_7668,plain,
    ! [X19799,X19800,X19801,X19802,X19803] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19802),hAPP(X19801,X19800)),hAPP(c_Set_Oimage(X19803,X19802,X19801),X19799)))
        | hBOOL(hAPP(hAPP(c_member(X19803),X19800),X19799))
        | ~ c_Fun_Oinj__on(X19803,X19802,X19801,c_Orderings_Otop__class_Otop(tc_fun(X19803,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19803),X19800),X19799))
        | hBOOL(hAPP(hAPP(c_member(X19802),hAPP(X19801,X19800)),hAPP(c_Set_Oimage(X19803,X19802,X19801),X19799)))
        | ~ c_Fun_Oinj__on(X19803,X19802,X19801,c_Orderings_Otop__class_Otop(tc_fun(X19803,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])]) ).

fof(i_0_7669,plain,
    ! [X21902,X21903,X21904,X21905,X21906] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21906)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21905,tc_HOL_Obool)),X21904),X21903))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21905,X21906),X21903),X21902)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21905,X21906),X21904),X21902))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).

fof(i_0_7670,plain,
    ! [X21154,X21155,X21156,X21157,X21158] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21158)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21157,tc_HOL_Obool)),X21156),X21155))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21157,X21158),X21156),X21154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21157,X21158),X21155),X21154))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).

fof(i_0_7671,plain,
    ! [X27556,X27557,X27558] :
      ( ~ c_Wellfounded_Owf(X27558,X27557)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27558,X27558)),hAPP(hAPP(c_Product__Type_OPair(X27558,X27558),X27556),X27556)),X27557)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5626])]) ).

fof(i_0_7672,plain,
    ! [X27545,X27546,X27547] :
      ( ~ c_Wellfounded_Owf(X27547,X27546)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27547,X27547)),hAPP(hAPP(c_Product__Type_OPair(X27547,X27547),X27545),X27545)),X27546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5627])]) ).

fof(i_0_7673,plain,
    ! [X21397,X21398,X21399,X21400,X21401] :
      ( ( X21401 != c_Orderings_Obot__class_Obot(tc_fun(X21400,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21400,tc_fun(X21399,tc_HOL_Obool)),X21401),hAPP(hAPP(c_COMBB(tc_fun(X21399,tc_HOL_Obool),tc_fun(X21399,tc_HOL_Obool),X21400),hAPP(c_Set_Oinsert(X21399),X21398)),X21397)) = c_Orderings_Obot__class_Obot(tc_fun(X21399,tc_HOL_Obool)) )
      & ( X21401 = c_Orderings_Obot__class_Obot(tc_fun(X21400,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21400,tc_fun(X21399,tc_HOL_Obool)),X21401),hAPP(hAPP(c_COMBB(tc_fun(X21399,tc_HOL_Obool),tc_fun(X21399,tc_HOL_Obool),X21400),hAPP(c_Set_Oinsert(X21399),X21398)),X21397)) = hAPP(hAPP(c_Set_Oinsert(X21399),X21398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21400,tc_fun(X21399,tc_HOL_Obool)),X21401),X21397)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).

fof(i_0_7674,plain,
    ! [X21390,X21391,X21392,X21393,X21394] :
      ( ( X21394 != c_Orderings_Obot__class_Obot(tc_fun(X21393,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X21392),X21391),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21393,tc_fun(X21392,tc_HOL_Obool)),X21394),X21390)) = hAPP(hAPP(c_Set_Oinsert(X21392),X21391),c_Orderings_Obot__class_Obot(tc_fun(X21392,tc_HOL_Obool))) )
      & ( X21394 = c_Orderings_Obot__class_Obot(tc_fun(X21393,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X21392),X21391),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21393,tc_fun(X21392,tc_HOL_Obool)),X21394),X21390)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21393,tc_fun(X21392,tc_HOL_Obool)),X21394),hAPP(hAPP(c_COMBB(tc_fun(X21392,tc_HOL_Obool),tc_fun(X21392,tc_HOL_Obool),X21393),hAPP(c_Set_Oinsert(X21392),X21391)),X21390)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).

cnf(i_0_7675,plain,
    c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5628]) ).

fof(i_0_7676,plain,
    ! [X18464,X18465,X18466,X18467,X18468] :
      ( ~ class_Rings_Osemiring__0(X18468)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18468),X18467),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18466,X18468),X18465),X18464)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18466,X18468),hAPP(hAPP(c_COMBB(X18468,X18468,X18466),hAPP(c_Groups_Otimes__class_Otimes(X18468),X18467)),X18465)),X18464) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).

fof(i_0_7677,plain,
    ! [X27091,X27092,X27093,X27094,X27095] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27095,X27094)),hAPP(X27095,X27093)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27092,X27092)),hAPP(hAPP(c_Product__Type_OPair(X27092,X27092),X27094),X27093)),c_Wellfounded_Omlex__prod(X27092,X27095,X27091))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_7678,plain,
    ! [X19663,X19664,X19665,X19666,X19667] : hAPP(c_Set_Oimage(X19667,X19666,hAPP(hAPP(c_COMBB(X19665,X19666,X19667),X19664),X19663)),c_Orderings_Otop__class_Otop(tc_fun(X19667,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X19665,X19666,X19664),hAPP(c_Set_Oimage(X19667,X19665,X19663),c_Orderings_Otop__class_Otop(tc_fun(X19667,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_7679,plain,
    ! [X32378,X32379] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk444_2(X32378,X32379)),esk445_2(X32378,X32379)))
        | c_List_Olinorder__class_Osorted(X32379,X32378)
        | ~ class_Orderings_Olinorder(X32379) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk445_2(X32378,X32379)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32379)),X32378)))
        | c_List_Olinorder__class_Osorted(X32379,X32378)
        | ~ class_Orderings_Olinorder(X32379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32379),hAPP(hAPP(c_List_Onth(X32379),X32378),esk444_2(X32378,X32379))),hAPP(hAPP(c_List_Onth(X32379),X32378),esk445_2(X32378,X32379))))
        | c_List_Olinorder__class_Osorted(X32379,X32378)
        | ~ class_Orderings_Olinorder(X32379) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__monoI])])])]) ).

fof(i_0_7680,plain,
    ! [X32109,X32110,X32111,X32112] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32110,X32109)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32110)),X32109)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32112),X32111))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32110),hAPP(hAPP(c_List_Onth(X32110),X32109),X32112)),hAPP(hAPP(c_List_Onth(X32110),X32109),X32111)))
        | ~ class_Orderings_Olinorder(X32110) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk439_2(X32109,X32110)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32110)),X32109)))
        | c_List_Olinorder__class_Osorted(X32110,X32109)
        | ~ class_Orderings_Olinorder(X32110) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk440_2(X32109,X32110)),esk439_2(X32109,X32110)))
        | c_List_Olinorder__class_Osorted(X32110,X32109)
        | ~ class_Orderings_Olinorder(X32110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32110),hAPP(hAPP(c_List_Onth(X32110),X32109),esk440_2(X32109,X32110))),hAPP(hAPP(c_List_Onth(X32110),X32109),esk439_2(X32109,X32110))))
        | c_List_Olinorder__class_Osorted(X32110,X32109)
        | ~ class_Orderings_Olinorder(X32110) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__equals__nth__mono])])])])]) ).

fof(i_0_7681,plain,
    ! [X21490,X21491,X21492,X21493,X21494,X21495] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21495),X21494),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21493,tc_fun(X21495,tc_HOL_Obool)),X21492),X21491)))
      | hBOOL(hAPP(hAPP(c_member(X21495),X21494),hAPP(X21491,X21490)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21493),X21490),X21492)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5629])]) ).

fof(i_0_7682,plain,
    ! [X21484,X21485,X21486,X21487,X21488,X21489] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21489),X21488),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21487,tc_fun(X21489,tc_HOL_Obool)),X21486),X21485)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21487),X21484),X21486))
      | hBOOL(hAPP(hAPP(c_member(X21489),X21488),hAPP(X21485,X21484))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).

fof(i_0_7683,plain,
    ! [X30822,X30823,X30824] :
      ( ~ class_Groups_Omonoid__add(X30824)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30824),X30823),hAPP(c_List_Ofoldl(X30824,X30824,c_Groups_Oplus__class_Oplus(X30824),c_Groups_Ozero__class_Ozero(X30824)),X30822)) = hAPP(c_List_Ofoldl(X30824,X30824,c_Groups_Oplus__class_Oplus(X30824),X30823),X30822) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).

fof(i_0_7684,plain,
    ! [X30050,X30051,X30052,X30053,X30054,X30055] :
      ( X30055 = X30054
      | hAPP(hAPP(c_List_Olist__update(X30053,hAPP(hAPP(c_List_Olist__update(X30053,X30052),X30055),X30051)),X30054),X30050) = hAPP(hAPP(c_List_Olist__update(X30053,hAPP(hAPP(c_List_Olist__update(X30053,X30052),X30054),X30050)),X30055),X30051) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).

fof(i_0_7685,plain,
    ! [X29304,X29305,X29306] : hAPP(hAPP(c_Relation_Orel__comp(X29306,X29306,X29306),X29305),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29306,X29306),tc_HOL_Obool),X29304),X29305)) = hAPP(hAPP(c_Relation_Orel__comp(X29306,X29306,X29306),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29306,X29306),tc_HOL_Obool),X29304),X29305)),X29305),
    inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).

fof(i_0_7686,plain,
    ! [X34277,X34278,X34279,X34280,X34281,X34282,X34283,X34284,X34285,X34286] :
      ( ( X34277 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34279,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ epred1_3(X34279,X34278,X34277) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34281))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34281),X34277))
        | X34278 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34277),X34280)),X34281)
        | hBOOL(hAPP(X34279,X34280))
        | ~ epred1_3(X34279,X34278,X34277) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34277),X34283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34283),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34278 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34277),X34282)),X34283)
        | hBOOL(hAPP(X34279,X34282))
        | ~ epred1_3(X34279,X34278,X34277) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | X34284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X34284,X34285,X34286)),X34284))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk571_3(X34284,X34285,X34286))),esk572_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34284),esk574_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X34284,X34285,X34286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( X34285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34284),esk573_3(X34284,X34285,X34286))),esk574_3(X34284,X34285,X34286))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) )
      & ( ~ hBOOL(hAPP(X34286,esk573_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,esk571_3(X34284,X34285,X34286)))
        | ~ hBOOL(hAPP(X34286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34286,X34285,X34284) ) ),
    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)],[i_0_5226])])])])])]) ).

fof(i_0_7687,plain,
    ! [X21997,X21998,X21999] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21999),X21998))
      | hAPP(c_Finite__Set_Ocard(X21999),hAPP(hAPP(c_Set_Oinsert(X21999),X21997),X21998)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21999,tc_HOL_Obool)),X21998),hAPP(hAPP(c_Set_Oinsert(X21999),X21997),c_Orderings_Obot__class_Obot(tc_fun(X21999,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).

cnf(i_0_7688,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5630]) ).

cnf(i_0_7689,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5631]) ).

cnf(i_0_7690,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5632]) ).

cnf(i_0_7691,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5633]) ).

fof(i_0_7692,plain,
    ! [X23904,X23905,X23906,X23907] :
      ( ~ class_Fields_Olinordered__field(X23907)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23907),X23906),X23905))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23907),c_Groups_Ozero__class_Ozero(X23907)),X23904))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23907),c_Groups_Ozero__class_Ozero(X23907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23907),X23905),X23906)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23907),X23904),X23905)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23907),X23904),X23906))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).

fof(i_0_7693,plain,
    ! [X23956,X23957,X23958,X23959] :
      ( ~ class_Fields_Olinordered__field(X23959)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23959),X23958),X23957))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23959),c_Groups_Ozero__class_Ozero(X23959)),X23956))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23959),c_Groups_Ozero__class_Ozero(X23959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23959),X23957),X23958)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23959),X23956),X23957)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23959),X23956),X23958))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).

fof(i_0_7694,plain,
    ! [X27247,X27248,X27249] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27249,X27249),tc_HOL_Obool)),X27248),X27247))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27249,tc_HOL_Obool)),hAPP(c_Relation_OField(X27249),X27248)),hAPP(c_Relation_OField(X27249),X27247))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).

fof(i_0_7695,plain,
    ! [X28664,X28665,X28666,X28667,X28668,X28669] :
      ( ~ c_Finite__Set_Ofolding(X28669,X28668,X28667,X28666)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28669),X28665))
      | hAPP(c_Fun_Ocomp(X28668,X28668,X28668,hAPP(X28667,X28664)),hAPP(X28666,X28665)) = hAPP(c_Fun_Ocomp(X28668,X28668,X28668,hAPP(X28666,X28665)),hAPP(X28667,X28664)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).

fof(i_0_7696,plain,
    ! [X34291,X34292,X34293,X34294,X34295,X34296,X34297,X34298,X34299,X34300] :
      ( ( X34291 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34293,X34292))
        | ~ epred2_3(X34293,X34292,X34291) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34291))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34295))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34295),X34291))
        | X34292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34291),X34294)),X34295)
        | hBOOL(hAPP(X34293,X34295))
        | ~ epred2_3(X34293,X34292,X34291) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34291),X34297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34297),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34291),X34296)),X34297)
        | hBOOL(hAPP(X34293,X34297))
        | ~ epred2_3(X34293,X34292,X34291) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | X34298 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X34298,X34299,X34300)),X34298))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk575_3(X34298,X34299,X34300))),esk576_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34298),esk578_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X34298,X34299,X34300)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( X34299 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34298),esk577_3(X34298,X34299,X34300))),esk578_3(X34298,X34299,X34300))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) )
      & ( ~ hBOOL(hAPP(X34300,esk578_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,esk576_3(X34298,X34299,X34300)))
        | ~ hBOOL(hAPP(X34300,X34299))
        | epred2_3(X34300,X34299,X34298) ) ),
    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)],[i_0_5225])])])])])]) ).

fof(i_0_7697,plain,
    ! [X21627,X21628,X21629,X21630,X21631] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21631,tc_fun(X21630,tc_HOL_Obool)),X21629),hAPP(hAPP(c_COMBB(tc_fun(X21630,tc_HOL_Obool),tc_fun(X21630,tc_HOL_Obool),X21631),hAPP(c_Set_Oinsert(X21630),X21628)),X21627)) = hAPP(hAPP(c_Set_Oinsert(X21630),X21628),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21631,tc_fun(X21630,tc_HOL_Obool)),X21629),X21627)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(i_0_7698,plain,
    ! [X21632,X21633,X21634,X21635,X21636] : hAPP(hAPP(c_Set_Oinsert(X21636),X21635),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21634,tc_fun(X21636,tc_HOL_Obool)),X21633),X21632)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21634,tc_fun(X21636,tc_HOL_Obool)),X21633),hAPP(hAPP(c_COMBB(tc_fun(X21636,tc_HOL_Obool),tc_fun(X21636,tc_HOL_Obool),X21634),hAPP(c_Set_Oinsert(X21636),X21635)),X21632)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(i_0_7699,plain,
    ! [X20250,X20251,X20252,X20253] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20253),X20252)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20251),X20252)),X20250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20253),X20251)),X20252)),X20250),
    inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(i_0_7700,plain,
    ! [X32259,X32260,X32261,X32262,X32263] : hAPP(hAPP(c_List_Ozip(X32263,X32262),X32261),c_List_OtakeWhile(X32262,X32260,X32259)) = c_List_OtakeWhile(tc_prod(X32263,X32262),hAPP(c_Fun_Ocomp(X32262,tc_HOL_Obool,tc_prod(X32263,X32262),X32260),c_Product__Type_Osnd(X32263,X32262)),hAPP(hAPP(c_List_Ozip(X32263,X32262),X32261),X32259)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd]) ).

cnf(i_0_7701,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5634]) ).

fof(i_0_7702,plain,
    ! [X32715,X32716,X32717,X32718,X32719] :
      ( ( X32719 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X32718,X32717,X32716,X32715),X32719) = c_Lazy__Sequence_Ohit__bound(X32717) )
      & ( X32719 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X32718,X32717,X32716,X32715),X32719) = c_Lazy__Sequence_Ohb__bind(X32718,X32717,hAPP(X32716,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32719),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X32718,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32717))),X32715),X32719)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).

fof(i_0_7703,plain,
    ! [X19668,X19669,X19670,X19671] :
      ( ~ c_Fun_Oinj__on(X19671,X19670,X19669,c_Orderings_Otop__class_Otop(tc_fun(X19671,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X19671,tc_fun(X19668,X19670),hAPP(hAPP(c_COMBB(X19670,tc_fun(X19668,X19670),X19671),c_COMBK(X19670,X19668)),X19669),c_Orderings_Otop__class_Otop(tc_fun(X19671,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_7704,plain,
    ! [X21606,X21607,X21608] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21608,tc_HOL_Obool)),X21607),X21606) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X21608,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X21608,tc_HOL_Obool)),X21607),hAPP(hAPP(c_Set_Oinsert(tc_fun(X21608,tc_HOL_Obool)),X21606),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X21608,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Int__eq__Inter]) ).

fof(i_0_7705,plain,
    ! [X25177,X25178,X25179] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25179,tc_HOL_Obool)),X25178),X25177) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X25179,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X25179,tc_HOL_Obool)),X25178),hAPP(hAPP(c_Set_Oinsert(tc_fun(X25179,tc_HOL_Obool)),X25177),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25179,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).

fof(i_0_7706,plain,
    ! [X23908,X23909,X23910,X23911] :
      ( ~ class_Fields_Olinordered__field(X23911)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23911),X23910),X23909))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23911),X23908),c_Groups_Ozero__class_Ozero(X23911)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23911),c_Groups_Ozero__class_Ozero(X23911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23911),X23910),X23909)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23911),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23911),X23908),X23910)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23911),X23908),X23909))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).

fof(i_0_7707,plain,
    ! [X23952,X23953,X23954,X23955] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X23955)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23955),X23954),X23953))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23955),X23952),c_Groups_Ozero__class_Ozero(X23955)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23955),c_Groups_Ozero__class_Ozero(X23955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23955),X23954),X23953)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23955),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23955),X23952),X23954)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23955),X23952),X23953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).

fof(i_0_7708,plain,
    ! [X32720,X32721,X32722,X32723,X32724] :
      ( ( X32724 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X32723,X32722,X32721,X32720),X32724) = c_Lazy__Sequence_Oempty(X32722) )
      & ( X32724 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X32723,X32722,X32721,X32720),X32724) = hAPP(c_Lazy__Sequence_Obind(X32723,X32722,hAPP(X32721,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32724),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X32723,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32722)),X32720),X32724)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).

fof(i_0_7709,plain,
    ! [X29974,X29975,X29976,X29977,X29978] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29978),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29977)),X29976)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29978),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29975)),X29974)))
      | hAPP(hAPP(c_List_Onth(tc_prod(X29977,X29975)),hAPP(hAPP(c_List_Ozip(X29977,X29975),X29976),X29974)),X29978) = hAPP(hAPP(c_Product__Type_OPair(X29977,X29975),hAPP(hAPP(c_List_Onth(X29977),X29976),X29978)),hAPP(hAPP(c_List_Onth(X29975),X29974),X29978)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).

fof(i_0_7710,plain,
    ! [X24898,X24899,X24900] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24899),X24898)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24899),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24900),X24899),X24898))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24900,X24899)),
    inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).

cnf(i_0_7711,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5583]) ).

fof(i_0_7712,plain,
    ! [X22982,X22983,X22984] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22984),X22983))
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X22984)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22982),X22983)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22982),X22984)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22983),X22984)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22982),X22983))
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X22984)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22982),X22983)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22984),X22983)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22982),X22983))
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X22984)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22982),X22983)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22984),X22983)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5635])])]) ).

cnf(i_0_7713,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5636]) ).

fof(i_0_7714,plain,
    ! [X30492,X30493,X30494,X30495,X30496] : hAPP(hAPP(c_List_Olist__update(X30496,hAPP(hAPP(c_List_Oappend(X30496),X30495),hAPP(hAPP(c_List_Olist_OCons(X30496),X30494),X30493))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30496)),X30495)),X30492) = hAPP(hAPP(c_List_Oappend(X30496),X30495),hAPP(hAPP(c_List_Olist_OCons(X30496),X30492),X30493)),
    inference(variable_rename,[status(thm)],[fact_list__update__length]) ).

cnf(i_0_7715,plain,
    ( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Oupt(X3,X2))),X1) = hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5637]) ).

fof(i_0_7716,plain,
    ! [X29615,X29616] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29616),tc_List_Olist(X29616)),tc_HOL_Obool)),c_List_Olistrel1(X29616,c_Transitive__Closure_Ortrancl(X29616,X29615))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29616),c_List_Olistrel1(X29616,X29615)))),
    inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(i_0_7717,plain,
    ! [X28985,X28986,X28987] : c_Transitive__Closure_Ortrancl(X28987,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28987,X28987),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28987,X28986)),c_Transitive__Closure_Ortrancl(X28987,X28985))) = c_Transitive__Closure_Ortrancl(X28987,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28987,X28987),tc_HOL_Obool)),X28986),X28985)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

fof(i_0_7718,plain,
    ! [X34136,X34137,X34138,X34139] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34139),X34137),X34138)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34139),X34136),X34138)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34137),X34136))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34138),X34136))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34138),X34137))
        | ~ class_Divides_Osemiring__div(X34139) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34137),X34136))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34139),X34137),X34138)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34139),X34136),X34138)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34138),X34136))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34139),X34138),X34137))
        | ~ class_Divides_Osemiring__div(X34139) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).

cnf(i_0_7719,plain,
    hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate(X1,X3),X4)) = hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_5638]) ).

cnf(i_0_7720,plain,
    ( c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,X3) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5639]) ).

fof(i_0_7721,plain,
    ! [X34084,X34085,X34086,X34087,X34089] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34086),X34084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34086),esk569_3(X34084,X34085,X34086)),c_Groups_Ozero__class_Ozero(X34086))))
        | ~ hBOOL(hAPP(X34085,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34086),X34084),X34087)))
        | ~ class_Rings_Odvd(X34086)
        | ~ class_Rings_Osemiring__0(X34086) )
      & ( hBOOL(hAPP(X34085,esk569_3(X34084,X34085,X34086)))
        | ~ hBOOL(hAPP(X34085,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34086),X34084),X34087)))
        | ~ class_Rings_Odvd(X34086)
        | ~ class_Rings_Osemiring__0(X34086) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34086),X34084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34086),X34089),c_Groups_Ozero__class_Ozero(X34086))))
        | ~ hBOOL(hAPP(X34085,X34089))
        | hBOOL(hAPP(X34085,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34086),X34084),esk570_3(X34084,X34085,X34086))))
        | ~ class_Rings_Odvd(X34086)
        | ~ class_Rings_Osemiring__0(X34086) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).

fof(i_0_7722,plain,
    ! [X31286,X31287,X31288] : hAPP(hAPP(c_List_Ozip(X31288,X31287),hAPP(hAPP(c_List_Omap(tc_prod(X31288,X31287),X31288),c_Product__Type_Ofst(X31288,X31287)),X31286)),hAPP(hAPP(c_List_Omap(tc_prod(X31288,X31287),X31287),c_Product__Type_Osnd(X31288,X31287)),X31286)) = X31286,
    inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(i_0_7723,plain,
    ! [X28547,X28548,X28549,X28550,X28551,X28552,X28553,X28554] :
      ( ~ class_Groups_Ocomm__monoid__mult(X28554)
      | ~ c_Fun_Oinj__on(X28553,X28552,X28551,X28550)
      | X28549 != hAPP(c_Set_Oimage(X28553,X28552,X28551),X28550)
      | X28548 != hAPP(c_Fun_Ocomp(X28552,X28554,X28553,X28547),X28551)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28552,X28554),X28547),X28549) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28553,X28554),X28548),X28550) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).

fof(i_0_7724,plain,
    ! [X22207,X22208,X22209] :
      ( ~ class_Rings_Olinordered__ring(X22209)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22209),c_Groups_Ozero__class_Ozero(X22209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22209),X22208),X22208)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22209),X22207),X22207)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).

fof(i_0_7725,plain,
    ! [X29058,X29059] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X29059),X29058)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29059),X29058)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29059),X29058))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X29059),X29058)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le])]) ).

fof(i_0_7726,plain,
    ! [X28617,X28618,X28619,X28620,X28621,X28622] :
      ( ~ c_Finite__Set_Ofolding(X28622,X28621,X28620,X28619)
      | hAPP(c_Fun_Ocomp(X28621,X28621,X28621,hAPP(X28620,X28618)),hAPP(X28620,X28617)) = hAPP(c_Fun_Ocomp(X28621,X28621,X28621,hAPP(X28620,X28617)),hAPP(X28620,X28618)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).

fof(i_0_7727,plain,
    ! [X27867,X27868,X27869,X27870,X27871] : hAPP(hAPP(c_Product__Type_OSigma(X27871,X27870),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27871,tc_HOL_Obool)),X27869),X27868)),X27867) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27871,X27870),X27869),X27867)),hAPP(hAPP(c_Product__Type_OSigma(X27871,X27870),X27868),X27867)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(i_0_7728,plain,
    ! [X27843,X27844,X27845,X27846,X27847] : hAPP(hAPP(c_Product__Type_OSigma(X27847,X27846),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27847,tc_HOL_Obool)),X27845),X27844)),X27843) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27847,X27846),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27847,X27846),X27845),X27843)),hAPP(hAPP(c_Product__Type_OSigma(X27847,X27846),X27844),X27843)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(i_0_7729,plain,
    ! [X27884,X27885,X27886,X27887,X27888] : hAPP(hAPP(c_Product__Type_OSigma(X27888,X27887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27888,tc_HOL_Obool)),X27886),X27885)),X27884) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27888,X27887),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27888,X27887),X27886),X27884)),hAPP(hAPP(c_Product__Type_OSigma(X27888,X27887),X27885),X27884)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

cnf(i_0_7730,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5640]) ).

fof(i_0_7731,plain,
    ! [X30501,X30502,X30503,X30504] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30504),X30503),hAPP(c_List_Oset(X30504),c_List_Obutlast(X30504,X30502))))
        | hBOOL(hAPP(hAPP(c_member(X30504),X30503),hAPP(c_List_Oset(X30504),c_List_Obutlast(X30504,hAPP(hAPP(c_List_Oappend(X30504),X30502),X30501))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30504),X30503),hAPP(c_List_Oset(X30504),c_List_Obutlast(X30504,X30501))))
        | hBOOL(hAPP(hAPP(c_member(X30504),X30503),hAPP(c_List_Oset(X30504),c_List_Obutlast(X30504,hAPP(hAPP(c_List_Oappend(X30504),X30502),X30501))))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).

fof(i_0_7732,plain,
    ! [X27406,X27407,X27408] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27408,X27408),tc_HOL_Obool)),X27407),X27406))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27408,tc_HOL_Obool)),c_Wellfounded_Oacc(X27408,X27406)),c_Wellfounded_Oacc(X27408,X27407))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).

fof(i_0_7733,plain,
    ! [X30919,X30920,X30921,X30922,X30923,X30924] :
      ( ~ class_Orderings_Olinorder(X30924)
      | hAPP(X30923,X30922) = hAPP(X30923,X30921)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30920,X30924,X30923),X30921),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30920,X30924,X30923),X30922),X30919)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30920,X30924,X30923),X30922),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30920,X30924,X30923),X30921),X30919)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).

fof(i_0_7734,plain,
    ! [X33520,X33521,X33522,X33523] :
      ( hAPP(c_Set_Oimage(X33523,X33522,X33521),c_Orderings_Otop__class_Otop(tc_fun(X33523,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33522,tc_HOL_Obool))
      | hAPP(X33521,hAPP(c_Hilbert__Choice_Oinv__into(X33523,X33522,c_Orderings_Otop__class_Otop(tc_fun(X33523,tc_HOL_Obool)),X33521),X33520)) = X33520 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

fof(i_0_7735,plain,
    ! [X26534,X26535] :
      ( X26535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26534,X26535),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26534),X26535)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26534,X26535)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).

fof(i_0_7736,plain,
    ! [X21669,X21670,X21671,X21672,X21673,X21674] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21674,tc_fun(X21673,tc_HOL_Obool)),X21672),hAPP(hAPP(c_COMBB(X21671,tc_fun(X21673,tc_HOL_Obool),X21674),X21670),X21669)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21671,tc_fun(X21673,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21674,X21671,X21669),X21672)),X21670),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(i_0_7737,plain,
    ! [X21298,X21299,X21300,X21301,X21302,X21303] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21303,tc_fun(X21302,tc_HOL_Obool)),X21301),hAPP(hAPP(c_COMBB(X21300,tc_fun(X21302,tc_HOL_Obool),X21303),X21299),X21298)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21300,tc_fun(X21302,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21303,X21300,X21298),X21301)),X21299),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(i_0_7738,plain,
    ! [X21675,X21676,X21677,X21678,X21679,X21680] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21680,tc_fun(X21679,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21678,X21680,X21677),X21676)),X21675) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21678,tc_fun(X21679,tc_HOL_Obool)),X21676),hAPP(hAPP(c_COMBB(X21680,tc_fun(X21679,tc_HOL_Obool),X21678),X21675),X21677)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(i_0_7739,plain,
    ! [X21286,X21287,X21288,X21289,X21290,X21291] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21291,tc_fun(X21290,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21289,X21291,X21288),X21287)),X21286) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21289,tc_fun(X21290,tc_HOL_Obool)),X21287),hAPP(hAPP(c_COMBB(X21291,tc_fun(X21290,tc_HOL_Obool),X21289),X21286),X21288)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(i_0_7740,plain,
    ! [X26871,X26872] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26872,X26871),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26872),X26871)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26872,X26871)))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).

cnf(i_0_7741,plain,
    hAPP(c_List_Orotate(X1,X2),X3) = hAPP(c_List_Orotate(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3),
    inference(split_conjunct,[status(thm)],[i_0_5641]) ).

fof(i_0_7742,plain,
    ! [X19021,X19022,X19023] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19023,tc_HOL_Obool)),X19022),X19021))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19023,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19023,tc_HOL_Obool)),X19021)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19023,tc_HOL_Obool)),X19022))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).

fof(i_0_7743,plain,
    ! [X17728,X17729,X17730] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17730),X17729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17730,tc_HOL_Obool)),X17729),hAPP(c_Set_Oimage(X17730,X17730,X17728),X17729)))
      | c_Fun_Oinj__on(X17730,X17730,X17728,X17729) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_7744,plain,
    ! [X27824,X27825,X27826] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27826,X27825),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27826,X27825),c_Orderings_Otop__class_Otop(tc_fun(X27826,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27825,tc_HOL_Obool),X27826),X27824))) = hAPP(hAPP(c_Product__Type_OSigma(X27826,X27825),c_Orderings_Otop__class_Otop(tc_fun(X27826,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27825,tc_HOL_Obool),X27826),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27825,tc_HOL_Obool)),X27824))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(i_0_7745,plain,
    ! [X27821,X27822,X27823] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27823,X27822),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27823,X27822),X27821),hAPP(c_COMBK(tc_fun(X27822,tc_HOL_Obool),X27823),c_Orderings_Otop__class_Otop(tc_fun(X27822,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X27823,X27822),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27823,tc_HOL_Obool)),X27821)),hAPP(c_COMBK(tc_fun(X27822,tc_HOL_Obool),X27823),c_Orderings_Otop__class_Otop(tc_fun(X27822,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(i_0_7746,plain,
    ! [X29608,X29609,X29610,X29611] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29611),X29610),c_Wellfounded_Oacc(X29611,X29609)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29611)),X29608),c_Wellfounded_Oacc(tc_List_Olist(X29611),c_List_Olistrel1(X29611,X29609))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29611)),hAPP(hAPP(c_List_Olist_OCons(X29611),X29610),X29608)),c_Wellfounded_Oacc(tc_List_Olist(X29611),c_List_Olistrel1(X29611,X29609)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).

fof(i_0_7747,plain,
    ! [X23900,X23901,X23902,X23903] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23903),X23901),X23902)),X23900))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23903),X23900),X23902)),X23901))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),X23902),c_Groups_Ozero__class_Ozero(X23903)))
        | ~ class_Fields_Olinordered__field(X23903) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23903),X23900),X23902)),X23901))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23903),X23901),X23902)),X23900))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23903),X23902),c_Groups_Ozero__class_Ozero(X23903)))
        | ~ class_Fields_Olinordered__field(X23903) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).

fof(i_0_7748,plain,
    ! [X23960,X23961,X23962,X23963] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23963),X23961),X23962)),X23960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23963),X23960),X23962)),X23961))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23963),X23962),c_Groups_Ozero__class_Ozero(X23963)))
        | ~ class_Fields_Olinordered__field(X23963) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23963),X23960),X23962)),X23961))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23963),X23961),X23962)),X23960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23963),X23962),c_Groups_Ozero__class_Ozero(X23963)))
        | ~ class_Fields_Olinordered__field(X23963) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).

cnf(i_0_7749,plain,
    ( c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1)))
    | ~ c_Relation_Ototal__on(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5573]) ).

fof(i_0_7750,plain,
    ! [X26933,X26934,X26935] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26935,tc_fun(X26935,tc_HOL_Obool))),X26934),X26933))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26935,tc_HOL_Obool)),c_Wellfounded_Oaccp(X26935,X26933)),c_Wellfounded_Oaccp(X26935,X26934))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).

fof(i_0_7751,plain,
    ! [X28758,X28759,X28760,X28761,X28762,X28763] :
      ( ~ c_Finite__Set_Ofolding__idem(X28763,X28762,X28761,X28760)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28763),X28759))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28763,tc_HOL_Obool)),X28758),X28759))
      | hAPP(c_Fun_Ocomp(X28762,X28762,X28762,hAPP(X28760,X28759)),hAPP(X28760,X28758)) = hAPP(X28760,X28759) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).

fof(i_0_7752,plain,
    ! [X30951,X30952,X30953] :
      ( ~ class_Orderings_Olinorder(X30953)
      | ~ hBOOL(hAPP(hAPP(c_member(X30953),X30952),hAPP(c_List_Oset(X30953),X30951)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30953,X30953,c_COMBI(X30953),X30952,X30951) = X30951 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).

fof(i_0_7753,plain,
    ! [X23545,X23546,X23547] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23547),X23546)),X23545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23547),hAPP(c_Nat_OSuc,X23546))))
        | X23546 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23545),X23547)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23547)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23547),X23546)),X23545))
        | X23546 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23545),X23547)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23547)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23547),hAPP(c_Nat_OSuc,X23546))))
        | X23546 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23545),X23547)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23547)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).

fof(i_0_7754,plain,
    ! [X17760,X17761,X17762,X17763,X17764] :
      ( ~ class_Groups_Oab__group__add(X17764)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17763),X17762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17763,tc_HOL_Obool)),X17761),X17762))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17763,X17764),X17760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17763,tc_HOL_Obool)),X17762),X17761)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17764),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17763,X17764),X17760),X17762)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17763,X17764),X17760),X17761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).

cnf(i_0_7755,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5642]) ).

fof(i_0_7756,plain,
    ! [X30704,X30705,X30706] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30706),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30705)),X30704)))
      | X30704 = hAPP(hAPP(c_List_Oappend(X30705),hAPP(hAPP(c_List_Otake(X30705),X30706),X30704)),hAPP(hAPP(c_List_Olist_OCons(X30705),hAPP(hAPP(c_List_Onth(X30705),X30704),X30706)),hAPP(hAPP(c_List_Odrop(X30705),hAPP(c_Nat_OSuc,X30706)),X30704))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).

cnf(i_0_7757,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5578]) ).

cnf(i_0_7758,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5579]) ).

cnf(i_0_7759,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5580]) ).

cnf(i_0_7760,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5581]) ).

fof(i_0_7761,plain,
    ! [X27208,X27209] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27209),X27208)),c_Wellfounded_Oless__than))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27209),X27208)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27209),X27208))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X27209),X27208)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).

cnf(i_0_7762,plain,
    c_Int_Opred(c_Int_OBit0(X1)) = c_Int_OBit1(c_Int_Opred(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5643]) ).

fof(i_0_7763,plain,
    ! [X17054,X17055,X17056,X17057,X17058,X17059] : hAPP(c_Set_Oimage(X17059,X17058,X17057),hAPP(c_Set_Oimage(X17056,X17059,X17055),X17054)) = hAPP(c_Set_Oimage(X17056,X17058,hAPP(hAPP(c_COMBB(X17059,X17058,X17056),X17057),X17055)),X17054),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_7764,plain,
    ! [X23564,X23565,X23566,X23567,X23568] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23567),X23564),X23566))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23567,X23568),X23565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23567,tc_HOL_Obool)),X23566),hAPP(hAPP(c_Set_Oinsert(X23567),X23564),c_Orderings_Obot__class_Obot(tc_fun(X23567,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23567,X23568),X23565),X23566)),hAPP(X23565,X23564))
        | hAPP(X23565,X23564) = c_Groups_Ozero__class_Ozero(X23568)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23567),X23566))
        | ~ class_Fields_Ofield(X23568) )
      & ( hBOOL(hAPP(hAPP(c_member(X23567),X23564),X23566))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23567,X23568),X23565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23567,tc_HOL_Obool)),X23566),hAPP(hAPP(c_Set_Oinsert(X23567),X23564),c_Orderings_Obot__class_Obot(tc_fun(X23567,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23567,X23568),X23565),X23566)
        | hAPP(X23565,X23564) = c_Groups_Ozero__class_Ozero(X23568)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23567),X23566))
        | ~ class_Fields_Ofield(X23568) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5644])])]) ).

cnf(i_0_7765,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5585]) ).

fof(i_0_7766,plain,
    ! [X31214,X31215,X31216,X31217,X31218] :
      ( hAPP(hAPP(c_List_Omap(X31218,X31217),X31216),X31215) != hAPP(hAPP(c_List_Omap(X31218,X31217),X31216),X31214)
      | ~ c_Fun_Oinj__on(X31218,X31217,X31216,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31218,tc_HOL_Obool)),hAPP(c_List_Oset(X31218),X31215)),hAPP(c_List_Oset(X31218),X31214)))
      | X31215 = X31214 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).

fof(i_0_7767,plain,
    ! [X31209,X31210,X31211,X31212,X31213] :
      ( ( hAPP(hAPP(c_List_Omap(X31213,X31212),X31211),X31210) != hAPP(hAPP(c_List_Omap(X31213,X31212),X31211),X31209)
        | X31210 = X31209
        | ~ c_Fun_Oinj__on(X31213,X31212,X31211,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31213,tc_HOL_Obool)),hAPP(c_List_Oset(X31213),X31210)),hAPP(c_List_Oset(X31213),X31209))) )
      & ( X31210 != X31209
        | hAPP(hAPP(c_List_Omap(X31213,X31212),X31211),X31210) = hAPP(hAPP(c_List_Omap(X31213,X31212),X31211),X31209)
        | ~ c_Fun_Oinj__on(X31213,X31212,X31211,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31213,tc_HOL_Obool)),hAPP(c_List_Oset(X31213),X31210)),hAPP(c_List_Oset(X31213),X31209))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).

fof(i_0_7768,plain,
    ! [X22969,X22970,X22971] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22969),X22970))
        | hBOOL(hAPP(X22971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22970)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22969))))
        | ~ hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22970),X22969))
        | hBOOL(hAPP(X22971,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22970),X22969))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22969),X22970))
        | hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) )
      & ( ~ hBOOL(hAPP(X22971,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22969),X22970))
        | hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22970),X22969))
        | ~ hBOOL(hAPP(X22971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22970)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22969))))
        | hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) )
      & ( ~ hBOOL(hAPP(X22971,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X22971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22970)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22969))))
        | hBOOL(hAPP(X22971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22970),X22969)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).

fof(i_0_7769,plain,
    ! [X31386,X31387,X31388,X31389] :
      ( ~ hBOOL(hAPP(c_List_Olistsp(X31389,X31388),X31387))
      | ~ hBOOL(hAPP(c_List_Olistsp(X31389,X31386),X31387))
      | hBOOL(hAPP(c_List_Olistsp(X31389,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31389,tc_HOL_Obool)),X31388),X31386)),X31387)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).

fof(i_0_7770,plain,
    ! [X33819,X33820] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33820),X33819))
      | c_Fun_Obij__betw(tc_Nat_Onat,X33820,esk538_2(X33819,X33820),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X33820),X33819)),X33819) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite__1])])]) ).

cnf(i_0_7771,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5645]) ).

fof(i_0_7772,plain,
    ! [X29270,X29271,X29272,X29273,X29274] :
      ( ~ c_Relation_Osingle__valued(X29274,X29273,hAPP(c_Relation_Oconverse(X29273,X29274),X29272))
      | hAPP(c_Relation_OImage(X29273,X29274,X29272),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29273,tc_HOL_Obool)),X29271),X29270)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29274,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29273,X29274,X29272),X29271)),hAPP(c_Relation_OImage(X29273,X29274,X29272),X29270)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).

fof(i_0_7773,plain,
    ! [X23851,X23852,X23853,X23854,X23855] :
      ( ~ class_Fields_Olinordered__field(X23855)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23855),c_Groups_Ozero__class_Ozero(X23855)),X23854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23855),X23854),X23853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23855),c_Groups_Ozero__class_Ozero(X23855)),X23852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23855),X23852),X23851))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23855),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23855),X23854),X23851)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23855),X23853),X23852))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

fof(i_0_7774,plain,
    ! [X23856,X23857,X23858,X23859,X23860] :
      ( ~ class_Fields_Olinordered__field(X23860)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23860),c_Groups_Ozero__class_Ozero(X23860)),X23859))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23860),X23859),X23858))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23860),c_Groups_Ozero__class_Ozero(X23860)),X23857))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23860),X23857),X23856))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23860),X23859),X23856)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23860),X23858),X23857))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_7775,plain,
    ! [X22550,X22551,X22552,X22553,X22554] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22554)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22554),X22553),X22552))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22554),X22551),X22550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22554),c_Groups_Ozero__class_Ozero(X22554)),X22552))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22554),c_Groups_Ozero__class_Ozero(X22554)),X22551))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22554),X22553),X22551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22554),X22552),X22550))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).

fof(i_0_7776,plain,
    ! [X22555,X22556,X22557,X22558,X22559] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22559)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22559),X22558),X22557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22559),X22556),X22555))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22559),c_Groups_Ozero__class_Ozero(X22559)),X22558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22559),c_Groups_Ozero__class_Ozero(X22559)),X22556))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22559),X22558),X22556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22559),X22557),X22555))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).

fof(i_0_7777,plain,
    ! [X22565,X22566,X22567,X22568,X22569] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22569)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),X22568),X22567))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),X22566),X22565))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),c_Groups_Ozero__class_Ozero(X22569)),X22568))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),c_Groups_Ozero__class_Ozero(X22569)),X22566))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22569),X22568),X22566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22569),X22567),X22565))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).

fof(i_0_7778,plain,
    ! [X22560,X22561,X22562,X22563,X22564] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22564)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22564),X22563),X22562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22564),X22561),X22560))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22564),c_Groups_Ozero__class_Ozero(X22564)),X22563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22564),c_Groups_Ozero__class_Ozero(X22564)),X22561))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22564),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22564),X22563),X22561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22564),X22562),X22560))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).

fof(i_0_7779,plain,
    ! [X23861,X23862,X23863,X23864,X23865] :
      ( ~ class_Fields_Olinordered__field(X23865)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23865),c_Groups_Ozero__class_Ozero(X23865)),X23864))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23865),X23864),X23863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23865),c_Groups_Ozero__class_Ozero(X23865)),X23862))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23865),X23862),X23861))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23865),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23865),X23864),X23861)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23865),X23863),X23862))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_7780,plain,
    ! [X22280,X22281,X22282,X22283,X22284] :
      ( ~ class_Rings_Oordered__semiring(X22284)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),X22283),X22282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),X22281),X22280))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),c_Groups_Ozero__class_Ozero(X22284)),X22283))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),c_Groups_Ozero__class_Ozero(X22284)),X22281))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22284),X22283),X22281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22284),X22282),X22280))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_7781,plain,
    ! [X22285,X22286,X22287,X22288,X22289] :
      ( ~ class_Rings_Oordered__semiring(X22289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),X22288),X22287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),X22286),X22285))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),c_Groups_Ozero__class_Ozero(X22289)),X22287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),c_Groups_Ozero__class_Ozero(X22289)),X22286))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22289),X22288),X22286)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22289),X22287),X22285))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

cnf(i_0_7782,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5646]) ).

fof(i_0_7783,plain,
    ! [X17544,X17545,X17546,X17547,X17548] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17547),X17545),X17546))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17547,X17548),X17544),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17547,tc_HOL_Obool)),X17546),hAPP(hAPP(c_Set_Oinsert(X17547),X17545),c_Orderings_Obot__class_Obot(tc_fun(X17547,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17548),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17547,X17548),X17544),X17546)),hAPP(X17544,X17545))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17547),X17546))
        | ~ class_Groups_Oab__group__add(X17548) )
      & ( hBOOL(hAPP(hAPP(c_member(X17547),X17545),X17546))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17547,X17548),X17544),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17547,tc_HOL_Obool)),X17546),hAPP(hAPP(c_Set_Oinsert(X17547),X17545),c_Orderings_Obot__class_Obot(tc_fun(X17547,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17547,X17548),X17544),X17546)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17547),X17546))
        | ~ class_Groups_Oab__group__add(X17548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5647])])]) ).

fof(i_0_7784,plain,
    ! [X17549,X17550,X17551,X17552,X17553] :
      ( ~ class_Rings_Oring(X17553)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17552),X17551))
      | ~ hBOOL(hAPP(hAPP(c_member(X17552),X17550),X17551))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17552,X17553),X17549),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17552,tc_HOL_Obool)),X17551),hAPP(hAPP(c_Set_Oinsert(X17552),X17550),c_Orderings_Obot__class_Obot(tc_fun(X17552,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17553),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17552,X17553),X17549),X17551)),hAPP(X17549,X17550)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).

fof(i_0_7785,plain,
    ! [X23750,X23751,X23752] :
      ( ~ class_Fields_Ofield(X23752)
      | X23751 = c_Groups_Oone__class_Oone(X23752)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23752),hAPP(c_Power_Opower__class_Opower(X23752),X23751)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23750)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23752),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23752),hAPP(hAPP(c_Power_Opower__class_Opower(X23752),X23751),X23750)),c_Groups_Oone__class_Oone(X23752))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23752),X23751),c_Groups_Oone__class_Oone(X23752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).

fof(i_0_7786,plain,
    ! [X31234,X31235] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X31235)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31235),hAPP(c_Groups_Oabs__class_Oabs(X31235),hAPP(c_List_Omonoid__add__class_Olistsum(X31235),X31234))),hAPP(c_List_Omonoid__add__class_Olistsum(X31235),hAPP(hAPP(c_List_Omap(X31235,X31235),c_Groups_Oabs__class_Oabs(X31235)),X31234)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).

cnf(i_0_7787,plain,
    hAPP(c_List_Oset(X1),c_List_Oconcat(X1,X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5648]) ).

fof(i_0_7788,plain,
    ! [X33829,X33830] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33830),X33829))
      | c_Fun_Obij__betw(tc_Nat_Onat,X33830,esk540_2(X33829,X33830),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X33830),X33829)),X33829) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite])])]) ).

fof(i_0_7789,plain,
    ! [X33832,X33833] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33833),X33832))
      | c_Fun_Obij__betw(X33833,tc_Nat_Onat,esk541_2(X33832,X33833),X33832,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X33833),X33832))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__finite__nat])])]) ).

fof(i_0_7790,plain,
    ! [X23144,X23145,X23146] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23146)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23145),X23144)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23145),X23146)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23144),X23146)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_7791,plain,
    ! [X23147,X23148,X23149,X23150,X23151] :
      ( ~ class_Groups_Ocomm__monoid__add(X23151)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23150),X23149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23149),X23148))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23151),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23151),X23147),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23150),X23149))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23151),X23147),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23149),X23148))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23151),X23147),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23150),X23148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).

fof(i_0_7792,plain,
    ! [X23152,X23153,X23154,X23155,X23156] :
      ( ~ class_Groups_Oab__group__add(X23156)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23155),X23154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23154),X23153))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23156),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23156),X23152),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23155),X23153))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23156),X23152),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23155),X23154))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23156),X23152),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23154),X23153)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).

fof(i_0_7793,plain,
    ! [X22570,X22571,X22572,X22573] :
      ( ~ class_Rings_Olinordered__semiring(X22573)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22573),X22572),X22571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22573),X22570),X22571)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22573),c_Groups_Ozero__class_Ozero(X22573)),X22571))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),X22570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).

fof(i_0_7794,plain,
    ! [X22574,X22575,X22576,X22577] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22577)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22577),X22576),X22575)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22577),X22574),X22575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22577),c_Groups_Ozero__class_Ozero(X22577)),X22575))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22576),X22574)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).

fof(i_0_7795,plain,
    ! [X22603,X22604,X22605,X22606] :
      ( ~ class_Rings_Olinordered__semidom(X22606)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22606),hAPP(hAPP(c_Power_Opower__class_Opower(X22606),X22605),X22604)),hAPP(hAPP(c_Power_Opower__class_Opower(X22606),X22603),X22604)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22606),c_Groups_Ozero__class_Ozero(X22606)),X22603))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22606),X22605),X22603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).

fof(i_0_7796,plain,
    ! [X22578,X22579,X22580,X22581] :
      ( ~ class_Rings_Olinordered__semiring(X22581)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22581),X22580),X22579)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22581),X22580),X22578)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22581),c_Groups_Ozero__class_Ozero(X22581)),X22580))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22579),X22578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).

fof(i_0_7797,plain,
    ! [X22582,X22583,X22584,X22585] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22585)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22585),X22584),X22583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22585),X22584),X22582)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22585),c_Groups_Ozero__class_Ozero(X22585)),X22584))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22585),X22583),X22582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).

fof(i_0_7798,plain,
    ! [X22320,X22321,X22322,X22323] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22323),X22322),X22321)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22323),X22322),X22320)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),X22321),X22320))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),c_Groups_Ozero__class_Ozero(X22323)),X22322))
        | ~ class_Rings_Olinordered__ring__strict(X22323) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),X22321),X22320))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22323),X22322),X22321)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22323),X22322),X22320)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22323),c_Groups_Ozero__class_Ozero(X22323)),X22322))
        | ~ class_Rings_Olinordered__ring__strict(X22323) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

fof(i_0_7799,plain,
    ! [X22586,X22587,X22588,X22589] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22589)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22589),X22588),X22587)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22589),X22586),X22587)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22589),c_Groups_Ozero__class_Ozero(X22589)),X22587))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),X22586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).

fof(i_0_7800,plain,
    ! [X22590,X22591,X22592,X22593] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22593)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22593),X22592),X22591)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22593),X22592),X22590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22593),c_Groups_Ozero__class_Ozero(X22593)),X22592))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),X22591),X22590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).

fof(i_0_7801,plain,
    ! [X22542,X22543,X22544,X22545] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22544),X22543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22544),X22542)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),X22543),X22542))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22545),c_Groups_Ozero__class_Ozero(X22545)),X22544))
        | ~ class_Rings_Olinordered__ring__strict(X22545) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),X22543),X22542))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22544),X22543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22544),X22542)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22545),c_Groups_Ozero__class_Ozero(X22545)),X22544))
        | ~ class_Rings_Olinordered__ring__strict(X22545) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).

cnf(i_0_7802,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oconcat(X1,X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5649]) ).

fof(i_0_7803,plain,
    ! [X17711,X17712,X17713,X17714] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17714),X17713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17714,tc_HOL_Obool)),X17713),X17712))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17714,tc_Nat_Onat),X17711),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17714,tc_HOL_Obool)),X17712),X17713)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17714,tc_Nat_Onat),X17711),X17712)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17714,tc_Nat_Onat),X17711),X17713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).

fof(i_0_7804,plain,
    ! [X19051,X19052,X19053,X19055] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19053),esk42_3(X19051,X19052,X19053)),X19052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19053),hAPP(c_Finite__Set_Ofold1(X19053,c_Orderings_Oord__class_Omin(X19053)),X19052)),X19051))
        | X19052 = c_Orderings_Obot__class_Obot(tc_fun(X19053,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19053),X19052))
        | ~ class_Orderings_Olinorder(X19053) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19053),esk42_3(X19051,X19052,X19053)),X19051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19053),hAPP(c_Finite__Set_Ofold1(X19053,c_Orderings_Oord__class_Omin(X19053)),X19052)),X19051))
        | X19052 = c_Orderings_Obot__class_Obot(tc_fun(X19053,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19053),X19052))
        | ~ class_Orderings_Olinorder(X19053) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19053),X19055),X19052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19053),X19055),X19051))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19053),hAPP(c_Finite__Set_Ofold1(X19053,c_Orderings_Oord__class_Omin(X19053)),X19052)),X19051))
        | X19052 = c_Orderings_Obot__class_Obot(tc_fun(X19053,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19053),X19052))
        | ~ class_Orderings_Olinorder(X19053) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff])])])])]) ).

fof(i_0_7805,plain,
    ! [X19037,X19038,X19039,X19041] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19039),esk40_3(X19037,X19038,X19039)),X19038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19039),hAPP(c_Finite__Set_Ofold1(X19039,c_Orderings_Oord__class_Omin(X19039)),X19038)),X19037))
        | X19038 = c_Orderings_Obot__class_Obot(tc_fun(X19039,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19039),X19038))
        | ~ class_Orderings_Olinorder(X19039) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19039),esk40_3(X19037,X19038,X19039)),X19037))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19039),hAPP(c_Finite__Set_Ofold1(X19039,c_Orderings_Oord__class_Omin(X19039)),X19038)),X19037))
        | X19038 = c_Orderings_Obot__class_Obot(tc_fun(X19039,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19039),X19038))
        | ~ class_Orderings_Olinorder(X19039) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19039),X19041),X19038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19039),X19041),X19037))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19039),hAPP(c_Finite__Set_Ofold1(X19039,c_Orderings_Oord__class_Omin(X19039)),X19038)),X19037))
        | X19038 = c_Orderings_Obot__class_Obot(tc_fun(X19039,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19039),X19038))
        | ~ class_Orderings_Olinorder(X19039) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__below__iff])])])])]) ).

fof(i_0_7806,plain,
    ! [X21478,X21479,X21480,X21481,X21482,X21483] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21483,tc_fun(X21482,tc_HOL_Obool)),X21481),X21480),X21479))
      | hBOOL(hAPP(hAPP(X21480,X21478),X21479))
      | ~ hBOOL(hAPP(hAPP(c_member(X21483),X21478),X21481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5650])]) ).

fof(i_0_7807,plain,
    ! [X21472,X21473,X21474,X21475,X21476,X21477] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21477,tc_fun(X21476,tc_HOL_Obool)),X21475),X21474),X21473))
      | ~ hBOOL(hAPP(hAPP(c_member(X21477),X21472),X21475))
      | hBOOL(hAPP(hAPP(X21474,X21472),X21473)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).

fof(i_0_7808,plain,
    ! [X20386,X20387,X20388,X20389] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20389),hAPP(hAPP(c_Power_Opower__class_Opower(X20389),X20388),X20387)),hAPP(hAPP(c_Power_Opower__class_Opower(X20389),X20388),X20386)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20387),X20386))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20389),c_Groups_Oone__class_Oone(X20389)),X20388))
        | ~ class_Rings_Olinordered__semidom(X20389) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20387),X20386))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20389),hAPP(hAPP(c_Power_Opower__class_Opower(X20389),X20388),X20387)),hAPP(hAPP(c_Power_Opower__class_Opower(X20389),X20388),X20386)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20389),c_Groups_Oone__class_Oone(X20389)),X20388))
        | ~ class_Rings_Olinordered__semidom(X20389) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).

fof(i_0_7809,plain,
    ! [X20382,X20383,X20384,X20385] :
      ( ~ class_Rings_Olinordered__semidom(X20385)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20385),c_Groups_Oone__class_Oone(X20385)),X20384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20385),hAPP(hAPP(c_Power_Opower__class_Opower(X20385),X20384),X20383)),hAPP(hAPP(c_Power_Opower__class_Opower(X20385),X20384),X20382)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20383),X20382)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).

fof(i_0_7810,plain,
    ! [X20367,X20368,X20369,X20370] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20370),hAPP(hAPP(c_Power_Opower__class_Opower(X20370),X20369),X20368)),hAPP(hAPP(c_Power_Opower__class_Opower(X20370),X20369),X20367)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20368),X20367))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20370),c_Groups_Oone__class_Oone(X20370)),X20369))
        | ~ class_Rings_Olinordered__semidom(X20370) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20368),X20367))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20370),hAPP(hAPP(c_Power_Opower__class_Opower(X20370),X20369),X20368)),hAPP(hAPP(c_Power_Opower__class_Opower(X20370),X20369),X20367)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20370),c_Groups_Oone__class_Oone(X20370)),X20369))
        | ~ class_Rings_Olinordered__semidom(X20370) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).

fof(i_0_7811,plain,
    ! [X20363,X20364,X20365,X20366] :
      ( ~ class_Rings_Olinordered__semidom(X20366)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20366),c_Groups_Oone__class_Oone(X20366)),X20365))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20366),hAPP(hAPP(c_Power_Opower__class_Opower(X20366),X20365),X20364)),hAPP(hAPP(c_Power_Opower__class_Opower(X20366),X20365),X20363)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20364),X20363)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).

fof(i_0_7812,plain,
    ! [X30312,X30313,X30314] :
      ( X30314 = c_List_Olist_ONil(X30313)
      | hBOOL(hAPP(hAPP(c_member(X30313),hAPP(c_Product__Type_Ofst(X30313,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X30313,X30314),X30312))),hAPP(c_List_Oset(X30313),X30314))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).

fof(i_0_7813,plain,
    ! [X27935,X27936,X27937,X27938] : hAPP(c_Finite__Set_Ocard(tc_prod(X27938,X27937)),hAPP(hAPP(c_Product__Type_OSigma(X27938,X27937),hAPP(hAPP(c_Set_Oinsert(X27938),X27936),c_Orderings_Obot__class_Obot(tc_fun(X27938,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X27937,tc_HOL_Obool),X27938),X27935))) = hAPP(c_Finite__Set_Ocard(X27937),X27935),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).

cnf(i_0_7814,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5651]) ).

fof(i_0_7815,plain,
    ! [X26749,X26750,X26751,X26752,X26753] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26753,X26752,tc_HOL_Obool),X26751),hAPP(hAPP(c_Product__Type_OPair(X26753,X26752),X26750),X26749)))
      | hBOOL(hAPP(hAPP(X26751,X26750),X26749)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).

fof(i_0_7816,plain,
    ! [X26660,X26661,X26662] : c_Fun_Oinj__on(tc_prod(X26662,X26661),tc_prod(X26661,X26662),hAPP(c_Product__Type_Oprod_Oprod__case(X26662,X26661,tc_prod(X26661,X26662)),hAPP(c_COMBC(X26661,X26662,tc_prod(X26661,X26662)),c_Product__Type_OPair(X26661,X26662))),X26660),
    inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).

fof(i_0_7817,plain,
    ! [X25241,X25242,X25243] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25243),esk234_3(X25241,X25242,X25243)),X25242))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25243,tc_Nat_Onat),X25241),X25242)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25243),X25242)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X25241,esk234_3(X25241,X25242,X25243))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25243,tc_Nat_Onat),X25241),X25242)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25243),X25242)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat])])])]) ).

fof(i_0_7818,plain,
    ! [X22679,X22680,X22681,X22682] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22681,tc_Nat_Onat),X22679),X22680)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22681),X22682),X22680))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X22679,X22682)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22681),X22680)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22681),esk131_3(X22679,X22680,X22681)),X22680))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22681,tc_Nat_Onat),X22679),X22680)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22681),X22680)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X22679,esk131_3(X22679,X22680,X22681))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22681,tc_Nat_Onat),X22679),X22680)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22681),X22680)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff])])])])]) ).

fof(i_0_7819,plain,
    ! [X24173,X24174,X24175,X24176] :
      ( ~ class_Groups_Ocomm__monoid__add(X24176)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24176),X24175),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24174),hAPP(c_Nat_OSuc,X24173))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24176),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24176,tc_Nat_Onat),X24175),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24174,X24173)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).

fof(i_0_7820,plain,
    ! [X22339,X22340,X22341,X22342] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22342),X22341),X22340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22342),X22341),X22339)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),X22339),X22340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),X22341),c_Groups_Ozero__class_Ozero(X22342)))
        | ~ class_Rings_Olinordered__ring__strict(X22342) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),X22339),X22340))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22342),X22341),X22340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22342),X22341),X22339)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22342),X22341),c_Groups_Ozero__class_Ozero(X22342)))
        | ~ class_Rings_Olinordered__ring__strict(X22342) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_7821,plain,
    ! [X22546,X22547,X22548,X22549] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22549),X22548),X22547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22549),X22548),X22546)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22549),X22546),X22547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22549),X22548),c_Groups_Ozero__class_Ozero(X22549)))
        | ~ class_Rings_Olinordered__ring__strict(X22549) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22549),X22546),X22547))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22549),X22548),X22547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22549),X22548),X22546)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22549),X22548),c_Groups_Ozero__class_Ozero(X22549)))
        | ~ class_Rings_Olinordered__ring__strict(X22549) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).

fof(i_0_7822,plain,
    ! [X20753,X20754,X20755] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20755,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20755,tc_HOL_Obool)),X20754),X20753)),X20754)),
    inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).

fof(i_0_7823,plain,
    ! [X20756,X20757,X20758] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20758,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20758,tc_HOL_Obool)),X20757),X20756)),X20756)),
    inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).

fof(i_0_7824,plain,
    ! [X17841,X17842,X17843] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17843,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17843,tc_HOL_Obool)),X17842),X17841)),X17842)),
    inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).

fof(i_0_7825,plain,
    ! [X31258,X31259,X31260,X31261,X31262] :
      ( ~ class_Groups_Ocomm__monoid__add(X31262)
      | ~ hBOOL(hAPP(hAPP(c_member(X31261),X31260),hAPP(c_List_Oset(X31261),X31259)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31262),hAPP(hAPP(c_List_Omap(X31261,X31262),X31258),X31259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31262),hAPP(X31258,X31260)),hAPP(c_List_Omonoid__add__class_Olistsum(X31262),hAPP(hAPP(c_List_Omap(X31261,X31262),X31258),c_List_Oremove1(X31261,X31260,X31259)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).

fof(i_0_7826,plain,
    ! [X20778,X20779,X20780,X20781] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20781,tc_HOL_Obool)),X20780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20781,tc_HOL_Obool)),X20779),X20778)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20781,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20781,tc_HOL_Obool)),X20780),X20779)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20781,tc_HOL_Obool)),X20780),X20778)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).

fof(i_0_7827,plain,
    ! [X20803,X20804,X20805,X20806] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20806,tc_HOL_Obool)),X20805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20806,tc_HOL_Obool)),X20804),X20803)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20806,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20806,tc_HOL_Obool)),X20805),X20804)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20806,tc_HOL_Obool)),X20805),X20803)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(i_0_7828,plain,
    ! [X20782,X20783,X20784,X20785] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20785,tc_HOL_Obool)),X20784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20785,tc_HOL_Obool)),X20783),X20782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20785,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20785,tc_HOL_Obool)),X20784),X20783)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20785,tc_HOL_Obool)),X20784),X20782)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).

fof(i_0_7829,plain,
    ! [X20908,X20909,X20910,X20911] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20911,tc_HOL_Obool)),X20910),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20911,tc_HOL_Obool)),X20909),X20908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20911,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20911,tc_HOL_Obool)),X20910),X20909)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20911,tc_HOL_Obool)),X20910),X20908)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).

fof(i_0_7830,plain,
    ! [X20904,X20905,X20906,X20907] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20907,tc_HOL_Obool)),X20906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20907,tc_HOL_Obool)),X20905),X20904)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20907,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20907,tc_HOL_Obool)),X20906),X20905)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20907,tc_HOL_Obool)),X20906),X20904)),
    inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).

fof(i_0_7831,plain,
    ! [X27104,X27105,X27106,X27107,X27108,X27109] : c_Product__Type_Oprod_Oprod__rec(X27109,X27108,X27107,X27106,hAPP(hAPP(c_Product__Type_OPair(X27109,X27108),X27105),X27104)) = hAPP(hAPP(X27106,X27105),X27104),
    inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).

fof(i_0_7832,plain,
    ! [X32739,X32740,X32741,X32742,X32743] : hAPP(c_New__DSequence_Oneg__bind(X32743,X32742,X32741,X32740),X32739) = c_Lazy__Sequence_Ohb__bind(X32743,X32742,hAPP(X32741,X32739),hAPP(hAPP(c_COMBC(X32743,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32742))),X32740),X32739)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(i_0_7833,plain,
    ! [X23123,X23124,X23125,X23126] :
      ( ~ class_Groups_Ocomm__monoid__add(X23126)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23126),X23125),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23124)),hAPP(c_Nat_OSuc,X23123))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23126),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23126,tc_Nat_Onat),X23125),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23124),X23123)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).

fof(i_0_7834,plain,
    ! [X24184,X24185,X24186] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24186)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24185,X24184)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24185),X24186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24184),X24186)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).

cnf(i_0_7835,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5652]) ).

cnf(i_0_7836,plain,
    ( c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5582]) ).

cnf(i_0_7837,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5653]) ).

fof(i_0_7838,plain,
    ! [X25332,X25333,X25334,X25335] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25335),X25334),X25333))
        | ~ hBOOL(hAPP(hAPP(c_member(X25335),X25334),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25335,tc_HOL_Obool)),X25333),hAPP(c_Set_OCollect(X25335),X25332)))) )
      & ( hBOOL(hAPP(X25332,X25334))
        | ~ hBOOL(hAPP(hAPP(c_member(X25335),X25334),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25335,tc_HOL_Obool)),X25333),hAPP(c_Set_OCollect(X25335),X25332)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25335),X25334),X25333))
        | ~ hBOOL(hAPP(X25332,X25334))
        | hBOOL(hAPP(hAPP(c_member(X25335),X25334),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25335,tc_HOL_Obool)),X25333),hAPP(c_Set_OCollect(X25335),X25332)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).

fof(i_0_7839,plain,
    ! [X31843,X31844,X31845,X31846] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31846),X31845),hAPP(c_List_Oset(X31846),X31844)))
      | hBOOL(hAPP(X31843,X31845))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31846)),hAPP(c_List_Ofilter(X31846,X31843),X31844))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31846)),X31844))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5654])]) ).

fof(i_0_7840,plain,
    ! [X23118,X23119,X23120,X23121,X23122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23122),X23119),X23121))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23122),X23120),X23121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23122,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23122,X23121),X23120)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23122,X23119),X23118)))
        | ~ class_Orderings_Olinorder(X23122) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23122),X23120),X23118))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23122),X23120),X23121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23122,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23122,X23121),X23120)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23122,X23119),X23118)))
        | ~ class_Orderings_Olinorder(X23122) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_7841,plain,
    ! [X28752,X28753,X28754,X28755,X28756,X28757] :
      ( ~ c_Finite__Set_Ofolding__idem(X28757,X28756,X28755,X28754)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28757),X28753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28757),X28752))
      | hAPP(X28754,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28757,tc_HOL_Obool)),X28753),X28752)) = hAPP(c_Fun_Ocomp(X28756,X28756,X28756,hAPP(X28754,X28753)),hAPP(X28754,X28752)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).

cnf(i_0_7842,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5655]) ).

cnf(i_0_7843,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5656]) ).

cnf(i_0_7844,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))
    | c_List_OdropWhile(X2,X3,X1) != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_5657]) ).

fof(i_0_7845,plain,
    ! [X27705,X27706,X27707] :
      ( ~ c_Wellfounded_Owf(X27707,X27706)
      | ~ c_Wellfounded_Owf(X27707,X27705)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27707,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27707,X27707),X27706)),hAPP(c_Relation_ORange(X27707,X27707),X27705)) != c_Orderings_Obot__class_Obot(tc_fun(X27707,tc_HOL_Obool))
      | c_Wellfounded_Owf(X27707,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27707,X27707),tc_HOL_Obool)),X27706),X27705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).

fof(i_0_7846,plain,
    ! [X31594,X31595,X31596,X31597,X31598] :
      ( ~ c_Finite__Set_Ofun__left__comm(X31598,X31597,X31596)
      | hAPP(hAPP(c_Finite__Set_Ofold(X31598,X31597,X31596),X31595),hAPP(c_List_Oset(X31598),X31594)) = hAPP(c_List_Ofoldl(X31597,X31598,hAPP(c_COMBC(X31598,X31597,X31597),X31596),X31595),c_List_Oremdups(X31598,X31594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])]) ).

fof(i_0_7847,plain,
    ! [X32846,X32847,X32848,X32849] : c_Predicate_Oconversep(X32849,X32848,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32849,tc_fun(X32848,tc_HOL_Obool))),X32847),X32846)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32848,tc_fun(X32849,tc_HOL_Obool))),c_Predicate_Oconversep(X32849,X32848,X32847)),c_Predicate_Oconversep(X32849,X32848,X32846)),
    inference(variable_rename,[status(thm)],[fact_converse__meet]) ).

fof(i_0_7848,plain,
    ! [X32842,X32843,X32844,X32845] : c_Predicate_Oconversep(X32845,X32844,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32845,tc_fun(X32844,tc_HOL_Obool))),X32843),X32842)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32844,tc_fun(X32845,tc_HOL_Obool))),c_Predicate_Oconversep(X32845,X32844,X32843)),c_Predicate_Oconversep(X32845,X32844,X32842)),
    inference(variable_rename,[status(thm)],[fact_converse__join]) ).

fof(i_0_7849,plain,
    ! [X19876,X19877,X19878] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19877),X19878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19876),X19878)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19877),X19876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19878),X19876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19878),X19877)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19877),X19876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19877),X19878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19876),X19878)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19878),X19876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19878),X19877)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).

fof(i_0_7850,plain,
    ! [X20129,X20130,X20131] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20130),X20131)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20129),X20131)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20130),X20129))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20131),X20129))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20131),X20130)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20130),X20129))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20130),X20131)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20129),X20131)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20131),X20129))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20131),X20130)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).

cnf(i_0_7851,plain,
    c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5658]) ).

fof(i_0_7852,plain,
    ! [X22316,X22317,X22318,X22319] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22318),c_Groups_Ozero__class_Ozero(X22319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),c_Groups_Ozero__class_Ozero(X22319)),X22318))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22316),X22317))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),c_Groups_Ozero__class_Ozero(X22319)),X22318))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22318),c_Groups_Ozero__class_Ozero(X22319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22317),X22316))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22316),X22317))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22317),X22316))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),c_Groups_Ozero__class_Ozero(X22319)),X22318))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22317),X22316))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22318),c_Groups_Ozero__class_Ozero(X22319)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),X22316),X22317))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22319),X22318),X22316)))
        | ~ class_Rings_Olinordered__ring__strict(X22319) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_7853,plain,
    ! [X22312,X22313,X22314,X22315] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22313),c_Groups_Ozero__class_Ozero(X22315)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),c_Groups_Ozero__class_Ozero(X22315)),X22313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22312),X22314))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),c_Groups_Ozero__class_Ozero(X22315)),X22313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22313),c_Groups_Ozero__class_Ozero(X22315)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22314),X22312))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22312),X22314))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22314),X22312))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),c_Groups_Ozero__class_Ozero(X22315)),X22313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22314),X22312))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22313),c_Groups_Ozero__class_Ozero(X22315)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),X22312),X22314))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22314),X22313)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22315),X22312),X22313)))
        | ~ class_Rings_Olinordered__ring__strict(X22315) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_7854,plain,
    ! [X17885,X17886,X17887,X17888] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17888),X17887),X17885))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17888,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17888),X17887),X17886)),X17885)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17888,tc_HOL_Obool)),X17886),X17885))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17888,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17888),X17887),X17886)),X17885)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17888),X17887),X17885))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17888,tc_HOL_Obool)),X17886),X17885))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17888,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17888),X17887),X17886)),X17885)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_7855,plain,
    ! [X23978,X23979,X23980] :
      ( ~ class_Groups_Ocomm__monoid__add(X23980)
      | ~ class_Groups_Ocomm__monoid__mult(X23980)
      | ~ c_Nat__Transfer_Onat__set(X23979)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X23980),X23978),X23979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X23980),hAPP(hAPP(c_COMBB(tc_Int_Oint,X23980,tc_Nat_Onat),X23978),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).

fof(i_0_7856,plain,
    ! [X24001,X24002,X24003] :
      ( ~ class_Groups_Ocomm__monoid__add(X24003)
      | ~ class_Groups_Ocomm__monoid__mult(X24003)
      | ~ c_Nat__Transfer_Onat__set(X24002)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24003),X24001),X24002) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24003),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24003,tc_Nat_Onat),X24001),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24002)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).

fof(i_0_7857,plain,
    ! [X21075,X21076,X21077,X21078,X21079] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21079)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21078),X21077))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21078),X21076))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21078,tc_HOL_Obool)),X21077),X21076) != c_Orderings_Obot__class_Obot(tc_fun(X21078,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21078,X21079),X21075),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21078,tc_HOL_Obool)),X21077),X21076)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21079),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21078,X21079),X21075),X21077)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21078,X21079),X21075),X21076)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).

fof(i_0_7858,plain,
    ! [X21070,X21071,X21072,X21073,X21074] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21074)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21073),X21072))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21073),X21071))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21073,tc_HOL_Obool)),X21072),X21071) != c_Orderings_Obot__class_Obot(tc_fun(X21073,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21073,X21074),X21070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21073,tc_HOL_Obool)),X21072),X21071)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21074),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21073,X21074),X21070),X21072)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21073,X21074),X21070),X21071)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).

fof(i_0_7859,plain,
    ! [X21060,X21061,X21062,X21063,X21064] :
      ( ~ class_Groups_Ocomm__monoid__add(X21064)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21063),X21062))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21063),X21061))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21063,tc_HOL_Obool)),X21062),X21061) != c_Orderings_Obot__class_Obot(tc_fun(X21063,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21063,X21064),X21060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21063,tc_HOL_Obool)),X21062),X21061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21063,X21064),X21060),X21062)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X21063,X21064),X21060),X21061)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).

fof(i_0_7860,plain,
    ! [X23669,X23670,X23671] :
      ( ~ class_Groups_Ocomm__monoid__add(X23671)
      | ~ class_Groups_Ocomm__monoid__mult(X23671)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X23671),X23670),X23669) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X23671),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23671,tc_Int_Oint),X23670),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).

fof(i_0_7861,plain,
    ! [X23691,X23692,X23693] :
      ( ~ class_Groups_Ocomm__monoid__add(X23693)
      | ~ class_Groups_Ocomm__monoid__mult(X23693)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23693),X23692),X23691) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23693),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23693,tc_Int_Oint),X23692),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23691)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).

cnf(i_0_7862,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) ),
    inference(split_conjunct,[status(thm)],[i_0_5659]) ).

fof(i_0_7863,plain,
    ! [X29666,X29667] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29667),tc_List_Olist(X29667)),tc_HOL_Obool)),c_List_Olistrel(X29667,X29666)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29667),c_List_Olistrel1(X29667,X29666)))),
    inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(i_0_7864,plain,
    ! [X26587,X26588,X26589,X26590] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26589))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26589))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26590,X26589),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26588),X26587)))
        | X26590 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26589),X26588)),X26587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26589),X26587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26587),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26589))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26590,X26589),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26588),X26587)))
        | X26590 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26589),X26588)),X26587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26589))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26587),X26589))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26590,X26589),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26588),X26587)))
        | X26590 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26589),X26588)),X26587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26589),X26587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26587),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26587),X26589))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26590,X26589),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26588),X26587)))
        | X26590 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26589),X26588)),X26587) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5660])])]) ).

fof(i_0_7865,plain,
    ! [X23229,X23230] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X23230)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23229),X23230))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23230),X23229),
    inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(i_0_7866,plain,
    ! [X30652,X30653,X30654,X30655] : hAPP(hAPP(c_List_Odrop(X30655),X30654),hAPP(hAPP(c_List_Oappend(X30655),X30653),X30652)) = hAPP(hAPP(c_List_Oappend(X30655),hAPP(hAPP(c_List_Odrop(X30655),X30654),X30653)),hAPP(hAPP(c_List_Odrop(X30655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30654),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30655)),X30653))),X30652)),
    inference(variable_rename,[status(thm)],[fact_drop__append]) ).

fof(i_0_7867,plain,
    ! [X30483,X30484,X30485,X30486] : hAPP(hAPP(c_List_Otake(X30486),X30485),hAPP(hAPP(c_List_Oappend(X30486),X30484),X30483)) = hAPP(hAPP(c_List_Oappend(X30486),hAPP(hAPP(c_List_Otake(X30486),X30485),X30484)),hAPP(hAPP(c_List_Otake(X30486),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30485),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30486)),X30484))),X30483)),
    inference(variable_rename,[status(thm)],[fact_take__append]) ).

fof(i_0_7868,plain,
    ! [X30262,X30263,X30264] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30264,tc_HOL_Obool)),hAPP(c_List_Oset(X30264),c_List_Oremove1(X30264,X30263,X30262))),hAPP(c_List_Oset(X30264),X30262))),
    inference(variable_rename,[status(thm)],[fact_set__remove1__subset]) ).

fof(i_0_7869,plain,
    ! [X29821,X29822,X29823] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29823,tc_HOL_Obool)),hAPP(c_List_Oset(X29823),c_List_Osublist(X29823,X29822,X29821))),hAPP(c_List_Oset(X29823),X29822))),
    inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).

fof(i_0_7870,plain,
    ! [X17701,X17702,X17703,X17704] :
      ( ~ c_Fun_Oinj__on(X17704,X17703,X17702,X17701)
      | c_Fun_Oinj__on(X17703,X17704,c_Fun_Othe__inv__into(X17704,X17703,X17701,X17702),hAPP(c_Set_Oimage(X17704,X17703,X17702),X17701)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).

fof(i_0_7871,plain,
    ! [X27762,X27763,X27764] : hAPP(c_Relation_ODomain(X27764,X27763),hAPP(c_Set_OCollect(tc_prod(X27764,X27763)),hAPP(c_Product__Type_Oprod_Oprod__case(X27764,X27763,tc_HOL_Obool),X27762))) = hAPP(c_Set_OCollect(X27764),hAPP(hAPP(c_COMBB(tc_fun(X27763,tc_HOL_Obool),tc_HOL_Obool,X27764),c_HOL_OEx(X27763)),X27762)),
    inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).

cnf(i_0_7872,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5661]) ).

fof(i_0_7873,plain,
    ! [X30844,X30845,X30846,X30847,X30848] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X30848,X30847,X30846)
      | hAPP(hAPP(c_Finite__Set_Ofold(X30848,X30847,X30846),X30845),hAPP(c_List_Oset(X30848),X30844)) = hAPP(c_List_Ofoldl(X30847,X30848,hAPP(c_COMBC(X30848,X30847,X30847),X30846),X30845),X30844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).

fof(i_0_7874,plain,
    ! [X17909,X17910,X17911,X17912] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17912),X17911),X17910))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17912,tc_Nat_Onat),X17909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17912,tc_HOL_Obool)),X17910),hAPP(hAPP(c_Set_Oinsert(X17912),X17911),c_Orderings_Obot__class_Obot(tc_fun(X17912,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17912,tc_Nat_Onat),X17909),X17910)),hAPP(X17909,X17911)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17912),X17911),X17910))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17912,tc_Nat_Onat),X17909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17912,tc_HOL_Obool)),X17910),hAPP(hAPP(c_Set_Oinsert(X17912),X17911),c_Orderings_Obot__class_Obot(tc_fun(X17912,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17912,tc_Nat_Onat),X17909),X17910) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5662])]) ).

fof(i_0_7875,plain,
    ! [X19047,X19048,X19049,X19050] :
      ( ~ class_Groups_Oab__group__add(X19050)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19049,X19050),hAPP(hAPP(c_COMBB(X19050,X19050,X19049),c_Groups_Ouminus__class_Ouminus(X19050)),X19048)),X19047) = hAPP(c_Groups_Ouminus__class_Ouminus(X19050),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X19049,X19050),X19048),X19047)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).

fof(i_0_7876,plain,
    ! [X25000,X25001,X25002,X25003] :
      ( ~ class_Fields_Olinordered__field(X25003)
      | hAPP(c_Groups_Oabs__class_Oabs(X25003),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25002,X25003),X25001),X25000)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25002,X25003),hAPP(hAPP(c_COMBB(X25003,X25003,X25002),c_Groups_Oabs__class_Oabs(X25003)),X25001)),X25000) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).

fof(i_0_7877,plain,
    ! [X29863,X29864,X29865,X29867,X29868,X29869,X29870,X29872] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29865),esk391_3(X29863,X29864,X29865)),hAPP(c_List_Oset(X29865),X29864)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29867),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29865)),X29864)))
        | hBOOL(hAPP(X29863,hAPP(hAPP(c_List_Onth(X29865),X29864),X29867))) )
      & ( ~ hBOOL(hAPP(X29863,esk391_3(X29863,X29864,X29865)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29867),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29865)),X29864)))
        | hBOOL(hAPP(X29863,hAPP(hAPP(c_List_Onth(X29865),X29864),X29867))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk392_3(X29868,X29869,X29870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29870)),X29869)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29870),X29872),hAPP(c_List_Oset(X29870),X29869)))
        | hBOOL(hAPP(X29868,X29872)) )
      & ( ~ hBOOL(hAPP(X29868,hAPP(hAPP(c_List_Onth(X29870),X29869),esk392_3(X29868,X29869,X29870))))
        | ~ hBOOL(hAPP(hAPP(c_member(X29870),X29872),hAPP(c_List_Oset(X29870),X29869)))
        | hBOOL(hAPP(X29868,X29872)) ) ),
    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_all__set__conv__all__nth])])])])])]) ).

fof(i_0_7878,plain,
    ! [X17804,X17805,X17806,X17807] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17807,tc_HOL_Obool)),X17806),X17805))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17807),X17804),X17806)),hAPP(hAPP(c_Set_Oinsert(X17807),X17804),X17805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

cnf(i_0_7879,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5617]) ).

cnf(i_0_7880,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5618]) ).

cnf(i_0_7881,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)))
    | ~ c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5663]) ).

fof(i_0_7882,plain,
    ! [X32086,X32087,X32088,X32089,X32090] :
      ( ( c_List_Olinorder__class_Osorted(X32088,X32087)
        | ~ c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) )
      & ( c_List_Olinorder__class_Osorted(X32088,X32086)
        | ~ c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32088),X32089),hAPP(c_List_Oset(X32088),X32087)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32088),X32090),hAPP(c_List_Oset(X32088),X32086)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32088),X32089),X32090))
        | ~ c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) )
      & ( hBOOL(hAPP(hAPP(c_member(X32088),esk436_3(X32086,X32087,X32088)),hAPP(c_List_Oset(X32088),X32087)))
        | ~ c_List_Olinorder__class_Osorted(X32088,X32087)
        | ~ c_List_Olinorder__class_Osorted(X32088,X32086)
        | c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) )
      & ( hBOOL(hAPP(hAPP(c_member(X32088),esk437_3(X32086,X32087,X32088)),hAPP(c_List_Oset(X32088),X32086)))
        | ~ c_List_Olinorder__class_Osorted(X32088,X32087)
        | ~ c_List_Olinorder__class_Osorted(X32088,X32086)
        | c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32088),esk436_3(X32086,X32087,X32088)),esk437_3(X32086,X32087,X32088)))
        | ~ c_List_Olinorder__class_Osorted(X32088,X32087)
        | ~ c_List_Olinorder__class_Osorted(X32088,X32086)
        | c_List_Olinorder__class_Osorted(X32088,hAPP(hAPP(c_List_Oappend(X32088),X32087),X32086))
        | ~ class_Orderings_Olinorder(X32088) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__append])])])])]) ).

fof(i_0_7883,plain,
    ! [X20390,X20391,X20392] :
      ( ~ class_Rings_Olinordered__semidom(X20392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20392),c_Groups_Oone__class_Oone(X20392)),X20391))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20392),hAPP(hAPP(c_Power_Opower__class_Opower(X20392),X20391),X20390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20392),X20391),hAPP(hAPP(c_Power_Opower__class_Opower(X20392),X20391),X20390)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).

fof(i_0_7884,plain,
    ! [X17832,X17833,X17834,X17835] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17835,tc_HOL_Obool)),X17834),X17833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17835,tc_HOL_Obool)),X17833),X17832))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17835,tc_HOL_Obool)),X17833),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17835,tc_HOL_Obool)),X17832),X17834)) = X17834 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).

fof(i_0_7885,plain,
    ! [X24532,X24533,X24534] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24534,tc_HOL_Obool)),X24533),X24532))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X24534,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X24534),X24533)),hAPP(c_Set_OPow(X24534),X24532))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).

fof(i_0_7886,plain,
    ! [X28434,X28435,X28436,X28437,X28438,X28439] : hAPP(hAPP(c_Fun_Ocomp(X28439,X28438,X28437,hAPP(c_COMBK(X28438,X28439),X28436)),X28435),X28434) = X28436,
    inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).

fof(i_0_7887,plain,
    ! [X30635,X30636,X30637] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30637,tc_HOL_Obool)),hAPP(c_List_Oset(X30637),hAPP(hAPP(c_List_Odrop(X30637),X30636),X30635))),hAPP(c_List_Oset(X30637),X30635))),
    inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).

fof(i_0_7888,plain,
    ! [X29814,X29815,X29816] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29816,tc_HOL_Obool)),hAPP(c_List_Oset(X29816),hAPP(hAPP(c_List_Otake(X29816),X29815),X29814))),hAPP(c_List_Oset(X29816),X29814))),
    inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).

fof(i_0_7889,plain,
    ! [X23880,X23881,X23882,X23883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),X23881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23883),X23880),X23882)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23883),X23881),X23882)),X23880))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),c_Groups_Ozero__class_Ozero(X23883)),X23882))
        | ~ class_Fields_Olinordered__field(X23883) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23883),X23881),X23882)),X23880))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),X23881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23883),X23880),X23882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23883),c_Groups_Ozero__class_Ozero(X23883)),X23882))
        | ~ class_Fields_Olinordered__field(X23883) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).

fof(i_0_7890,plain,
    ! [X23884,X23885,X23886,X23887] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23887),X23885),X23886)),X23884))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),X23885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23887),X23884),X23886)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),c_Groups_Ozero__class_Ozero(X23887)),X23886))
        | ~ class_Fields_Olinordered__field(X23887) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),X23885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23887),X23884),X23886)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23887),X23885),X23886)),X23884))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23887),c_Groups_Ozero__class_Ozero(X23887)),X23886))
        | ~ class_Fields_Olinordered__field(X23887) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).

fof(i_0_7891,plain,
    ! [X23892,X23893,X23894,X23895] :
      ( ~ class_Fields_Olinordered__field(X23895)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23895),c_Groups_Ozero__class_Ozero(X23895)),X23894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23895),X23893),X23894)),X23892))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23895),X23893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23895),X23892),X23894))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).

fof(i_0_7892,plain,
    ! [X23761,X23762,X23763,X23764] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23764),X23762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23764),X23761),X23763)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23764),X23762),X23763)),X23761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23764),c_Groups_Ozero__class_Ozero(X23764)),X23763))
        | ~ class_Fields_Olinordered__field(X23764) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23764),X23762),X23763)),X23761))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23764),X23762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23764),X23761),X23763)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23764),c_Groups_Ozero__class_Ozero(X23764)),X23763))
        | ~ class_Fields_Olinordered__field(X23764) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).

fof(i_0_7893,plain,
    ! [X23765,X23766,X23767,X23768] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23768),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23768),X23766),X23767)),X23765))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23768),X23766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23768),X23765),X23767)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23768),c_Groups_Ozero__class_Ozero(X23768)),X23767))
        | ~ class_Fields_Olinordered__field(X23768) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23768),X23766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23768),X23765),X23767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23768),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23768),X23766),X23767)),X23765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23768),c_Groups_Ozero__class_Ozero(X23768)),X23767))
        | ~ class_Fields_Olinordered__field(X23768) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).

fof(i_0_7894,plain,
    ! [X23968,X23969,X23970,X23971] :
      ( ~ class_Fields_Olinordered__field(X23971)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23971),c_Groups_Ozero__class_Ozero(X23971)),X23970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23971),X23969),X23970)),X23968))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23971),X23969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23971),X23968),X23970))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).

fof(i_0_7895,plain,
    ! [X32297,X32298,X32299,X32300] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32300),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32299)),c_List_OtakeWhile(X32299,X32298,X32297))))
      | hAPP(hAPP(c_List_Onth(X32299),c_List_OtakeWhile(X32299,X32298,X32297)),X32300) = hAPP(hAPP(c_List_Onth(X32299),X32297),X32300) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])]) ).

fof(i_0_7896,plain,
    ! [X24082,X24083,X24084,X24085] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24085)
      | ~ class_Rings_Oring__1(X24085)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24085),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24084,tc_Int_Oint),X24083),X24082)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24084,X24085),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24085,X24084),c_Int_Oring__1__class_Oof__int(X24085)),X24083)),X24082) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).

fof(i_0_7897,plain,
    ! [X22948,X22949,X22950,X22951] :
      ( ~ class_Groups_Ocomm__monoid__mult(X22951)
      | ~ class_Rings_Osemiring__1(X22951)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22951),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22950,tc_Nat_Onat),X22949),X22948)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22950,X22951),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X22951,X22950),c_Nat_Osemiring__1__class_Oof__nat(X22951)),X22949)),X22948) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).

cnf(i_0_7898,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X3),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5593]) ).

cnf(i_0_7899,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Oconcat(X1,X2) != c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5664]) ).

cnf(i_0_7900,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oconcat(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5665]) ).

fof(i_0_7901,plain,
    ! [X29105,X29106,X29107,X29108] : hAPP(c_Relation_Oconverse(X29108,X29107),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29108,X29107),tc_HOL_Obool)),X29106),X29105)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29107,X29108),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X29108,X29107),X29106)),hAPP(c_Relation_Oconverse(X29108,X29107),X29105)),
    inference(variable_rename,[status(thm)],[fact_converse__Int]) ).

fof(i_0_7902,plain,
    ! [X29095,X29096,X29097,X29098] : hAPP(c_Relation_Oconverse(X29098,X29097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29098,X29097),tc_HOL_Obool)),X29096),X29095)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29097,X29098),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X29098,X29097),X29096)),hAPP(c_Relation_Oconverse(X29098,X29097),X29095)),
    inference(variable_rename,[status(thm)],[fact_converse__Un]) ).

fof(i_0_7903,plain,
    ! [X32244,X32245,X32246] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32246)),c_List_OtakeWhile(X32246,X32245,X32244))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32246)),X32244))),
    inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).

fof(i_0_7904,plain,
    ! [X29355,X29356,X29357,X29358] : hAPP(hAPP(c_Nat_Ocompow(X29358,X29358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29357),X29356)),X29355) = hAPP(c_Fun_Ocomp(X29358,X29358,X29358,hAPP(hAPP(c_Nat_Ocompow(X29358,X29358),X29357),X29355)),hAPP(hAPP(c_Nat_Ocompow(X29358,X29358),X29356),X29355)),
    inference(variable_rename,[status(thm)],[fact_funpow__add]) ).

fof(i_0_7905,plain,
    ! [X24076,X24077,X24078,X24079] :
      ( ~ class_Rings_Oring__1(X24079)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24079),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24078,tc_Int_Oint),X24077),X24076)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24078,X24079),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24079,X24078),c_Int_Oring__1__class_Oof__int(X24079)),X24077)),X24076) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).

fof(i_0_7906,plain,
    ! [X22927,X22928,X22929,X22930] :
      ( ~ class_Rings_Osemiring__1(X22930)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22930),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22929,tc_Nat_Onat),X22928),X22927)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22929,X22930),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X22930,X22929),c_Nat_Osemiring__1__class_Oof__nat(X22930)),X22928)),X22927) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).

fof(i_0_7907,plain,
    ! [X19746] : c_Fun_Oinj__on(X19746,tc_fun(X19746,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X19746,tc_fun(X19746,tc_HOL_Obool),tc_fun(X19746,tc_HOL_Obool)),c_Set_Oinsert(X19746)),c_Orderings_Obot__class_Obot(tc_fun(X19746,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X19746,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).

fof(i_0_7908,plain,
    ! [X27860,X27861,X27862,X27863] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27863),X27862))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27861),X27860))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27863,X27861)),hAPP(hAPP(c_Product__Type_OSigma(X27863,X27861),X27862),hAPP(c_COMBK(tc_fun(X27861,tc_HOL_Obool),X27863),X27860)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).

fof(i_0_7909,plain,
    ! [X19786,X19787,X19788] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19788),X19787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19788,tc_HOL_Obool)),X19786),X19787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19788),X19786)),hAPP(c_Finite__Set_Ocard(X19788),X19787)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19788,tc_HOL_Obool)),X19786),X19787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_7910,plain,
    ! [X17892,X17893,X17894,X17895,X17896] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17896),X17895))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17894,tc_HOL_Obool)),X17893),hAPP(c_Set_Oimage(X17896,X17894,X17892),X17895)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17894),X17893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

cnf(i_0_7911,plain,
    ( c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),c_List_Oupt(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5666]) ).

fof(i_0_7912,plain,
    ! [X33789] : c_Fun_Obij__betw(X33789,X33789,c_Fun_Oid(X33789),c_Orderings_Otop__class_Otop(tc_fun(X33789,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33789,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_bij__id]) ).

fof(i_0_7913,plain,
    ! [X20819,X20820,X20821,X20822,X20823] :
      ( ~ c_Fun_Oinj__on(X20823,X20822,X20821,X20820)
      | ~ c_Fun_Oinj__on(X20823,X20822,X20821,X20819)
      | c_Fun_Oinj__on(X20823,X20822,X20821,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20823,tc_HOL_Obool)),X20820),X20819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).

fof(i_0_7914,plain,
    ! [X30668,X30669,X30670,X30671] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30671),X30670)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30669)),X30668)))
      | hAPP(hAPP(c_List_Onth(X30669),hAPP(hAPP(c_List_Odrop(X30669),X30671),X30668)),X30670) = hAPP(hAPP(c_List_Onth(X30669),X30668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30671),X30670)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).

fof(i_0_7915,plain,
    ! [X24237,X24238,X24239,X24240] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24239)),X24238))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24240),X24237),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24238,hAPP(c_Nat_OSuc,X24239))) = c_Groups_Ozero__class_Ozero(X24240)
        | ~ class_Groups_Ocomm__monoid__add(X24240) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24239)),X24238))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24240),X24237),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24238,hAPP(c_Nat_OSuc,X24239))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24240),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24240),X24237),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24238,X24239))),hAPP(X24237,hAPP(c_Nat_OSuc,X24239)))
        | ~ class_Groups_Ocomm__monoid__add(X24240) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5667])])]) ).

fof(i_0_7916,plain,
    ! [X32227,X32228,X32229,X32230] :
      ( ~ class_Orderings_Olinorder(X32230)
      | ~ c_List_Olinorder__class_Osorted(X32230,hAPP(c_List_Orev(X32230),X32229))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32228),X32227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32227),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32230)),X32229)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32230),hAPP(hAPP(c_List_Onth(X32230),X32229),X32227)),hAPP(hAPP(c_List_Onth(X32230),X32229),X32228))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).

fof(i_0_7917,plain,
    ! [X30438,X30439,X30440,X30441,X30442,X30443] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30443)),X30442) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30441)),X30440)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30443)),X30439) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30441)),X30438)
      | hAPP(hAPP(c_List_Ozip(X30443,X30441),hAPP(hAPP(c_List_Oappend(X30443),X30442),X30439)),hAPP(hAPP(c_List_Oappend(X30441),X30440),X30438)) = hAPP(hAPP(c_List_Oappend(tc_prod(X30443,X30441)),hAPP(hAPP(c_List_Ozip(X30443,X30441),X30442),X30440)),hAPP(hAPP(c_List_Ozip(X30443,X30441),X30439),X30438)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).

fof(i_0_7918,plain,
    ! [X31204,X31205,X31206,X31207,X31208] : c_List_Olist_Olist__size(X31208,X31207,hAPP(hAPP(c_List_Omap(X31206,X31208),X31205),X31204)) = c_List_Olist_Olist__size(X31206,hAPP(c_Fun_Ocomp(X31208,tc_Nat_Onat,X31206,X31207),X31205),X31204),
    inference(variable_rename,[status(thm)],[fact_list__size__map]) ).

fof(i_0_7919,plain,
    ! [X28201,X28202,X28203,X28204] :
      ( ~ c_Relation_Orefl__on(X28204,X28203,X28202)
      | ~ hBOOL(hAPP(hAPP(c_member(X28204),X28201),X28203))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28204,X28204)),hAPP(hAPP(c_Product__Type_OPair(X28204,X28204),X28201),X28201)),X28202)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).

fof(i_0_7920,plain,
    ! [X21380,X21381,X21382,X21383,X21384] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21384),X21383),X21382))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21381,tc_HOL_Obool)),hAPP(X21380,X21383)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21384,tc_fun(X21381,tc_HOL_Obool)),X21382),X21380))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).

fof(i_0_7921,plain,
    ! [X30169,X30170,X30171,X30172] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30172) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X30171),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30172)),hAPP(hAPP(c_List_Olist_OCons(X30171),X30170),X30169)) = c_List_Olist_ONil(X30171) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30172) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X30171),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30172)),hAPP(hAPP(c_List_Olist_OCons(X30171),X30170),X30169)) = hAPP(hAPP(c_List_Olist_OCons(X30171),X30170),hAPP(hAPP(c_List_Otake(X30171),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30172)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30169)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).

fof(i_0_7922,plain,
    ! [X26681,X26682,X26683,X26684,X26685,X26686] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26686,tc_fun(X26685,tc_HOL_Obool))),X26684),X26683))
      | ~ hBOOL(hAPP(hAPP(X26684,X26682),X26681))
      | hBOOL(hAPP(hAPP(X26683,X26682),X26681)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_7923,plain,
    ! [X26675,X26676,X26677,X26678,X26679,X26680] :
      ( ~ hBOOL(hAPP(hAPP(X26680,X26679),X26678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26677,tc_fun(X26676,tc_HOL_Obool))),X26680),X26675))
      | hBOOL(hAPP(hAPP(X26675,X26679),X26678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_7924,plain,
    ! [X19061,X19062,X19063] :
      ( ~ class_Orderings_Olinorder(X19063)
      | X19062 = c_Orderings_Obot__class_Obot(tc_fun(X19063,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19063,tc_HOL_Obool)),X19062),X19061))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19063),X19061))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19063),hAPP(c_Finite__Set_Ofold1(X19063,c_Orderings_Oord__class_Omin(X19063)),X19061)),hAPP(c_Finite__Set_Ofold1(X19063,c_Orderings_Oord__class_Omin(X19063)),X19062))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).

fof(i_0_7925,plain,
    ! [X19566,X19567,X19568,X19569] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19569),X19568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19569,tc_HOL_Obool)),X19567),X19566)))
        | hBOOL(hAPP(hAPP(c_member(X19569),X19568),X19567))
        | hBOOL(hAPP(hAPP(c_member(X19569),X19568),X19566)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19569),X19568),X19567))
        | hBOOL(hAPP(hAPP(c_member(X19569),X19568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19569,tc_HOL_Obool)),X19567),X19566))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19569),X19568),X19566))
        | hBOOL(hAPP(hAPP(c_member(X19569),X19568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19569,tc_HOL_Obool)),X19567),X19566))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).

fof(i_0_7926,plain,
    ! [X19355,X19356,X19357,X19358] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19358),X19357),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19358,tc_HOL_Obool)),X19356),X19355)))
      | hBOOL(hAPP(hAPP(c_member(X19358),X19357),X19356))
      | hBOOL(hAPP(hAPP(c_member(X19358),X19357),X19355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5668])]) ).

cnf(i_0_7927,plain,
    ( hBOOL(hAPP(X2,X4))
    | c_List_OdropWhile(X1,X2,X3) != c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5669]) ).

fof(i_0_7928,plain,
    ! [X32988,X32989,X32990] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X32990),c_Groups_Ozero__class_Ozero(X32990)),esk489_3(X32988,X32989,X32990)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32990),X32989),X32988))
        | ~ class_Fields_Olinordered__field(X32990) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32990),X32989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32990),X32988),esk489_3(X32988,X32989,X32990))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32990),X32989),X32988))
        | ~ class_Fields_Olinordered__field(X32990) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__epsilon])])])]) ).

fof(i_0_7929,plain,
    ! [X30825,X30826,X30827,X30828,X30829,X30830] : hAPP(c_List_Ofoldl(X30830,X30829,X30828,X30827),hAPP(hAPP(c_List_Olist_OCons(X30829),X30826),X30825)) = hAPP(c_List_Ofoldl(X30830,X30829,X30828,hAPP(hAPP(X30828,X30827),X30826)),X30825),
    inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).

fof(i_0_7930,plain,
    ! [X32234,X32235] :
      ( ( X32234 != c_List_Olist_ONil(tc_List_Olist(X32235))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32235))),c_List_Otranspose(X32235,X32234)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32235),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32235))),X32234))) )
      & ( X32234 = c_List_Olist_ONil(tc_List_Olist(X32235))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32235))),c_List_Otranspose(X32235,X32234)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32235)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32235)),X32234),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32235),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32235))),X32234))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).

fof(i_0_7931,plain,
    ! [X22200,X22201,X22202,X22203] :
      ( ~ class_Rings_Olinordered__semidom(X22203)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22203),X22202),X22201))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22203),c_Groups_Ozero__class_Ozero(X22203)),X22202))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22200))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22203),hAPP(hAPP(c_Power_Opower__class_Opower(X22203),X22202),X22200)),hAPP(hAPP(c_Power_Opower__class_Opower(X22203),X22201),X22200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).

fof(i_0_7932,plain,
    ! [X22696,X22697,X22698,X22699] :
      ( ~ class_Rings_Olinordered__semidom(X22699)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22698),X22697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22699),c_Groups_Ozero__class_Ozero(X22699)),X22696))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22699),X22696),c_Groups_Oone__class_Oone(X22699)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22699),hAPP(hAPP(c_Power_Opower__class_Opower(X22699),X22696),X22697)),hAPP(hAPP(c_Power_Opower__class_Opower(X22699),X22696),X22698))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).

fof(i_0_7933,plain,
    ! [X22700,X22701,X22702,X22703] :
      ( ~ class_Rings_Olinordered__semidom(X22703)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22702),X22701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22703),c_Groups_Ozero__class_Ozero(X22703)),X22700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22703),X22700),c_Groups_Oone__class_Oone(X22703)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22703),hAPP(hAPP(c_Power_Opower__class_Opower(X22703),X22700),X22701)),hAPP(hAPP(c_Power_Opower__class_Opower(X22703),X22700),X22702))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).

fof(i_0_7934,plain,
    ! [X25538,X25539,X25540,X25541,X25542] : hAPP(c_Relation_OImage(X25542,X25541,X25540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25542,tc_HOL_Obool)),X25539),X25538)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25541,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25542,X25541,X25540),X25539)),hAPP(c_Relation_OImage(X25542,X25541,X25540),X25538)),
    inference(variable_rename,[status(thm)],[fact_Image__Un]) ).

fof(i_0_7935,plain,
    ! [X20510,X20511,X20512,X20513,X20514] : hAPP(c_Set_Ovimage(X20514,X20513,X20512),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20513,tc_HOL_Obool)),X20511),X20510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20514,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20514,X20513,X20512),X20511)),hAPP(c_Set_Ovimage(X20514,X20513,X20512),X20510)),
    inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).

fof(i_0_7936,plain,
    ! [X20748,X20749,X20750,X20751,X20752] : hAPP(c_Set_Ovimage(X20752,X20751,X20750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20751,tc_HOL_Obool)),X20749),X20748)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20752,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20752,X20751,X20750),X20749)),hAPP(c_Set_Ovimage(X20752,X20751,X20750),X20748)),
    inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).

fof(i_0_7937,plain,
    ! [X20798,X20799,X20800,X20801,X20802] : hAPP(c_Set_Ovimage(X20802,X20801,X20800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20801,tc_HOL_Obool)),X20799),X20798)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20802,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20802,X20801,X20800),X20799)),hAPP(c_Set_Ovimage(X20802,X20801,X20800),X20798)),
    inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).

fof(i_0_7938,plain,
    ! [X19624,X19625,X19626,X19627,X19628] : hAPP(c_Set_Oimage(X19628,X19627,X19626),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19628,tc_HOL_Obool)),X19625),X19624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19627,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19628,X19627,X19626),X19625)),hAPP(c_Set_Oimage(X19628,X19627,X19626),X19624)),
    inference(variable_rename,[status(thm)],[fact_image__Un]) ).

fof(i_0_7939,plain,
    ! [X30396,X30397,X30398,X30399] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),X30398),c_List_Olists(X30399,X30396)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),hAPP(hAPP(c_List_Oappend(X30399),X30398),X30397)),c_List_Olists(X30399,X30396))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),X30397),c_List_Olists(X30399,X30396)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),hAPP(hAPP(c_List_Oappend(X30399),X30398),X30397)),c_List_Olists(X30399,X30396))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),X30398),c_List_Olists(X30399,X30396)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),X30397),c_List_Olists(X30399,X30396)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30399)),hAPP(hAPP(c_List_Oappend(X30399),X30398),X30397)),c_List_Olists(X30399,X30396))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).

cnf(i_0_7940,plain,
    ( hBOOL(hAPP(X3,X4))
    | c_List_OdropWhile(X2,X3,X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_5657]) ).

fof(i_0_7941,plain,
    ! [X23428,X23429,X23430] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23430,tc_HOL_Obool)),X23429),X23428))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X23430,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X23430,X23429)),c_Predicate_OPowp(X23430,X23428))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).

fof(i_0_7942,plain,
    ! [X31546,X31547,X31548,X31549] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31549),X31548))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31547),X31546))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X31549,X31547)),c_Enum_Oproduct(X31549,X31547,X31548,X31546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__product])]) ).

fof(i_0_7943,plain,
    ! [X23523,X23524,X23525,X23526] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23526),X23525))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23524),X23523))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X23526,X23524)),c_Sum__Type_OPlus(X23526,X23524,X23525,X23523))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

cnf(i_0_7944,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(c_List_OremoveAll(X1,X2),X3) = X3 ),
    inference(split_conjunct,[status(thm)],[i_0_5670]) ).

fof(i_0_7945,plain,
    ! [X28709,X28710,X28711,X28712,X28713,X28714] :
      ( ~ c_Finite__Set_Ofolding(X28714,X28713,X28712,X28711)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28714),X28710))
      | hBOOL(hAPP(hAPP(c_member(X28714),X28709),X28710))
      | hAPP(X28711,hAPP(hAPP(c_Set_Oinsert(X28714),X28709),X28710)) = hAPP(c_Fun_Ocomp(X28713,X28713,X28713,hAPP(X28711,X28710)),hAPP(X28712,X28709)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5671])]) ).

fof(i_0_7946,plain,
    ! [X27265,X27266,X27267,X27268] :
      ( X27268 != X27267
      | ~ hBOOL(hAPP(hAPP(c_member(X27266),X27268),X27265))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27266,X27266)),hAPP(hAPP(c_Product__Type_OPair(X27266,X27266),X27268),X27267)),c_Relation_OId__on(X27266,X27265))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).

fof(i_0_7947,plain,
    ! [X28241,X28242] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X28242),c_Int_OInteg))
      | ~ hBOOL(hAPP(X28241,hAPP(c_Int_ORep__Integ,esk313_2(X28241,X28242))))
      | hBOOL(hAPP(X28241,X28242)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).

cnf(i_0_7948,plain,
    ( c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)
    | c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5594]) ).

fof(i_0_7949,plain,
    ! [X30487,X30488,X30489,X30490,X30491] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30491),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30490)),X30489)))
      | hAPP(hAPP(c_List_Olist__update(X30490,hAPP(hAPP(c_List_Oappend(X30490),X30489),X30488)),X30491),X30487) = hAPP(hAPP(c_List_Oappend(X30490),hAPP(hAPP(c_List_Olist__update(X30490,X30489),X30491),X30487)),X30488) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).

fof(i_0_7950,plain,
    ! [X33994,X33995,X33996] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33996),X33995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33996),X33994)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33995),X33994))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33996)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33995),X33994))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33996),X33995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33996),X33994)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33996)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).

fof(i_0_7951,plain,
    ! [X33991,X33992,X33993] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33993),X33992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33993),X33991)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33993))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33992),X33991)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).

fof(i_0_7952,plain,
    ! [X22147,X22148,X22149] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22149),X22148)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22149),X22147)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22148),X22147)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).

fof(i_0_7953,plain,
    ! [X22498,X22499,X22500] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22500),X22499)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22500),X22498)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22499),X22498))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22500)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22499),X22498))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22500),X22499)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22500),X22498)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22500)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).

fof(i_0_7954,plain,
    ! [X22649,X22650,X22651] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22651),X22650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22649),X22650)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22650))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22651),X22649)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22650))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22651),X22650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22649),X22650))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22651),X22649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22651),X22650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22649),X22650))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).

fof(i_0_7955,plain,
    ! [X22652,X22653,X22654] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22654),X22653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22654),X22652)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22653),X22652))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22654)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22653),X22652))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22654),X22653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22654),X22652)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22654)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).

fof(i_0_7956,plain,
    ! [X22646,X22647,X22648] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22646)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22648))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22647),X22646)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22648))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22646))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22647),X22646))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22648),X22646))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).

fof(i_0_7957,plain,
    ! [X33982,X33983,X33984] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33984),X33983)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33984),X33982)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33984))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33983),X33982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).

fof(i_0_7958,plain,
    ! [X27583,X27584,X27585] :
      ( ~ c_Wellfounded_Owf(X27585,X27584)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27585,tc_HOL_Obool)),X27583),hAPP(c_Relation_OImage(X27585,X27585,X27584),X27583)))
      | X27583 = c_Orderings_Obot__class_Obot(tc_fun(X27585,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).

fof(i_0_7959,plain,
    ! [X22889,X22890,X22891] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22891,tc_Nat_Onat),X22890),X22889)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22891,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X22891),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22890)),X22889),
    inference(variable_rename,[status(thm)],[fact_int__setprod]) ).

fof(i_0_7960,plain,
    ! [X22886,X22887,X22888] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22888,tc_Nat_Onat),X22887),X22886)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22888,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X22888),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22887)),X22886),
    inference(variable_rename,[status(thm)],[fact_int__setsum]) ).

fof(i_0_7961,plain,
    ! [X17939,X17940,X17941,X17942] : c_Fun_Ooverride__on(X17942,X17941,X17940,X17939,c_Orderings_Obot__class_Obot(tc_fun(X17942,tc_HOL_Obool))) = X17940,
    inference(variable_rename,[status(thm)],[fact_override__on__emptyset]) ).

fof(i_0_7962,plain,
    ! [X28416,X28417,X28418,X28419,X28420] :
      ( ~ c_Finite__Set_Ofun__left__comm(X28420,X28419,X28418)
      | hAPP(c_Fun_Ocomp(X28419,X28419,X28419,hAPP(X28418,X28417)),hAPP(X28418,X28416)) = hAPP(c_Fun_Ocomp(X28419,X28419,X28419,hAPP(X28418,X28416)),hAPP(X28418,X28417)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).

fof(i_0_7963,plain,
    ! [X17194,X17195,X17196] : c_Hoare__Mirabelle_Ohoare__derivs(X17196,X17195,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17196)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17196),X17194),c_Com_Ocom_OSKIP),X17194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17196),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_OSkip]) ).

fof(i_0_7964,plain,
    ! [X17191,X17192,X17193] : c_Hoare__Mirabelle_Ohoare__derivs(X17193,X17192,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17193)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17193),X17191),c_Com_Ocom_OSKIP),X17191)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17193),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).

fof(i_0_7965,plain,
    ! [X30100,X30101,X30102,X30103] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30102)),X30101)))
      | hBOOL(hAPP(hAPP(c_member(X30102),X30100),hAPP(c_List_Oset(X30102),hAPP(hAPP(c_List_Olist__update(X30102,X30101),X30103),X30100)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).

fof(i_0_7966,plain,
    ! [X21143,X21144,X21145,X21146,X21147,X21148] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21148),X21147),X21146))
      | ~ hBOOL(hAPP(hAPP(c_member(X21145),X21144),hAPP(X21143,X21147)))
      | hBOOL(hAPP(hAPP(c_member(X21145),X21144),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21148,tc_fun(X21145,tc_HOL_Obool)),X21146),X21143))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).

fof(i_0_7967,plain,
    ! [X26465,X26466,X26467,X26468,X26469,X26470] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26470,X26469),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26468),X26467)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26470,X26469),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26466),X26465)))
      | X26469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X26468 = X26466 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).

fof(i_0_7968,plain,
    ! [X26459,X26460,X26461,X26462,X26463,X26464] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26464,X26463),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26462),X26461)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26464,X26463),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26460),X26459)))
      | X26463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X26461 = X26459 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).

fof(i_0_7969,plain,
    ! [X17877,X17878,X17879,X17880] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17880),hAPP(c_Set_Oimage(X17879,X17880,X17878),X17877)))
      | ~ c_Fun_Oinj__on(X17879,X17880,X17878,X17877)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17879),X17877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

cnf(i_0_7970,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_OdropWhile(X1,X3,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5672]) ).

fof(i_0_7971,plain,
    ! [X34073,X34074,X34075,X34076] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34073)))
        | X34075 = c_Groups_Ozero__class_Ozero(X34076)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34076),X34074),X34073))
        | ~ class_Rings_Oidom(X34076) )
      & ( X34075 != c_Groups_Ozero__class_Ozero(X34076)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34073)))
        | ~ class_Rings_Oidom(X34076) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34076),X34074),X34073))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34076),X34075),X34073)))
        | ~ class_Rings_Oidom(X34076) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).

fof(i_0_7972,plain,
    ! [X34077,X34078,X34079,X34080] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34079),X34078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34077),X34078)))
        | X34078 = c_Groups_Ozero__class_Ozero(X34080)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34080),X34079),X34077))
        | ~ class_Rings_Oidom(X34080) )
      & ( X34078 != c_Groups_Ozero__class_Ozero(X34080)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34079),X34078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34077),X34078)))
        | ~ class_Rings_Oidom(X34080) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34080),X34079),X34077))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34079),X34078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34080),X34077),X34078)))
        | ~ class_Rings_Oidom(X34080) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).

fof(i_0_7973,plain,
    ! [X29203,X29204,X29205,X29206] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29206,X29205),tc_HOL_Obool)),X29204),X29203))
      | ~ c_Relation_Osingle__valued(X29206,X29205,X29203)
      | c_Relation_Osingle__valued(X29206,X29205,X29204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).

fof(i_0_7974,plain,
    ! [X32631,X32632,X32633,X32636,X32637,X32638,X32639,X32640] :
      ( ( X32631 = hAPP(hAPP(c_List_Oappend(X32633),esk479_3(X32631,X32632,X32633)),hAPP(hAPP(c_List_Olist_OCons(X32633),X32632),esk480_3(X32631,X32632,X32633)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32633),X32632),hAPP(c_List_Oset(X32633),X32631))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32633),X32632),hAPP(c_List_Oset(X32633),esk480_3(X32631,X32632,X32633))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32633),X32632),hAPP(c_List_Oset(X32633),X32631))) )
      & ( X32636 != hAPP(hAPP(c_List_Oappend(X32638),X32639),hAPP(hAPP(c_List_Olist_OCons(X32638),X32637),X32640))
        | hBOOL(hAPP(hAPP(c_member(X32638),X32637),hAPP(c_List_Oset(X32638),X32640)))
        | hBOOL(hAPP(hAPP(c_member(X32638),X32637),hAPP(c_List_Oset(X32638),X32636))) ) ),
    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)],[i_0_5673])])])])])]) ).

fof(i_0_7975,plain,
    ! [X32621,X32622,X32623,X32626,X32627,X32628,X32629,X32630] :
      ( ( X32621 = hAPP(hAPP(c_List_Oappend(X32623),esk477_3(X32621,X32622,X32623)),hAPP(hAPP(c_List_Olist_OCons(X32623),X32622),esk478_3(X32621,X32622,X32623)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32623),X32622),hAPP(c_List_Oset(X32623),X32621))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32623),X32622),hAPP(c_List_Oset(X32623),esk477_3(X32621,X32622,X32623))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32623),X32622),hAPP(c_List_Oset(X32623),X32621))) )
      & ( X32626 != hAPP(hAPP(c_List_Oappend(X32628),X32629),hAPP(hAPP(c_List_Olist_OCons(X32628),X32627),X32630))
        | hBOOL(hAPP(hAPP(c_member(X32628),X32627),hAPP(c_List_Oset(X32628),X32629)))
        | hBOOL(hAPP(hAPP(c_member(X32628),X32627),hAPP(c_List_Oset(X32628),X32626))) ) ),
    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)],[i_0_5674])])])])])]) ).

cnf(i_0_7976,plain,
    c_Int_Osucc(c_Int_OBit1(X1)) = c_Int_OBit0(c_Int_Osucc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5675]) ).

fof(i_0_7977,plain,
    ! [X18430,X18431,X18432,X18433] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18433)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18433),X18432),X18431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18433),X18430),X18431)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18433),X18432),X18430)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_7978,plain,
    ! [X18409,X18410,X18411,X18412] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18412),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18412),X18411),X18410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18412),X18409),X18410)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18412),X18411),X18409))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18412) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18412),X18411),X18409))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18412),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18412),X18411),X18410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18412),X18409),X18410)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18412) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_7979,plain,
    ! [X18434,X18435,X18436,X18437] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18437)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18437),X18436),X18435)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18437),X18436),X18434)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18437),X18435),X18434)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_7980,plain,
    ! [X18413,X18414,X18415,X18416] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18416),X18415),X18414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18416),X18415),X18413)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18416),X18414),X18413))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18416) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18416),X18414),X18413))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18416),X18415),X18414)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18416),X18415),X18413)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18416) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_7981,plain,
    ! [X18094,X18095,X18096,X18097] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18097),X18096),X18095)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18097),X18094),X18095)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18097),X18096),X18094))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18097) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18097),X18096),X18094))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18097),X18096),X18095)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18097),X18094),X18095)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18097) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_7982,plain,
    ! [X18073,X18074,X18075,X18076] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18076)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18076),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18076),X18075),X18074)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18076),X18073),X18074)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18076),X18075),X18073)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_7983,plain,
    ! [X18090,X18091,X18092,X18093] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18093),X18092),X18091)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18093),X18092),X18090)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18093),X18091),X18090))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18093) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18093),X18091),X18090))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18093),X18092),X18091)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18093),X18092),X18090)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18093) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_7984,plain,
    ! [X18069,X18070,X18071,X18072] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18072)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18072),X18071),X18070)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18072),X18071),X18069)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18072),X18070),X18069)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_7985,plain,
    ! [X32115,X32116,X32117,X32118] :
      ( ~ class_Orderings_Olinorder(X32118)
      | ~ c_List_Olinorder__class_Osorted(X32118,X32117)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32116),X32115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32118)),X32117)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32118),hAPP(hAPP(c_List_Onth(X32118),X32117),X32116)),hAPP(hAPP(c_List_Onth(X32118),X32117),X32115))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).

fof(i_0_7986,plain,
    ! [X29319,X29320,X29321] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29321,X29321),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29320)),X29319) = hAPP(hAPP(c_Relation_Orel__comp(X29321,X29321,X29321),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29321,X29321),tc_HOL_Obool),X29320),X29319)),X29319),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(i_0_7987,plain,
    ! [X23925,X23926,X23927,X23928] :
      ( ~ class_Fields_Ofield(X23928)
      | X23927 = c_Groups_Ozero__class_Ozero(X23928)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23928),X23926),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23928),X23925),X23927)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23928),X23927),X23926)),X23925)),X23927) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).

fof(i_0_7988,plain,
    ! [X23942,X23943,X23944,X23945] :
      ( ~ class_Fields_Ofield(X23945)
      | X23944 = c_Groups_Ozero__class_Ozero(X23945)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23945),X23943),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23945),X23942),X23944)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23945),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23945),X23944),X23943)),X23942)),X23944) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).

fof(i_0_7989,plain,
    ! [X32093,X32094,X32095,X32096,X32097,X32098] :
      ( ~ class_Orderings_Olinorder(X32098)
      | ~ c_List_Olinorder__class_Osorted(X32098,hAPP(hAPP(c_List_Omap(X32097,X32098),X32096),X32095))
      | ~ hBOOL(hAPP(X32094,X32093))
      | hAPP(c_List_Ofilter(X32097,X32094),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32097,X32098,X32096),X32093),X32095)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32097,X32098,X32096),X32093),hAPP(c_List_Ofilter(X32097,X32094),X32095)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).

cnf(i_0_7990,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5676]) ).

cnf(i_0_7991,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(X2)
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5442]) ).

fof(i_0_7992,plain,
    ! [X17889,X17890,X17891] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17891,tc_HOL_Obool)),X17890),hAPP(hAPP(c_Set_Oinsert(X17891),X17889),c_Orderings_Obot__class_Obot(tc_fun(X17891,tc_HOL_Obool)))))
      | X17890 = c_Orderings_Obot__class_Obot(tc_fun(X17891,tc_HOL_Obool))
      | X17890 = hAPP(hAPP(c_Set_Oinsert(X17891),X17889),c_Orderings_Obot__class_Obot(tc_fun(X17891,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).

fof(i_0_7993,plain,
    ! [X17324,X17325,X17326,X17327] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17327),X17326),X17325))
        | ~ hBOOL(hAPP(hAPP(c_member(X17327),X17326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17327,tc_HOL_Obool)),X17325),X17324))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17327),X17326),X17324))
        | ~ hBOOL(hAPP(hAPP(c_member(X17327),X17326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17327,tc_HOL_Obool)),X17325),X17324))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17327),X17326),X17325))
        | hBOOL(hAPP(hAPP(c_member(X17327),X17326),X17324))
        | hBOOL(hAPP(hAPP(c_member(X17327),X17326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17327,tc_HOL_Obool)),X17325),X17324))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5677])])]) ).

fof(i_0_7994,plain,
    ! [X17295,X17296,X17297,X17298] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17298),X17297),X17296))
        | ~ hBOOL(hAPP(hAPP(c_member(X17298),X17297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17298,tc_HOL_Obool)),X17296),X17295))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17298),X17297),X17295))
        | ~ hBOOL(hAPP(hAPP(c_member(X17298),X17297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17298,tc_HOL_Obool)),X17296),X17295))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).

fof(i_0_7995,plain,
    ! [X17316,X17317,X17318,X17319] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17319),X17318),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17319,tc_HOL_Obool)),X17317),X17316)))
      | ~ hBOOL(hAPP(hAPP(c_member(X17319),X17318),X17316)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5678])]) ).

fof(i_0_7996,plain,
    ! [X17433,X17434,X17435,X17436] : c_Fun_Ofun__upd(X17436,X17435,X17434,X17433,hAPP(X17434,X17433)) = X17434,
    inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).

cnf(i_0_7997,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_List_OremoveAll(X3,X2),hAPP(c_List_Ofilter(X3,X1),X4)) = hAPP(c_List_Ofilter(X3,X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5679]) ).

cnf(i_0_7998,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X1)),c_List_Oembed__list(X2))),
    inference(split_conjunct,[status(thm)],[i_0_5680]) ).

cnf(i_0_7999,plain,
    c_List_Oreturn__list(X1) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_5681]) ).

cnf(i_0_8000,plain,
    c_List_Oembed__list(X1) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1),
    inference(split_conjunct,[status(thm)],[i_0_5682]) ).

fof(i_0_8001,plain,
    ! [X17472,X17473,X17474,X17475,X17476] :
      ( hAPP(X17476,X17475) != X17474
      | c_Fun_Ofun__upd(X17473,X17472,X17476,X17475,X17474) = X17476 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).

fof(i_0_8002,plain,
    ! [X22803,X22804,X22805,X22808,X22809,X22810,X22811,X22812] :
      ( ( X22804 = hAPP(hAPP(c_Set_Oinsert(X22805),esk136_3(X22803,X22804,X22805)),esk137_3(X22803,X22804,X22805))
        | hAPP(c_Finite__Set_Ocard(X22805),X22804) != hAPP(c_Nat_OSuc,X22803) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22805),esk136_3(X22803,X22804,X22805)),esk137_3(X22803,X22804,X22805)))
        | hAPP(c_Finite__Set_Ocard(X22805),X22804) != hAPP(c_Nat_OSuc,X22803) )
      & ( hAPP(c_Finite__Set_Ocard(X22805),esk137_3(X22803,X22804,X22805)) = X22803
        | hAPP(c_Finite__Set_Ocard(X22805),X22804) != hAPP(c_Nat_OSuc,X22803) )
      & ( X22803 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | esk137_3(X22803,X22804,X22805) = c_Orderings_Obot__class_Obot(tc_fun(X22805,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X22805),X22804) != hAPP(c_Nat_OSuc,X22803) )
      & ( X22808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22809 != hAPP(hAPP(c_Set_Oinsert(X22810),X22811),X22812)
        | hBOOL(hAPP(hAPP(c_member(X22810),X22811),X22812))
        | hAPP(c_Finite__Set_Ocard(X22810),X22812) != X22808
        | hAPP(c_Finite__Set_Ocard(X22810),X22809) = hAPP(c_Nat_OSuc,X22808) )
      & ( X22812 != c_Orderings_Obot__class_Obot(tc_fun(X22810,tc_HOL_Obool))
        | X22809 != hAPP(hAPP(c_Set_Oinsert(X22810),X22811),X22812)
        | hBOOL(hAPP(hAPP(c_member(X22810),X22811),X22812))
        | hAPP(c_Finite__Set_Ocard(X22810),X22812) != X22808
        | hAPP(c_Finite__Set_Ocard(X22810),X22809) = hAPP(c_Nat_OSuc,X22808) ) ),
    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)],[i_0_5683])])])])])]) ).

fof(i_0_8003,plain,
    ! [X28782,X28783,X28784,X28785,X28786,X28787] :
      ( ~ c_Finite__Set_Ofolding__idem(X28787,X28786,X28785,X28784)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28787),X28783))
      | ~ hBOOL(hAPP(hAPP(c_member(X28787),X28782),X28783))
      | hAPP(c_Fun_Ocomp(X28786,X28786,X28786,hAPP(X28784,X28783)),hAPP(X28785,X28782)) = hAPP(X28784,X28783) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).

fof(i_0_8004,plain,
    ! [X30550,X30551,X30552] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30552),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30551)),X30550)))
      | hAPP(hAPP(c_List_Otake(X30551),hAPP(c_Nat_OSuc,X30552)),X30550) = hAPP(hAPP(c_List_Oappend(X30551),hAPP(hAPP(c_List_Otake(X30551),X30552),X30550)),hAPP(hAPP(c_List_Olist_OCons(X30551),hAPP(hAPP(c_List_Onth(X30551),X30550),X30552)),c_List_Olist_ONil(X30551))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).

fof(i_0_8005,plain,
    ! [X21122,X21123,X21124] :
      ( ~ class_Orderings_Olinorder(X21124)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21124),X21123))
      | X21123 = c_Orderings_Obot__class_Obot(tc_fun(X21124,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21124),X21122))
      | X21122 = c_Orderings_Obot__class_Obot(tc_fun(X21124,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21124,tc_HOL_Obool)),X21123),X21122) != c_Orderings_Obot__class_Obot(tc_fun(X21124,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X21124,c_Orderings_Oord__class_Omin(X21124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21124,tc_HOL_Obool)),X21123),X21122)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21124),c_Big__Operators_Olattice_OInf__fin(X21124,c_Orderings_Oord__class_Omin(X21124),X21123)),c_Big__Operators_Olattice_OInf__fin(X21124,c_Orderings_Oord__class_Omin(X21124),X21122)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).

fof(i_0_8006,plain,
    ! [X21128,X21129,X21130] :
      ( ~ class_Orderings_Olinorder(X21130)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21130),X21129))
      | X21129 = c_Orderings_Obot__class_Obot(tc_fun(X21130,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21130),X21128))
      | X21128 = c_Orderings_Obot__class_Obot(tc_fun(X21130,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21130,tc_HOL_Obool)),X21129),X21128) != c_Orderings_Obot__class_Obot(tc_fun(X21130,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X21130,c_Orderings_Oord__class_Omax(X21130),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21130,tc_HOL_Obool)),X21129),X21128)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X21130),c_Big__Operators_Olattice_OSup__fin(X21130,c_Orderings_Oord__class_Omax(X21130),X21129)),c_Big__Operators_Olattice_OSup__fin(X21130,c_Orderings_Oord__class_Omax(X21130),X21128)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).

fof(i_0_8007,plain,
    ! [X29287,X29288,X29289,X29290] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X29290,X29289),tc_fun(X29290,X29289)),X29288),c_Fun_Ocomp(X29289,X29289,X29290,X29287)) = c_Fun_Ocomp(X29289,X29289,X29290,hAPP(hAPP(c_Nat_Ocompow(X29289,X29289),X29288),X29287)),
    inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).

fof(i_0_8008,plain,
    ! [X32757,X32758,X32759,X32760,X32761] : hAPP(c_New__DSequence_Opos__bind(X32761,X32760,X32759,X32758),X32757) = hAPP(c_Lazy__Sequence_Obind(X32761,X32760,hAPP(X32759,X32757)),hAPP(hAPP(c_COMBC(X32761,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32760)),X32758),X32757)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(i_0_8009,plain,
    ! [X33704,X33705,X33706,X33707,X33708,X33709] : hAPP(hAPP(c_Product__Type_Ocurry(X33709,X33708,X33707,X33706),X33705),X33704) = hAPP(X33706,hAPP(hAPP(c_Product__Type_OPair(X33709,X33708),X33705),X33704)),
    inference(variable_rename,[status(thm)],[fact_curry__conv]) ).

fof(i_0_8010,plain,
    ! [X33624,X33625,X33626,X33627,X33628,X33629] : hAPP(hAPP(c_Product__Type_Ocurry(X33629,X33628,X33627,X33626),X33625),X33624) = hAPP(X33626,hAPP(hAPP(c_Product__Type_OPair(X33629,X33628),X33625),X33624)),
    inference(variable_rename,[status(thm)],[fact_curry__def]) ).

fof(i_0_8011,plain,
    ! [X19712,X19713,X19714,X19715,X19716] :
      ( ( hAPP(c_Set_Oimage(X19716,X19715,X19714),X19713) != hAPP(c_Set_Oimage(X19716,X19715,X19714),X19712)
        | X19713 = X19712
        | ~ c_Fun_Oinj__on(X19716,X19715,X19714,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19716,tc_HOL_Obool)),X19713),X19712)) )
      & ( X19713 != X19712
        | hAPP(c_Set_Oimage(X19716,X19715,X19714),X19713) = hAPP(c_Set_Oimage(X19716,X19715,X19714),X19712)
        | ~ c_Fun_Oinj__on(X19716,X19715,X19714,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19716,tc_HOL_Obool)),X19713),X19712)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).

cnf(i_0_8012,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk442_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_OdropWhile(X1,X3,X2) = c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5669]) ).

fof(i_0_8013,plain,
    ! [X23888,X23889,X23890,X23891] :
      ( ~ class_Fields_Olinordered__field(X23891)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23891),c_Groups_Ozero__class_Ozero(X23891)),X23890))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23891),X23889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23891),X23888),X23890)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23891),X23889),X23890)),X23888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).

fof(i_0_8014,plain,
    ! [X23769,X23770,X23771,X23772] :
      ( ~ class_Fields_Olinordered__field(X23772)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23772),c_Groups_Ozero__class_Ozero(X23772)),X23771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23772),X23770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23772),X23769),X23771)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23772),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23772),X23770),X23771)),X23769)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).

fof(i_0_8015,plain,
    ! [X28196,X28197,X28198,X28199,X28200] :
      ( ~ c_Relation_Orefl__on(X28200,X28199,X28198)
      | ~ c_Relation_Orefl__on(X28200,X28197,X28196)
      | c_Relation_Orefl__on(X28200,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28200,tc_HOL_Obool)),X28199),X28197),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28200,X28200),tc_HOL_Obool)),X28198),X28196)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).

fof(i_0_8016,plain,
    ! [X28191,X28192,X28193,X28194,X28195] :
      ( ~ c_Relation_Orefl__on(X28195,X28194,X28193)
      | ~ c_Relation_Orefl__on(X28195,X28192,X28191)
      | c_Relation_Orefl__on(X28195,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28195,tc_HOL_Obool)),X28194),X28192),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool)),X28193),X28191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).

fof(i_0_8017,plain,
    ! [X33607,X33608,X33609,X33610] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33610,X33609,X33608,X33607,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33609)) = X33608,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I1_J]) ).

fof(i_0_8018,plain,
    ! [X33559,X33560,X33561] :
      ( hAPP(c_Set_Oimage(X33561,X33560,X33559),c_Orderings_Otop__class_Otop(tc_fun(X33561,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33560,tc_HOL_Obool))
      | c_Fun_Oinj__on(X33560,X33561,c_Hilbert__Choice_Oinv__into(X33561,X33560,c_Orderings_Otop__class_Otop(tc_fun(X33561,tc_HOL_Obool)),X33559),c_Orderings_Otop__class_Otop(tc_fun(X33560,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_8019,plain,
    ! [X33635,X33636] : c_Fun_Obij__betw(X33636,X33636,c_Fun_Oid(X33636),X33635,X33635),
    inference(variable_rename,[status(thm)],[fact_bij__betw__id]) ).

fof(i_0_8020,plain,
    ! [X27744,X27745,X27746,X27747,X27748] : hAPP(c_Relation_ODomain(X27748,X27747),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27748,X27747)),hAPP(hAPP(c_Product__Type_OPair(X27748,X27747),X27746),X27745)),X27744)) = hAPP(hAPP(c_Set_Oinsert(X27748),X27746),hAPP(c_Relation_ODomain(X27748,X27747),X27744)),
    inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).

fof(i_0_8021,plain,
    ! [X27666,X27667,X27668,X27669,X27670] : hAPP(c_Relation_ORange(X27670,X27669),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27670,X27669)),hAPP(hAPP(c_Product__Type_OPair(X27670,X27669),X27668),X27667)),X27666)) = hAPP(hAPP(c_Set_Oinsert(X27669),X27667),hAPP(c_Relation_ORange(X27670,X27669),X27666)),
    inference(variable_rename,[status(thm)],[fact_Range__insert]) ).

cnf(i_0_8022,plain,
    ( c_List_Oremove1(X1,X3,X2) = hAPP(c_List_OremoveAll(X1,X3),X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5684]) ).

fof(i_0_8023,plain,
    ! [X18330,X18331,X18332,X18333] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18333,tc_HOL_Obool)),X18332),X18331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18333,tc_HOL_Obool)),X18331),X18330))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18333,tc_HOL_Obool)),X18332),X18330)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_8024,plain,
    ! [X18445,X18446,X18447,X18448] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18448,tc_HOL_Obool)),X18447),X18446))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18448,tc_HOL_Obool)),X18446),X18445))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18448,tc_HOL_Obool)),X18447),X18445)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_8025,plain,
    ! [X18449,X18450,X18451,X18452] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18452,tc_HOL_Obool)),X18451),X18450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18452,tc_HOL_Obool)),X18450),X18449))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18452,tc_HOL_Obool)),X18451),X18449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_8026,plain,
    ! [X17652,X17653,X17654,X17655] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17655,tc_HOL_Obool)),X17654),X17653))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17655,tc_HOL_Obool)),X17653),X17652))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17655,tc_HOL_Obool)),X17654),X17652)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_8027,plain,
    ! [X23019,X23020] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23020),X23019))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23020)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23019))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23020)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23019)))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23020),X23019)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).

fof(i_0_8028,plain,
    ! [X28846,X28847,X28848,X28849,X28850] : hAPP(hAPP(c_Product__Type_Oscomp(X28850,X28849,X28850,X28848),hAPP(c_Product__Type_OPair(X28849,X28850),X28847)),X28846) = hAPP(X28846,X28847),
    inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).

cnf(i_0_8029,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Oupt(X1,X3)) = c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5685]) ).

fof(i_0_8030,plain,
    ! [X24758,X24759,X24760] :
      ( ~ class_Divides_Osemiring__div(X24760)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24760),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24760),X24759),X24758)),X24758)),c_Divides_Odiv__class_Omod(X24760,X24759,X24758)) = X24759 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).

fof(i_0_8031,plain,
    ! [X29450,X29451,X29452] :
      ( ~ class_Divides_Osemiring__div(X29452)
      | X29451 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29452),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X29452),X29451),X29450)),X29450)),c_Divides_Odiv__class_Omod(X29452,X29451,X29450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).

fof(i_0_8032,plain,
    ! [X32049,X32050,X32051,X32052] :
      ( ~ class_Orderings_Olinorder(X32052)
      | c_List_Olinorder__class_Osorted(X32052,hAPP(hAPP(c_List_Omap(X32051,X32052),X32050),c_List_Olinorder__class_Osort__key(X32051,X32052,X32050,X32049))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])]) ).

cnf(i_0_8033,plain,
    hAPP(c_List_Orotate(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Orotate(X3,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5686]) ).

cnf(i_0_8034,plain,
    c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5687]) ).

fof(i_0_8035,plain,
    ! [X21395,X21396] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21396,tc_fun(X21396,tc_HOL_Obool)),X21395),hAPP(hAPP(c_COMBC(X21396,tc_fun(X21396,tc_HOL_Obool),tc_fun(X21396,tc_HOL_Obool)),c_Set_Oinsert(X21396)),c_Orderings_Obot__class_Obot(tc_fun(X21396,tc_HOL_Obool)))) = X21395,
    inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).

fof(i_0_8036,plain,
    ! [X30575,X30576,X30577,X30578] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30578),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30577)),X30576)))
      | hAPP(hAPP(c_List_Olist__update(X30577,X30576),X30578),X30575) = hAPP(hAPP(c_List_Oappend(X30577),hAPP(hAPP(c_List_Otake(X30577),X30578),X30576)),hAPP(hAPP(c_List_Olist_OCons(X30577),X30575),hAPP(hAPP(c_List_Odrop(X30577),hAPP(c_Nat_OSuc,X30578)),X30576))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).

fof(i_0_8037,plain,
    ! [X30898,X30899,X30900,X30901,X30902,X30903] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30903),hAPP(X30902,X30901)),hAPP(X30902,X30900)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30899,X30903,X30902),X30901),hAPP(hAPP(c_List_Olist_OCons(X30899),X30900),X30898)) = hAPP(hAPP(c_List_Olist_OCons(X30899),X30901),hAPP(hAPP(c_List_Olist_OCons(X30899),X30900),X30898))
        | ~ class_Orderings_Olinorder(X30903) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30903),hAPP(X30902,X30901)),hAPP(X30902,X30900)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30899,X30903,X30902),X30901),hAPP(hAPP(c_List_Olist_OCons(X30899),X30900),X30898)) = hAPP(hAPP(c_List_Olist_OCons(X30899),X30900),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30899,X30903,X30902),X30901),X30898))
        | ~ class_Orderings_Olinorder(X30903) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5688])])]) ).

fof(i_0_8038,plain,
    ! [X31562,X31563] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31563),X31562))
      | hBOOL(hAPP(c_List_Odistinct(tc_fun(X31563,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31563),tc_fun(X31563,tc_HOL_Obool)),c_List_Oset(X31563)),c_Enum_Osublists(X31563,X31562)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])]) ).

fof(i_0_8039,plain,
    ! [X30301,X30302] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30301)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30301)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30301))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30301)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30302),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30301)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5689])]) ).

fof(i_0_8040,plain,
    ! [X24535,X24536,X24537] : hAPP(c_Set_OPow(X24537),hAPP(hAPP(c_Set_Oinsert(X24537),X24536),X24535)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X24537,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X24537),X24535)),hAPP(c_Set_Oimage(tc_fun(X24537,tc_HOL_Obool),tc_fun(X24537,tc_HOL_Obool),hAPP(c_Set_Oinsert(X24537),X24536)),hAPP(c_Set_OPow(X24537),X24535))),
    inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).

fof(i_0_8041,plain,
    ! [X20949,X20950,X20951,X20952] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20952),hAPP(c_Set_Ovimage(X20952,X20951,X20950),X20949)))
      | hAPP(c_Set_Oimage(X20952,X20951,X20950),c_Orderings_Otop__class_Otop(tc_fun(X20952,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20951,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20951),X20949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).

fof(i_0_8042,plain,
    ! [X29739,X29740,X29741,X29742] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29742),X29741),X29739))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29742)),hAPP(hAPP(c_List_Olist_OCons(X29742),X29741),X29740)),c_List_Olists(X29742,X29739))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29742)),X29740),c_List_Olists(X29742,X29739)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29742)),hAPP(hAPP(c_List_Olist_OCons(X29742),X29741),X29740)),c_List_Olists(X29742,X29739))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29742),X29741),X29739))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29742)),X29740),c_List_Olists(X29742,X29739)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29742)),hAPP(hAPP(c_List_Olist_OCons(X29742),X29741),X29740)),c_List_Olists(X29742,X29739))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).

fof(i_0_8043,plain,
    ! [X17881,X17882,X17883,X17884] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17884,tc_HOL_Obool)),X17882),hAPP(hAPP(c_Set_Oinsert(X17884),X17883),X17881)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17884,tc_HOL_Obool)),X17882),X17881))
        | hBOOL(hAPP(hAPP(c_member(X17884),X17883),X17882)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17884,tc_HOL_Obool)),X17882),X17881))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17884,tc_HOL_Obool)),X17882),hAPP(hAPP(c_Set_Oinsert(X17884),X17883),X17881)))
        | hBOOL(hAPP(hAPP(c_member(X17884),X17883),X17882)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5690])])]) ).

fof(i_0_8044,plain,
    ! [X29072,X29073] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X29073))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X29073),X29072))),X29073)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).

fof(i_0_8045,plain,
    ! [X20710,X20711,X20712,X20713] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20713),X20712),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20713,tc_HOL_Obool)),X20711),X20710)))
      | hBOOL(hAPP(hAPP(c_member(X20713),X20712),X20711)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).

fof(i_0_8046,plain,
    ! [X20706,X20707,X20708,X20709] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20709),X20708),X20707))
        | ~ hBOOL(hAPP(hAPP(c_member(X20709),X20708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20709,tc_HOL_Obool)),X20707),X20706))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20709),X20708),X20706))
        | ~ hBOOL(hAPP(hAPP(c_member(X20709),X20708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20709,tc_HOL_Obool)),X20707),X20706))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20709),X20708),X20707))
        | ~ hBOOL(hAPP(hAPP(c_member(X20709),X20708),X20706))
        | hBOOL(hAPP(hAPP(c_member(X20709),X20708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20709,tc_HOL_Obool)),X20707),X20706))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).

fof(i_0_8047,plain,
    ! [X20483,X20484,X20485,X20486] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20486),X20485),X20484))
        | ~ hBOOL(hAPP(hAPP(c_member(X20486),X20485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20486,tc_HOL_Obool)),X20484),X20483))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20486),X20485),X20483))
        | ~ hBOOL(hAPP(hAPP(c_member(X20486),X20485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20486,tc_HOL_Obool)),X20484),X20483))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5691])])]) ).

fof(i_0_8048,plain,
    ! [X17320,X17321,X17322,X17323] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17323),X17322),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17323,tc_HOL_Obool)),X17321),X17320)))
      | hBOOL(hAPP(hAPP(c_member(X17323),X17322),X17321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).

fof(i_0_8049,plain,
    ! [X20714,X20715,X20716,X20717] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20717),X20716),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20717,tc_HOL_Obool)),X20715),X20714)))
      | hBOOL(hAPP(hAPP(c_member(X20717),X20716),X20714)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).

fof(i_0_8050,plain,
    ! [X17360,X17361,X17362,X17363] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17363,tc_HOL_Obool)),X17362),hAPP(hAPP(c_Set_Oinsert(X17363),X17361),X17360)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17363,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17363,tc_HOL_Obool)),X17362),X17360)),hAPP(hAPP(c_Set_Oinsert(X17363),X17361),c_Orderings_Obot__class_Obot(tc_fun(X17363,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).

fof(i_0_8051,plain,
    ! [X30310,X30311] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30311),X30310))
        | c_List_Oupto(X30311,X30310) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X30311),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30311),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30310))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30311),X30310))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30311),X30310))
        | c_List_Oupto(X30311,X30310) = c_List_Olist_ONil(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30311),X30310))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])])]) ).

fof(i_0_8052,plain,
    ! [X21098,X21099,X21100] :
      ( ~ class_Groups_Oab__semigroup__mult(X21100)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21100),X21099))
      | X21099 = c_Orderings_Obot__class_Obot(tc_fun(X21100,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21100),X21098))
      | X21098 = c_Orderings_Obot__class_Obot(tc_fun(X21100,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21100,tc_HOL_Obool)),X21099),X21098) != c_Orderings_Obot__class_Obot(tc_fun(X21100,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X21100,c_Groups_Otimes__class_Otimes(X21100)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21100,tc_HOL_Obool)),X21099),X21098)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21100),hAPP(c_Finite__Set_Ofold1(X21100,c_Groups_Otimes__class_Otimes(X21100)),X21099)),hAPP(c_Finite__Set_Ofold1(X21100,c_Groups_Otimes__class_Otimes(X21100)),X21098)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).

fof(i_0_8053,plain,
    ! [X18022,X18023,X18024,X18025,X18026,X18027] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18027,X18026,X18025)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18027),X18024))
      | hBOOL(hAPP(hAPP(c_member(X18027),X18023),X18024))
      | hAPP(hAPP(c_Finite__Set_Ofold(X18027,X18026,X18025),X18022),hAPP(hAPP(c_Set_Oinsert(X18027),X18023),X18024)) = hAPP(hAPP(X18025,X18023),hAPP(hAPP(c_Finite__Set_Ofold(X18027,X18026,X18025),X18022),X18024)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5693])]) ).

cnf(i_0_8054,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(X2)
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5459]) ).

fof(i_0_8055,plain,
    ! [X28764,X28765,X28766,X28767,X28768,X28769] :
      ( ~ c_Finite__Set_Ofolding__idem(X28769,X28768,X28767,X28766)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28769),X28765))
      | hAPP(X28766,hAPP(hAPP(c_Set_Oinsert(X28769),X28764),X28765)) = hAPP(c_Fun_Ocomp(X28768,X28768,X28768,hAPP(X28766,X28765)),hAPP(X28767,X28764)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).

fof(i_0_8056,plain,
    ! [X28851,X28852,X28853,X28854] : hAPP(hAPP(c_Product__Type_Oscomp(X28854,X28853,X28852,tc_prod(X28853,X28852)),X28851),c_Product__Type_OPair(X28853,X28852)) = X28851,
    inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).

fof(i_0_8057,plain,
    ! [X25419,X25420] : hAPP(c_Set_OPow(X25420),X25419) = hAPP(c_Set_OCollect(tc_fun(X25420,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X25420,tc_HOL_Obool),tc_fun(X25420,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X25420,tc_HOL_Obool))),X25419)),
    inference(variable_rename,[status(thm)],[fact_Pow__def]) ).

fof(i_0_8058,plain,
    ! [X32209,X32210] : hAPP(c_List_Orev(X32210),X32209) = hAPP(c_List_Ofoldl(tc_List_Olist(X32210),X32210,hAPP(c_COMBC(X32210,tc_List_Olist(X32210),tc_List_Olist(X32210)),c_List_Olist_OCons(X32210)),c_List_Olist_ONil(X32210)),X32209),
    inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).

fof(i_0_8059,plain,
    ! [X33001,X33002] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33002),X33001))
        | c_Lazy__Sequence_Osmall__lazy_H(X33002,X33001) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X33002),X33001))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33002),X33001))
        | c_Lazy__Sequence_Osmall__lazy_H(X33002,X33001) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X33001),c_Lazy__Sequence_Osmall__lazy_H(X33002,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33001),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X33002),X33001))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5694])])]) ).

cnf(i_0_8060,plain,
    ( c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3) = X3
    | X1 != c_List_Olist_ONil(X2)
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5652]) ).

fof(i_0_8061,plain,
    ! [X24123,X24124] :
      ( ~ class_Rings_Ocomm__semiring__1(X24124)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24124),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24124),c_Groups_Oone__class_Oone(X24124)),c_Groups_Oone__class_Oone(X24124))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24124),c_Nat_Osemiring__1__class_Oof__nat(X24124)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X24123))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24124),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24124),X24123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24124),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24124),X24123)),c_Groups_Oone__class_Oone(X24124))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).

fof(i_0_8062,plain,
    ! [X31579,X31580,X31581,X31582] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31582)),X31581),hAPP(c_List_Oset(tc_List_Olist(X31582)),c_Enum_On__lists(X31582,X31580,X31579))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31582)),X31581) = X31580 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])]) ).

cnf(i_0_8063,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5473]) ).

fof(i_0_8064,plain,
    ! [X33354,X33355,X33356] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33356,X33356),tc_HOL_Obool)),X33355),X33354))
      | ~ c_Relation_Oantisym(X33356,X33354)
      | c_Relation_Oantisym(X33356,X33355) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__subset])]) ).

fof(i_0_8065,plain,
    ! [X28227,X28228,X28229] :
      ( ~ c_Wellfounded_Oacyclic(X28229,X28228)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28229,X28229),tc_HOL_Obool)),X28227),X28228))
      | c_Wellfounded_Oacyclic(X28229,X28227) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).

fof(i_0_8066,plain,
    ! [X27512,X27513,X27514] :
      ( ~ c_Wellfounded_Owf(X27514,X27513)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27514,X27514),tc_HOL_Obool)),X27512),X27513))
      | c_Wellfounded_Owf(X27514,X27512) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).

fof(i_0_8067,plain,
    ! [X30256,X30257,X30258,X30259] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30257),X30259),hAPP(c_List_Oset(X30257),c_List_Oremove1(X30257,X30258,X30256))))
        | hBOOL(hAPP(hAPP(c_member(X30257),X30259),hAPP(c_List_Oset(X30257),X30256)))
        | X30259 = X30258 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30257),X30259),hAPP(c_List_Oset(X30257),X30256)))
        | hBOOL(hAPP(hAPP(c_member(X30257),X30259),hAPP(c_List_Oset(X30257),c_List_Oremove1(X30257,X30258,X30256))))
        | X30259 = X30258 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).

fof(i_0_8068,plain,
    ! [X20515,X20516,X20517,X20518] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20518,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20518,tc_HOL_Obool)),X20517),X20516)),X20515) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20518,tc_HOL_Obool)),X20517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20518,tc_HOL_Obool)),X20516),X20515)),
    inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).

fof(i_0_8069,plain,
    ! [X19386,X19387,X19388,X19389] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19389,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19389,tc_HOL_Obool)),X19388),X19387)),X19386) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19389,tc_HOL_Obool)),X19388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19389,tc_HOL_Obool)),X19387),X19386)),
    inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).

fof(i_0_8070,plain,
    ! [X20807,X20808,X20809,X20810] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20810,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20810,tc_HOL_Obool)),X20809),X20808)),X20807) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20810,tc_HOL_Obool)),X20809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20810,tc_HOL_Obool)),X20808),X20807)),
    inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).

fof(i_0_8071,plain,
    ! [X20168,X20169,X20170] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20170),X20169))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20168),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20169),X20168)),X20170))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).

fof(i_0_8072,plain,
    ! [X32247,X32248,X32249,X32250] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32250),X32249),hAPP(c_List_Oset(X32250),X32247)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32250),X32249),hAPP(c_List_Oset(X32250),c_List_OtakeWhile(X32250,X32248,X32247)))) )
      & ( hBOOL(hAPP(X32248,X32249))
        | ~ hBOOL(hAPP(hAPP(c_member(X32250),X32249),hAPP(c_List_Oset(X32250),c_List_OtakeWhile(X32250,X32248,X32247)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__takeWhileD])])]) ).

fof(i_0_8073,plain,
    ! [X30252,X30253,X30254,X30255] :
      ( hBOOL(hAPP(hAPP(c_member(X30255),X30254),hAPP(c_List_Oset(X30255),X30253)))
      | ~ hBOOL(hAPP(hAPP(c_member(X30255),X30254),hAPP(c_List_Oset(X30255),c_List_Oremove1(X30255,X30252,X30253)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5695])]) ).

fof(i_0_8074,plain,
    ! [X29836,X29837,X29838,X29839] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29839),X29838),hAPP(c_List_Oset(X29839),c_List_Osublist(X29839,X29837,X29836))))
      | hBOOL(hAPP(hAPP(c_member(X29839),X29838),hAPP(c_List_Oset(X29839),X29837))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).

fof(i_0_8075,plain,
    ! [X29828,X29829,X29830,X29831] :
      ( hBOOL(hAPP(hAPP(c_member(X29831),X29830),hAPP(c_List_Oset(X29831),X29829)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29831),X29830),hAPP(c_List_Oset(X29831),c_List_Osublist(X29831,X29829,X29828)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5696])]) ).

fof(i_0_8076,plain,
    ! [X31752,X31753,X31754] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31754,tc_HOL_Obool)),hAPP(c_List_Oset(X31754),hAPP(c_List_Ofilter(X31754,X31753),X31752))),hAPP(c_List_Oset(X31754),X31752))),
    inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).

fof(i_0_8077,plain,
    ! [X18555,X18556,X18557,X18558,X18559] :
      ( ( X18558 = X18557
        | X18556 = X18555
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18555)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18555)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18556))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18559) )
      & ( X18558 != X18557
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18555)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18556))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18559) )
      & ( X18556 != X18555
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18558),X18555)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18559),X18557),X18556))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18559) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_8078,plain,
    ! [X18629,X18630,X18631,X18632,X18633] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18631)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18629)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18631))
        | X18632 = X18630
        | X18631 = X18629
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18633) )
      & ( X18632 != X18630
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18631)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18631))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18633) )
      & ( X18631 != X18629
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18631)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18632),X18629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18633),X18630),X18631))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18633) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

cnf(i_0_8079,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X1,X3)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5697]) ).

fof(i_0_8080,plain,
    ! [X28219,X28220] :
      ( ( ~ c_Predicate_Oreflp(X28220,X28219)
        | c_Relation_Orefl__on(X28220,c_Orderings_Otop__class_Otop(tc_fun(X28220,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X28220,X28220)),hAPP(c_Product__Type_Oprod_Oprod__case(X28220,X28220,tc_HOL_Obool),X28219))) )
      & ( ~ c_Relation_Orefl__on(X28220,c_Orderings_Otop__class_Otop(tc_fun(X28220,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X28220,X28220)),hAPP(c_Product__Type_Oprod_Oprod__case(X28220,X28220,tc_HOL_Obool),X28219)))
        | c_Predicate_Oreflp(X28220,X28219) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).

fof(i_0_8081,plain,
    ! [X20152,X20153,X20154] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20153),X20154)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20152),X20154)),X20153))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20154),X20153)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20152),X20154)),X20153))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20153),X20154)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20154),X20153)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).

cnf(i_0_8082,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_5698]) ).

fof(i_0_8083,plain,
    ! [X33098,X33099,X33100,X33101,X33103,X33104,X33105,X33107] :
      ( ( hBOOL(hAPP(X33100,esk495_4(X33098,X33099,X33100,X33101)))
        | ~ hBOOL(hAPP(X33100,X33101))
        | c_FunDef_OTHE__default(X33099,X33098,X33100) = c_HOL_OThe(X33099,X33100) )
      & ( esk495_4(X33098,X33099,X33100,X33101) != X33101
        | ~ hBOOL(hAPP(X33100,X33101))
        | c_FunDef_OTHE__default(X33099,X33098,X33100) = c_HOL_OThe(X33099,X33100) )
      & ( hBOOL(hAPP(X33105,esk496_3(X33103,X33104,X33105)))
        | c_FunDef_OTHE__default(X33104,X33103,X33105) = X33103 )
      & ( ~ hBOOL(hAPP(X33105,X33107))
        | X33107 = esk496_3(X33103,X33104,X33105)
        | c_FunDef_OTHE__default(X33104,X33103,X33105) = X33103 ) ),
    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_THE__default__def])])])])])]) ).

fof(i_0_8084,plain,
    ! [X20696,X20697,X20698,X20699,X20700] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20700),X20699),hAPP(c_Set_Ovimage(X20700,X20698,X20697),X20696)))
      | hBOOL(hAPP(hAPP(c_member(X20698),hAPP(X20697,X20699)),X20696)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).

fof(i_0_8085,plain,
    ! [X20691,X20692,X20693,X20694,X20695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20695),X20694),hAPP(c_Set_Ovimage(X20695,X20693,X20692),X20691)))
        | hBOOL(hAPP(hAPP(c_member(X20693),hAPP(X20692,X20694)),X20691)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20693),hAPP(X20692,X20694)),X20691))
        | hBOOL(hAPP(hAPP(c_member(X20695),X20694),hAPP(c_Set_Ovimage(X20695,X20693,X20692),X20691))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).

fof(i_0_8086,plain,
    ! [X18334,X18335,X18336,X18337] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,X18337)),X18335),X18334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,X18337)),X18335),X18334))
        | ~ class_Orderings_Oord(X18337) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,X18337)),X18334),X18335))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,X18337)),X18335),X18334))
        | ~ class_Orderings_Oord(X18337) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,X18337)),X18335),X18334))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,X18337)),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,X18337)),X18335),X18334))
        | ~ class_Orderings_Oord(X18337) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5699])])]) ).

fof(i_0_8087,plain,
    ! [X30660,X30661,X30662,X30663] : hAPP(hAPP(c_List_Odrop(X30663),X30662),hAPP(hAPP(c_List_Olist_OCons(X30663),X30661),X30660)) = c_Nat_Onat_Onat__case(tc_List_Olist(X30663),hAPP(hAPP(c_List_Olist_OCons(X30663),X30661),X30660),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X30663),tc_List_Olist(X30663)),c_List_Odrop(X30663)),X30660),X30662),
    inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).

fof(i_0_8088,plain,
    ! [X22596,X22597,X22598] :
      ( ~ class_Rings_Olinordered__idom(X22598)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),c_Groups_Ozero__class_Ozero(X22598)),X22597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),c_Groups_Ozero__class_Ozero(X22598)),X22596))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),X22596),c_Groups_Oone__class_Oone(X22598)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22598),X22597),X22596)),X22597)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).

fof(i_0_8089,plain,
    ! [X22599,X22600,X22601] :
      ( ~ class_Rings_Olinordered__idom(X22601)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),c_Groups_Ozero__class_Ozero(X22601)),X22600))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),c_Groups_Ozero__class_Ozero(X22601)),X22599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),X22599),c_Groups_Oone__class_Oone(X22601)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22601),X22599),X22600)),X22600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).

fof(i_0_8090,plain,
    ! [X29581,X29582,X29583,X29584] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29584),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29583),X29582)))
        | hAPP(c_Random_Opick(X29583,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29583)),X29582),X29581)),X29584) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X29583),X29582) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29584),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29583),X29582)))
        | hAPP(c_Random_Opick(X29583,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29583)),X29582),X29581)),X29584) = hAPP(c_Random_Opick(X29583,X29581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X29584),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29583),X29582))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5700])]) ).

cnf(i_0_8091,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5630]) ).

cnf(i_0_8092,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5632]) ).

cnf(i_0_8093,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5631]) ).

cnf(i_0_8094,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5633]) ).

fof(i_0_8095,plain,
    ! [X25087,X25088,X25089,X25090,X25091,X25092,X25093] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25089,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25089,tc_HOL_Obool),X25088)),X25087) != c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25089,tc_HOL_Obool)),X25090),X25088))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25089,tc_HOL_Obool)),X25090),X25087) = c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25093,tc_HOL_Obool)),esk221_3(X25091,X25092,X25093)),X25092))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25093,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25093,tc_HOL_Obool),X25092)),X25091) = c_Orderings_Obot__class_Obot(tc_fun(X25093,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25093,tc_HOL_Obool)),esk221_3(X25091,X25092,X25093)),X25091) != c_Orderings_Obot__class_Obot(tc_fun(X25093,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25093,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25093,tc_HOL_Obool),X25092)),X25091) = c_Orderings_Obot__class_Obot(tc_fun(X25093,tc_HOL_Obool)) ) ),
    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_Union__disjoint])])])])])]) ).

fof(i_0_8096,plain,
    ! [X23345,X23346,X23347] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23347))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23346))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23346),X23345))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23347),X23345)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23347),X23346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).

fof(i_0_8097,plain,
    ! [X27724,X27725,X27726,X27727] : hAPP(c_Relation_ODomain(X27727,X27726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27727,X27726),tc_HOL_Obool)),X27725),X27724)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27727,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27727,X27726),X27725)),hAPP(c_Relation_ODomain(X27727,X27726),X27724)),
    inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).

fof(i_0_8098,plain,
    ! [X27646,X27647,X27648,X27649] : hAPP(c_Relation_ORange(X27649,X27648),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27649,X27648),tc_HOL_Obool)),X27647),X27646)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27648,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27649,X27648),X27647)),hAPP(c_Relation_ORange(X27649,X27648),X27646)),
    inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).

fof(i_0_8099,plain,
    ! [X31084,X31085,X31086,X31087,X31088,X31089] : hAPP(hAPP(c_List_Omap(X31089,X31088),X31087),hAPP(hAPP(c_List_Olist__update(X31089,X31086),X31085),X31084)) = hAPP(hAPP(c_List_Olist__update(X31088,hAPP(hAPP(c_List_Omap(X31089,X31088),X31087),X31086)),X31085),hAPP(X31087,X31084)),
    inference(variable_rename,[status(thm)],[fact_map__update]) ).

fof(i_0_8100,plain,
    ! [X29840,X29841,X29842,X29843] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29843),X29842),hAPP(c_List_Oset(X29843),hAPP(hAPP(c_List_Olist_OCons(X29843),X29841),X29840))))
      | X29842 = X29841
      | hBOOL(hAPP(hAPP(c_member(X29843),X29842),hAPP(c_List_Oset(X29843),X29840))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).

fof(i_0_8101,plain,
    ! [X31352] :
      ( X31352 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31352)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X31352))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).

fof(i_0_8102,plain,
    ! [X30631,X30632,X30633,X30634] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30634),X30633),hAPP(c_List_Oset(X30634),hAPP(hAPP(c_List_Odrop(X30634),X30632),X30631))))
      | hBOOL(hAPP(hAPP(c_member(X30634),X30633),hAPP(c_List_Oset(X30634),X30631))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).

fof(i_0_8103,plain,
    ! [X29832,X29833,X29834,X29835] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29835),X29834),hAPP(c_List_Oset(X29835),hAPP(hAPP(c_List_Otake(X29835),X29833),X29832))))
      | hBOOL(hAPP(hAPP(c_member(X29835),X29834),hAPP(c_List_Oset(X29835),X29832))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).

fof(i_0_8104,plain,
    ! [X22693,X22694,X22695] :
      ( ~ class_Rings_Olinordered__semidom(X22695)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22695),c_Groups_Ozero__class_Ozero(X22695)),X22694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22695),X22694),c_Groups_Oone__class_Oone(X22695)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22695),hAPP(hAPP(c_Power_Opower__class_Opower(X22695),X22694),hAPP(c_Nat_OSuc,X22693))),c_Groups_Oone__class_Oone(X22695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).

fof(i_0_8105,plain,
    ! [X29474,X29475,X29476] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29476),X29475),esk372_3(X29474,X29475,X29476)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29476),X29475),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29476,tc_HOL_Obool),X29474))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29476,tc_HOL_Obool)),esk372_3(X29474,X29475,X29476)),X29474))
        | ~ hBOOL(hAPP(hAPP(c_member(X29476),X29475),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29476,tc_HOL_Obool),X29474))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5701])])])]) ).

fof(i_0_8106,plain,
    ! [X23356,X23357,X23358] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23358),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23357))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23357),X23356))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23358),X23357)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23358),X23356))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).

fof(i_0_8107,plain,
    ! [X27293,X27294,X27295] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27295),esk281_3(X27293,X27294,X27295)),X27293))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27295,X27295)),X27294),c_Relation_OId__on(X27295,X27293))) )
      & ( X27294 = hAPP(hAPP(c_Product__Type_OPair(X27295,X27295),esk281_3(X27293,X27294,X27295)),esk281_3(X27293,X27294,X27295))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27295,X27295)),X27294),c_Relation_OId__on(X27295,X27293))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).

fof(i_0_8108,plain,
    ! [X33485,X33486,X33487,X33488] :
      ( ~ c_Fun_Oinj__on(X33488,X33487,X33486,c_Orderings_Otop__class_Otop(tc_fun(X33488,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33488,X33487,c_Orderings_Otop__class_Otop(tc_fun(X33488,tc_HOL_Obool)),X33486),hAPP(X33486,X33485)) = X33485 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_8109,plain,
    ! [X19752,X19753,X19754,X19755] :
      ( ~ c_Fun_Oinj__on(X19755,X19754,X19753,c_Orderings_Otop__class_Otop(tc_fun(X19755,tc_HOL_Obool)))
      | hAPP(c_Fun_Othe__inv__into(X19755,X19754,c_Orderings_Otop__class_Otop(tc_fun(X19755,tc_HOL_Obool)),X19753),hAPP(X19753,X19752)) = X19752 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).

fof(i_0_8110,plain,
    ! [X18138,X18139,X18140,X18141,X18142,X18143] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18143,X18142,X18141)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18143),X18140))
      | hAPP(hAPP(X18141,X18139),hAPP(hAPP(c_Finite__Set_Ofold(X18143,X18142,X18141),X18138),X18140)) = hAPP(hAPP(c_Finite__Set_Ofold(X18143,X18142,X18141),hAPP(hAPP(X18141,X18139),X18138)),X18140) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).

fof(i_0_8111,plain,
    ! [X33480,X33481,X33482,X33483,X33484] :
      ( ~ c_Fun_Oinj__on(X33484,X33483,X33482,c_Orderings_Otop__class_Otop(tc_fun(X33484,tc_HOL_Obool)))
      | hAPP(X33482,X33481) != X33480
      | hAPP(c_Hilbert__Choice_Oinv__into(X33484,X33483,c_Orderings_Otop__class_Otop(tc_fun(X33484,tc_HOL_Obool)),X33482),X33480) = X33481 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_8112,plain,
    ! [X28187,X28188,X28189] :
      ( ~ c_Wellfounded_OwfP(X28189,X28188)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28189,tc_fun(X28189,tc_HOL_Obool))),X28187),X28188))
      | c_Wellfounded_OwfP(X28189,X28187) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).

fof(i_0_8113,plain,
    ! [X17221,X17222,X17223] :
      ( ( hAPP(hAPP(c_COMBC(X17223,tc_fun(X17223,tc_HOL_Obool),tc_HOL_Obool),c_member(X17223)),X17222) != hAPP(hAPP(c_COMBC(X17223,tc_fun(X17223,tc_HOL_Obool),tc_HOL_Obool),c_member(X17223)),X17221)
        | X17222 = X17221 )
      & ( X17222 != X17221
        | hAPP(hAPP(c_COMBC(X17223,tc_fun(X17223,tc_HOL_Obool),tc_HOL_Obool),c_member(X17223)),X17222) = hAPP(hAPP(c_COMBC(X17223,tc_fun(X17223,tc_HOL_Obool),tc_HOL_Obool),c_member(X17223)),X17221) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_8114,plain,
    ! [X22486,X22487,X22488] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22488))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22486))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22487),X22486))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22486))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22488))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22487),X22486))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22488),X22486))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).

fof(i_0_8115,plain,
    ! [X22489,X22490,X22491] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22490))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22491),X22490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22489),X22490))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22491),X22489))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22491),X22490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22489),X22490))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22490))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22491),X22489))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22491),X22490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22489),X22490))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).

fof(i_0_8116,plain,
    ! [X31710,X31711,X31712,X31713,X31714] :
      ( ~ class_Orderings_Olinorder(X31714)
      | c_List_Olinorder__class_Osort__key(X31713,X31714,X31712,hAPP(hAPP(c_List_Olist_OCons(X31713),X31711),X31710)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31713,X31714,X31712),X31711),c_List_Olinorder__class_Osort__key(X31713,X31714,X31712,X31710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])]) ).

fof(i_0_8117,plain,
    ! [X23816,X23817,X23818,X23819] :
      ( ~ class_Fields_Olinordered__field(X23819)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23819),X23818),X23817))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23819),c_Groups_Ozero__class_Ozero(X23819)),X23816))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23819),X23818),X23816)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23819),X23817),X23816))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_8118,plain,
    ! [X22349,X22350,X22351,X22352] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22352)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),X22350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),c_Groups_Ozero__class_Ozero(X22352)),X22349))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22352),X22351),X22349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22352),X22350),X22349))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_8119,plain,
    ! [X22357,X22358,X22359,X22360] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X22360)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22360),X22359),X22358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22360),c_Groups_Ozero__class_Ozero(X22360)),X22357))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22360),X22357),X22359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22360),X22357),X22358))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_8120,plain,
    ! [X22353,X22354,X22355,X22356] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),X22355),X22354))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),c_Groups_Ozero__class_Ozero(X22356)),X22353))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22356),X22353),X22355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22356),X22353),X22354))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_8121,plain,
    ! [X23790,X23791,X23792,X23793] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X23793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23793),X23792),X23791))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23793),c_Groups_Ozero__class_Ozero(X23793)),X23790))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23793),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23793),X23792),X23790)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23793),X23791),X23790))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_8122,plain,
    ! [X22413,X22414,X22415,X22416] :
      ( ~ class_Rings_Olinordered__semidom(X22416)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22416),X22415),X22414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22416),c_Groups_Ozero__class_Ozero(X22416)),X22415))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22416),hAPP(hAPP(c_Power_Opower__class_Opower(X22416),X22415),X22413)),hAPP(hAPP(c_Power_Opower__class_Opower(X22416),X22414),X22413))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).

fof(i_0_8123,plain,
    ! [X22260,X22261,X22262,X22263] :
      ( ~ class_Rings_Oordered__semiring(X22263)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22263),X22262),X22261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22263),c_Groups_Ozero__class_Ozero(X22263)),X22260))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22263),X22262),X22260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22263),X22261),X22260))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_8124,plain,
    ! [X22268,X22269,X22270,X22271] :
      ( ~ class_Rings_Oordered__comm__semiring(X22271)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22271),X22270),X22269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22271),c_Groups_Ozero__class_Ozero(X22271)),X22268))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22271),X22268),X22270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22271),X22268),X22269))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_8125,plain,
    ! [X22264,X22265,X22266,X22267] :
      ( ~ class_Rings_Oordered__semiring(X22267)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22267),X22266),X22265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22267),c_Groups_Ozero__class_Ozero(X22267)),X22264))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22267),X22264),X22266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22267),X22264),X22265))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_8126,plain,
    ! [X29938,X29939,X29940,X29941,X29942,X29943] : hAPP(hAPP(c_List_Ozip(X29943,X29942),hAPP(hAPP(c_List_Olist_OCons(X29943),X29941),X29940)),hAPP(hAPP(c_List_Olist_OCons(X29942),X29939),X29938)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X29943,X29942)),hAPP(hAPP(c_Product__Type_OPair(X29943,X29942),X29941),X29939)),hAPP(hAPP(c_List_Ozip(X29943,X29942),X29940),X29938)),
    inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(i_0_8127,plain,
    ! [X23801,X23802,X23803] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23802),c_Groups_Ozero__class_Ozero(X23803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23802),c_Groups_Ozero__class_Ozero(X23803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23801),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23801),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23801),c_Groups_Ozero__class_Ozero(X23803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),X23802),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),c_Groups_Ozero__class_Ozero(X23803)),X23801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23803),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23803),X23802),X23801)),c_Groups_Ozero__class_Ozero(X23803)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23803) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_8128,plain,
    ! [X23787,X23788,X23789] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),c_Groups_Ozero__class_Ozero(X23789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23787))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),c_Groups_Ozero__class_Ozero(X23789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23787),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23787))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23787),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23787),c_Groups_Ozero__class_Ozero(X23789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),c_Groups_Ozero__class_Ozero(X23789)),X23787))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23789),X23788),X23787)),c_Groups_Ozero__class_Ozero(X23789)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23789) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_8129,plain,
    ! [X22242,X22243,X22244] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22243),c_Groups_Ozero__class_Ozero(X22244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22242))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22243),c_Groups_Ozero__class_Ozero(X22244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22242),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22242))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22242),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22242),c_Groups_Ozero__class_Ozero(X22244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),X22243),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),c_Groups_Ozero__class_Ozero(X22244)),X22242))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22244),X22243),X22242)),c_Groups_Ozero__class_Ozero(X22244)))
        | ~ class_Rings_Olinordered__ring__strict(X22244) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_8130,plain,
    ! [X24010,X24011] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24011),X24010))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X24011)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24010)))
        | ~ c_Nat__Transfer_Onat__set(X24010)
        | ~ c_Nat__Transfer_Ois__nat(X24011) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X24011)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24010)))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24011),X24010))
        | ~ c_Nat__Transfer_Onat__set(X24010)
        | ~ c_Nat__Transfer_Ois__nat(X24011) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J])])]) ).

fof(i_0_8131,plain,
    ! [X18670,X18671,X18672] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18672),esk39_3(X18670,X18671,X18672)),X18671))
        | ~ hBOOL(hAPP(hAPP(c_member(X18672),X18670),X18671))
        | c_Big__Operators_Olinorder__class_OMax(X18672,X18671) = X18670
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18672),X18671))
        | ~ class_Orderings_Olinorder(X18672) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18672),esk39_3(X18670,X18671,X18672)),X18670))
        | ~ hBOOL(hAPP(hAPP(c_member(X18672),X18670),X18671))
        | c_Big__Operators_Olinorder__class_OMax(X18672,X18671) = X18670
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18672),X18671))
        | ~ class_Orderings_Olinorder(X18672) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).

fof(i_0_8132,plain,
    ! [X34081,X34082,X34083] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34081)))
        | X34083 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34082),X34081)) )
      & ( X34083 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34081))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34082),X34081))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34083),X34081))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).

fof(i_0_8133,plain,
    ! [X32641,X32642,X32643,X32644,X32645,X32646,X32647] :
      ( ( ~ c_List_Olist__all(X32643,X32642,X32641)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32644),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32643)),X32641)))
        | hBOOL(hAPP(X32642,hAPP(hAPP(c_List_Onth(X32643),X32641),X32644))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_3(X32645,X32646,X32647)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32647)),X32645)))
        | c_List_Olist__all(X32647,X32646,X32645) )
      & ( ~ hBOOL(hAPP(X32646,hAPP(hAPP(c_List_Onth(X32647),X32645),esk481_3(X32645,X32646,X32647))))
        | c_List_Olist__all(X32647,X32646,X32645) ) ),
    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_list__all__length])])])])])]) ).

fof(i_0_8134,plain,
    ! [X26884] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26884)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26884)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26884))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).

fof(i_0_8135,plain,
    ! [X17667,X17668,X17669,X17670,X17671] :
      ( ~ c_Fun_Oinj__on(X17671,X17670,X17669,X17668)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17671,tc_HOL_Obool)),X17667),X17668))
      | c_Fun_Oinj__on(X17671,X17670,X17669,X17667) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_8136,plain,
    ! [X31766,X31767,X31768] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31768)),hAPP(c_List_Ofilter(X31768,X31767),X31766))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31768)),X31766))),
    inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).

fof(i_0_8137,plain,
    ! [X28946,X28947,X28948] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28948,X28948)),hAPP(hAPP(c_Product__Type_OPair(X28948,X28948),X28947),X28947)),c_Transitive__Closure_Ortrancl(X28948,X28946))),
    inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

cnf(i_0_8138,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5702]) ).

cnf(i_0_8139,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5703]) ).

fof(i_0_8140,plain,
    ! [X20066,X20067,X20068] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20068),X20067)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20068),X20066)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20067),X20066)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20067),X20066))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20068),X20067)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20068),X20066))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

cnf(i_0_8141,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5704]) ).

cnf(i_0_8142,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5705]) ).

fof(i_0_8143,plain,
    ! [X19905,X19906,X19907] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19907),X19906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19907),X19905)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19906),X19905)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19906),X19905))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19907),X19906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19907),X19905))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_8144,plain,
    ! [X33495,X33496,X33497,X33498,X33499] :
      ( ~ c_Fun_Oinj__on(X33499,X33498,X33497,X33496)
      | ~ hBOOL(hAPP(hAPP(c_member(X33499),X33495),X33496))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33499,X33498,X33496,X33497),hAPP(X33497,X33495)) = X33495 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_8145,plain,
    ! [X17692,X17693,X17694,X17695,X17696] :
      ( ~ c_Fun_Oinj__on(X17696,X17695,X17694,X17693)
      | ~ hBOOL(hAPP(hAPP(c_member(X17696),X17692),X17693))
      | hAPP(c_Fun_Othe__inv__into(X17696,X17695,X17693,X17694),hAPP(X17694,X17692)) = X17692 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).

cnf(i_0_8146,plain,
    hAPP(c_List_OremoveAll(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5706]) ).

fof(i_0_8147,plain,
    ! [X26974] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26974)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26974)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26974))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).

fof(i_0_8148,plain,
    ! [X33489,X33490,X33491,X33492,X33493,X33494] :
      ( ~ c_Fun_Oinj__on(X33494,X33493,X33492,X33491)
      | ~ hBOOL(hAPP(hAPP(c_member(X33494),X33490),X33491))
      | hAPP(X33492,X33490) != X33489
      | hAPP(c_Hilbert__Choice_Oinv__into(X33494,X33493,X33491,X33492),X33489) = X33490 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_8149,plain,
    ! [X17686,X17687,X17688,X17689,X17690,X17691] :
      ( ~ c_Fun_Oinj__on(X17691,X17690,X17689,X17688)
      | hAPP(X17689,X17687) != X17686
      | ~ hBOOL(hAPP(hAPP(c_member(X17691),X17687),X17688))
      | hAPP(c_Fun_Othe__inv__into(X17691,X17690,X17688,X17689),X17686) = X17687 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).

fof(i_0_8150,plain,
    ! [X21512,X21513,X21514,X21515,X21516] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21515),X21516),X21514))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21513),hAPP(X21512,X21516)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21515,tc_fun(X21513,tc_HOL_Obool)),X21514),X21512))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).

fof(i_0_8151,plain,
    ! [X20378,X20379,X20380,X20381] :
      ( ~ class_Rings_Olinordered__semidom(X20381)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20380),X20379))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20381),c_Groups_Oone__class_Oone(X20381)),X20378))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20381),hAPP(hAPP(c_Power_Opower__class_Opower(X20381),X20378),X20380)),hAPP(hAPP(c_Power_Opower__class_Opower(X20381),X20378),X20379))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).

fof(i_0_8152,plain,
    ! [X20374,X20375,X20376,X20377] :
      ( ~ class_Rings_Olinordered__semidom(X20377)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20376),X20375))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20377),c_Groups_Oone__class_Oone(X20377)),X20374))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20377),hAPP(hAPP(c_Power_Opower__class_Opower(X20377),X20374),X20376)),hAPP(hAPP(c_Power_Opower__class_Opower(X20377),X20374),X20375))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).

fof(i_0_8153,plain,
    ! [X23820,X23821,X23822,X23823] :
      ( ~ class_Fields_Olinordered__field(X23823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23823),X23822),X23821))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23823),X23820),c_Groups_Ozero__class_Ozero(X23823)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23823),X23821),X23820)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23823),X23822),X23820))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_8154,plain,
    ! [X22361,X22362,X22363,X22364] :
      ( ~ class_Rings_Olinordered__ring__strict(X22364)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22364),X22363),X22362))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22364),X22361),c_Groups_Ozero__class_Ozero(X22364)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22364),X22362),X22361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22364),X22363),X22361))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_8155,plain,
    ! [X22365,X22366,X22367,X22368] :
      ( ~ class_Rings_Olinordered__ring__strict(X22368)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22368),X22367),X22366))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22368),X22365),c_Groups_Ozero__class_Ozero(X22368)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22368),X22365),X22366)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22368),X22365),X22367))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

fof(i_0_8156,plain,
    ! [X23794,X23795,X23796,X23797] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X23797)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23797),X23796),X23795))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23797),X23794),c_Groups_Ozero__class_Ozero(X23797)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23797),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23797),X23795),X23794)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23797),X23796),X23794))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

fof(i_0_8157,plain,
    ! [X22272,X22273,X22274,X22275] :
      ( ~ class_Rings_Oordered__ring(X22275)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22275),X22274),X22273))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22275),X22272),c_Groups_Ozero__class_Ozero(X22275)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22275),X22273),X22272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22275),X22274),X22272))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_8158,plain,
    ! [X22276,X22277,X22278,X22279] :
      ( ~ class_Rings_Oordered__ring(X22279)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22279),X22278),X22277))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22279),X22276),c_Groups_Ozero__class_Ozero(X22279)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22279),X22276),X22277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22279),X22276),X22278))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

cnf(i_0_8159,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | c_List_OdropWhile(X3,X1,X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_5657]) ).

fof(i_0_8160,plain,
    ! [X19870,X19871,X19872] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19872),X19871))
      | ~ hBOOL(hAPP(hAPP(c_member(X19872),X19870),X19871))
      | hAPP(c_Finite__Set_Ocard(X19872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19872,tc_HOL_Obool)),X19871),hAPP(hAPP(c_Set_Oinsert(X19872),X19870),c_Orderings_Obot__class_Obot(tc_fun(X19872,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19872),X19871)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton])]) ).

fof(i_0_8161,plain,
    ! [X19867,X19868,X19869] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19869),X19867),X19868))
        | hAPP(c_Finite__Set_Ocard(X19869),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19869,tc_HOL_Obool)),X19868),hAPP(hAPP(c_Set_Oinsert(X19869),X19867),c_Orderings_Obot__class_Obot(tc_fun(X19869,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19869),X19868)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19869),X19868)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19869),X19867),X19868))
        | hAPP(c_Finite__Set_Ocard(X19869),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19869,tc_HOL_Obool)),X19868),hAPP(hAPP(c_Set_Oinsert(X19869),X19867),c_Orderings_Obot__class_Obot(tc_fun(X19869,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X19869),X19868)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19869),X19868)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5707])])]) ).

fof(i_0_8162,plain,
    ! [X17334,X17335,X17336] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17336,tc_HOL_Obool)),X17334),X17335)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),X17334))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),X17335)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),X17334))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17336,tc_HOL_Obool)),X17334),X17335)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17336),X17335)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).

cnf(i_0_8163,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5708]) ).

fof(i_0_8164,plain,
    ! [X25711,X25712,X25713] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25713),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25712)),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25711)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25713),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25711)),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25712)))
        | ~ class_Int_Onumber(X25713)
        | ~ class_Orderings_Olinorder(X25713) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25713),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25711)),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25713),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25712)),hAPP(c_Int_Onumber__class_Onumber__of(X25713),X25711)))
        | ~ class_Int_Onumber(X25713)
        | ~ class_Orderings_Olinorder(X25713) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5709])])]) ).

fof(i_0_8165,plain,
    ! [X26649,X26650,X26651,X26652] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X26652,tc_fun(X26651,tc_HOL_Obool))),X26650),X26649)),
    inference(variable_rename,[status(thm)],[i_0_5710]) ).

fof(i_0_8166,plain,
    ! [X30006,X30007,X30008] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30008),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X30007)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X30007),X30008),X30006)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X30007)),X30006)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X30007),X30008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).

fof(i_0_8167,plain,
    ! [X28440,X28441,X28442,X28443,X28444,X28445] : hAPP(hAPP(c_Fun_Ocomp(X28445,X28444,X28443,X28442),X28441),X28440) = hAPP(X28442,hAPP(X28441,X28440)),
    inference(variable_rename,[status(thm)],[fact_o__def]) ).

fof(i_0_8168,plain,
    ! [X28368,X28369,X28370,X28371,X28372,X28373] : hAPP(hAPP(c_Fun_Ocomp(X28373,X28372,X28371,X28370),X28369),X28368) = hAPP(X28370,hAPP(X28369,X28368)),
    inference(variable_rename,[status(thm)],[fact_o__apply]) ).

fof(i_0_8169,plain,
    ! [X34056,X34057,X34058,X34059,X34060] :
      ( ~ class_Rings_Ocomm__semiring__1(X34060)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34060),X34059),X34058))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34060),X34057),X34056))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34060),X34059),X34057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34060),X34058),X34056))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).

fof(i_0_8170,plain,
    ! [X18425,X18426,X18427,X18428,X18429] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18429)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18429),X18428),X18427))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18429),X18426),X18425))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18429),X18428),X18426)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18429),X18427),X18425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_8171,plain,
    ! [X18481,X18482,X18483,X18484,X18485] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18485)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18485),X18484),X18483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18485),X18482),X18481))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18485),X18484),X18482)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18485),X18483),X18481))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_8172,plain,
    ! [X18486,X18487,X18488,X18489,X18490] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18490)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18490),X18489),X18488))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18490),X18487),X18486))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18490),X18489),X18487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18490),X18488),X18486))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_8173,plain,
    ! [X20641,X20642,X20643,X20644,X20645] :
      ( ~ class_Lattices_Osemilattice__inf(X20645)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20645),X20644),X20643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20645),X20642),X20641))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20645),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20645),X20644),X20642)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20645),X20643),X20641))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).

fof(i_0_8174,plain,
    ! [X19542,X19543,X19544,X19545,X19546] :
      ( ~ class_Lattices_Osemilattice__sup(X19546)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19546),X19545),X19544))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19546),X19543),X19542))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19546),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19546),X19545),X19543)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19546),X19544),X19542))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).

fof(i_0_8175,plain,
    ! [X18811,X18812,X18813,X18814,X18815] :
      ( ~ class_Orderings_Olinorder(X18815)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),X18814),X18813))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),X18812),X18811))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18815),X18814),X18812)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18815),X18813),X18811))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).

fof(i_0_8176,plain,
    ! [X18877,X18878,X18879,X18880,X18881] :
      ( ~ class_Orderings_Olinorder(X18881)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18881),X18880),X18879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18881),X18878),X18877))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18881),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18881),X18880),X18878)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18881),X18879),X18877))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).

fof(i_0_8177,plain,
    ! [X18077,X18078,X18079,X18080,X18081] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18081)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18081),X18080),X18079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18081),X18078),X18077))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18081),X18080),X18078)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18081),X18079),X18077))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_8178,plain,
    ! [X25714,X25715,X25716,X25717] :
      ( ~ class_Int_Onumber(X25717)
      | ~ class_Rings_Osemiring(X25717)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25717),hAPP(c_Int_Onumber__class_Onumber__of(X25717),X25716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25717),X25715),X25714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25717),hAPP(c_Int_Onumber__class_Onumber__of(X25717),X25716)),X25715)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25717),hAPP(c_Int_Onumber__class_Onumber__of(X25717),X25716)),X25714)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

fof(i_0_8179,plain,
    ! [X25722,X25723,X25724,X25725] :
      ( ~ class_Int_Onumber(X25725)
      | ~ class_Rings_Oring(X25725)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25725),hAPP(c_Int_Onumber__class_Onumber__of(X25725),X25724)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25725),X25723),X25722)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25725),hAPP(c_Int_Onumber__class_Onumber__of(X25725),X25724)),X25723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25725),hAPP(c_Int_Onumber__class_Onumber__of(X25725),X25724)),X25722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).

fof(i_0_8180,plain,
    ! [X34037,X34038,X34039,X34040,X34041] :
      ( ~ class_Divides_Osemiring__div(X34041)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34041),X34040),X34039))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34041),X34038),X34037))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34041),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34041),X34039),X34040)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34041),X34037),X34038)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34041),X34039),X34037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34041),X34040),X34038)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).

fof(i_0_8181,plain,
    ! [X20937,X20938,X20939,X20940] :
      ( ~ class_Lattices_Osemilattice__inf(X20940)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20940),X20939))
      | hAPP(hAPP(c_Finite__Set_Ofold(X20940,X20940,c_Lattices_Osemilattice__inf__class_Oinf(X20940)),X20938),hAPP(hAPP(c_Set_Oinsert(X20940),X20937),X20939)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20940),X20937),hAPP(hAPP(c_Finite__Set_Ofold(X20940,X20940,c_Lattices_Osemilattice__inf__class_Oinf(X20940)),X20938),X20939)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).

fof(i_0_8182,plain,
    ! [X19782,X19783,X19784,X19785] :
      ( ~ class_Lattices_Osemilattice__sup(X19785)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19785),X19784))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19785,X19785,c_Lattices_Osemilattice__sup__class_Osup(X19785)),X19783),hAPP(hAPP(c_Set_Oinsert(X19785),X19782),X19784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19785),X19782),hAPP(hAPP(c_Finite__Set_Ofold(X19785,X19785,c_Lattices_Osemilattice__sup__class_Osup(X19785)),X19783),X19784)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).

fof(i_0_8183,plain,
    ! [X19094,X19095,X19096,X19097] :
      ( ~ class_Orderings_Olinorder(X19097)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19097),X19096))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19097,X19097,c_Orderings_Oord__class_Omax(X19097)),X19095),hAPP(hAPP(c_Set_Oinsert(X19097),X19094),X19096)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19097),X19094),hAPP(hAPP(c_Finite__Set_Ofold(X19097,X19097,c_Orderings_Oord__class_Omax(X19097)),X19095),X19096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).

fof(i_0_8184,plain,
    ! [X19101,X19102,X19103,X19104] :
      ( ~ class_Orderings_Olinorder(X19104)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19104),X19103))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19104,X19104,c_Orderings_Oord__class_Omin(X19104)),X19102),hAPP(hAPP(c_Set_Oinsert(X19104),X19101),X19103)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19104),X19101),hAPP(hAPP(c_Finite__Set_Ofold(X19104,X19104,c_Orderings_Oord__class_Omin(X19104)),X19102),X19103)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).

fof(i_0_8185,plain,
    ! [X20958,X20959,X20960,X20961] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20961),X20960))
      | ~ c_Fun_Oinj__on(X20959,X20961,X20958,c_Orderings_Otop__class_Otop(tc_fun(X20959,tc_HOL_Obool)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20959),hAPP(c_Set_Ovimage(X20959,X20961,X20958),X20960))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).

fof(i_0_8186,plain,
    ! [X21948,X21949,X21950,X21951,X21952] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21952)
      | ~ hBOOL(hAPP(hAPP(c_member(X21951),X21950),X21949))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21952),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21951,X21952),X21949),X21948)),hAPP(X21948,X21950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).

fof(i_0_8187,plain,
    ! [X25818,X25819,X25820,X25821] :
      ( ~ class_Int_Onumber__ring(X25821)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25821),hAPP(c_Int_Onumber__class_Onumber__of(X25821),X25820)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25821),X25819),hAPP(c_Int_Onumber__class_Onumber__of(X25821),X25818))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25821),hAPP(c_Int_Onumber__class_Onumber__of(X25821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25820),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25818)))),X25819) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).

fof(i_0_8188,plain,
    ! [X24832,X24833] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24833)),X24832))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24833),X24832)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24833),X24832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24833)),X24832)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_8189,plain,
    ! [X20465,X20466,X20467,X20468,X20469,X20470] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20470),X20469),X20468))
      | ~ hBOOL(hAPP(hAPP(X20467,X20469),X20466))
      | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20470,tc_fun(X20465,tc_HOL_Obool)),X20468),X20467),X20466)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).

fof(i_0_8190,plain,
    ! [X25022,X25023,X25024,X25025] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),c_Complete__Lattice_OSup__class_OSup(X25024,X25023)),X25022))
        | ~ hBOOL(hAPP(hAPP(c_member(X25024),X25025),X25023))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),X25025),X25022))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) )
      & ( hBOOL(hAPP(hAPP(c_member(X25024),esk219_3(X25022,X25023,X25024)),X25023))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),c_Complete__Lattice_OSup__class_OSup(X25024,X25023)),X25022))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),esk219_3(X25022,X25023,X25024)),X25022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),c_Complete__Lattice_OSup__class_OSup(X25024,X25023)),X25022))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__le__iff])])])])]) ).

fof(i_0_8191,plain,
    ! [X17949,X17950,X17951,X17952,X17953,X17954] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17954,X17953,X17952)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17954),X17951))
      | hAPP(hAPP(c_Finite__Set_Ofold(X17954,X17953,X17952),X17950),hAPP(hAPP(c_Set_Oinsert(X17954),X17949),X17951)) = hAPP(hAPP(X17952,X17949),hAPP(hAPP(c_Finite__Set_Ofold(X17954,X17953,X17952),X17950),X17951)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).

fof(i_0_8192,plain,
    ! [X30838,X30839,X30840,X30841,X30842] :
      ( ( X30839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30839),X30838) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30840),hAPP(c_List_Oset(tc_Nat_Onat),X30838)))
        | X30840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30839),X30838) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk415_2(X30841,X30842)),hAPP(c_List_Oset(tc_Nat_Onat),X30841)))
        | X30842 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30842),X30841) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk415_2(X30841,X30842) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30842 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30842),X30841) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    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_sum__eq__0__conv])])])])])]) ).

fof(i_0_8193,plain,
    ! [X22626,X22627] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22627))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22626))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22626),X22627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).

fof(i_0_8194,plain,
    ! [X22644,X22645] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22645))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22645),X22644))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22644))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22645),X22644))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22645))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22644))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22645),X22644))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).

fof(i_0_8195,plain,
    ! [X24891,X24892,X24893] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24893),X24892)),X24891)),X24892) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24891),X24892),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).

fof(i_0_8196,plain,
    ! [X25114,X25115,X25116] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25116,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X25116,tc_HOL_Obool),tc_HOL_Obool)),X25115),X25114)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25116,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25116,tc_HOL_Obool),X25115)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25116,tc_HOL_Obool),X25114)),
    inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).

fof(i_0_8197,plain,
    ! [X21612,X21613,X21614] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X21614,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X21614,tc_HOL_Obool),tc_HOL_Obool)),X21613),X21612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21614,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21614,tc_HOL_Obool),X21613)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21614,tc_HOL_Obool),X21612)),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(i_0_8198,plain,
    ! [X24910,X24911,X24912,X24913,X24914,X24915,X24916,X24917] :
      ( ( X24910 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X24912,X24911))
        | ~ hBOOL(hAPP(X24912,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24911,X24910))) )
      & ( X24910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24914),X24910))
        | X24911 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24910),X24913)),X24914)
        | hBOOL(hAPP(X24912,X24914))
        | ~ hBOOL(hAPP(X24912,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24911,X24910))) )
      & ( X24915 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X24915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk217_3(X24915,X24916,X24917)),X24915))
        | X24915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( X24916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24915),esk216_3(X24915,X24916,X24917))),esk217_3(X24915,X24916,X24917))
        | X24915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( ~ hBOOL(hAPP(X24917,esk217_3(X24915,X24916,X24917)))
        | X24915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( X24915 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X24917,X24916))
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk217_3(X24915,X24916,X24917)),X24915))
        | ~ hBOOL(hAPP(X24917,X24916))
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( X24916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24915),esk216_3(X24915,X24916,X24917))),esk217_3(X24915,X24916,X24917))
        | ~ hBOOL(hAPP(X24917,X24916))
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) )
      & ( ~ hBOOL(hAPP(X24917,esk217_3(X24915,X24916,X24917)))
        | ~ hBOOL(hAPP(X24917,X24916))
        | hBOOL(hAPP(X24917,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24916,X24915))) ) ),
    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_split__mod])])])])])]) ).

fof(i_0_8199,plain,
    ! [X29883,X29884,X29885,X29886,X29887,X29888,X29889] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29885)),X29884),c_List_Olists(X29885,X29883)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29885),X29886),hAPP(c_List_Oset(X29885),X29884)))
        | hBOOL(hAPP(hAPP(c_member(X29885),X29886),X29883)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29889),esk393_3(X29887,X29888,X29889)),hAPP(c_List_Oset(X29889),X29888)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29889)),X29888),c_List_Olists(X29889,X29887))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29889),esk393_3(X29887,X29888,X29889)),X29887))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29889)),X29888),c_List_Olists(X29889,X29887))) ) ),
    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_in__lists__conv__set])])])])])]) ).

fof(i_0_8200,plain,
    ! [X29604,X29605,X29606,X29607] : c_List_Olist_Olist__size(X29607,X29606,hAPP(hAPP(c_List_Olist_OCons(X29607),X29605),X29604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X29606,X29605)),c_List_Olist_Olist__size(X29607,X29606,X29604))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J]) ).

fof(i_0_8201,plain,
    ! [X29585,X29586,X29587] : c_Random_Oselect__weight(X29587,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29587)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X29587),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X29586)),X29585)) = c_Random_Oselect__weight(X29587,X29585),
    inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(i_0_8202,plain,
    ! [X24802,X24803,X24804,X24805] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24804))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24804))
        | X24804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24805,X24804) = X24802
        | X24805 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24804),X24803)),X24802) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24804),X24802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24802),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24804))
        | X24804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24805,X24804) = X24802
        | X24805 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24804),X24803)),X24802) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24802),X24804))
        | X24804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24805,X24804) = X24802
        | X24805 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24804),X24803)),X24802) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24804),X24802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24802),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24802))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24802),X24804))
        | X24804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24805,X24804) = X24802
        | X24805 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24804),X24803)),X24802) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5711])])]) ).

fof(i_0_8203,plain,
    ! [X31871,X31872] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31872)),c_List_Otranspose__rel(X31872)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31872)),c_List_Olist_ONil(X31872)),X31871)))
      | c_List_Otranspose(X31872,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31872)),c_List_Olist_ONil(X31872)),X31871)) = c_List_Otranspose(X31872,X31871) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).

cnf(i_0_8204,plain,
    c_List_Ofoldr(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X4,
    inference(split_conjunct,[status(thm)],[i_0_5712]) ).

fof(i_0_8205,plain,
    ! [X20977,X20978,X20979] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20979,tc_HOL_Obool)),X20978),X20977) != c_Orderings_Obot__class_Obot(tc_fun(X20979,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20979,tc_HOL_Obool)),X20978),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20979,tc_HOL_Obool)),X20977))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20979,tc_HOL_Obool)),X20978),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20979,tc_HOL_Obool)),X20977)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20979,tc_HOL_Obool)),X20978),X20977) = c_Orderings_Obot__class_Obot(tc_fun(X20979,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).

cnf(i_0_8206,plain,
    c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),X3),X4)) = c_List_Omaps(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_5713]) ).

cnf(i_0_8207,plain,
    c_List_Omaps(X1,X2,X3,X4) = c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_5714]) ).

fof(i_0_8208,plain,
    ! [X19684,X19685,X19686] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19686),X19685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19686,tc_HOL_Obool)),X19684),X19685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19686),X19685)),hAPP(c_Finite__Set_Ocard(X19686),X19684)))
      | X19684 = X19685 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_8209,plain,
    ! [X21602,X21603,X21604] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X21604,tc_HOL_Obool)),X21603),X21602))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21604,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21604,tc_HOL_Obool),X21602)),X21603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).

fof(i_0_8210,plain,
    ! [X29090,X29091,X29092,X29093,X29094] : hAPP(c_Relation_Oconverse(X29094,X29093),hAPP(hAPP(c_Relation_Orel__comp(X29094,X29092,X29093),X29091),X29090)) = hAPP(hAPP(c_Relation_Orel__comp(X29093,X29092,X29094),hAPP(c_Relation_Oconverse(X29092,X29093),X29090)),hAPP(c_Relation_Oconverse(X29094,X29092),X29091)),
    inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).

fof(i_0_8211,plain,
    ! [X23407,X23408,X23409,X23410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23409))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23409))
        | X23409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23410),X23409) = X23408
        | X23410 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23409),X23408)),X23407) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23409),X23407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23409))
        | X23409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23410),X23409) = X23408
        | X23410 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23409),X23408)),X23407) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23409))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23407),X23409))
        | X23409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23410),X23409) = X23408
        | X23410 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23409),X23408)),X23407) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23409),X23407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23407),X23409))
        | X23409 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23410),X23409) = X23408
        | X23410 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23409),X23408)),X23407) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5715])])]) ).

fof(i_0_8212,plain,
    ! [X18954,X18955,X18956,X18957] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18957),X18956),X18955)),X18954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),X18956),X18954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),X18955),X18954))
        | ~ class_Orderings_Olinorder(X18957) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),X18956),X18954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18957),X18956),X18955)),X18954))
        | ~ class_Orderings_Olinorder(X18957) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),X18955),X18954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18957),X18956),X18955)),X18954))
        | ~ class_Orderings_Olinorder(X18957) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).

fof(i_0_8213,plain,
    ! [X18917,X18918,X18919,X18920] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18920),X18919),X18918)),X18917))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),X18919),X18917))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),X18918),X18917))
        | ~ class_Orderings_Olinorder(X18920) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),X18919),X18917))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18920),X18919),X18918)),X18917))
        | ~ class_Orderings_Olinorder(X18920) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),X18918),X18917))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18920),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18920),X18919),X18918)),X18917))
        | ~ class_Orderings_Olinorder(X18920) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).

fof(i_0_8214,plain,
    ! [X23494,X23495,X23496,X23497,X23498,X23499,X23500,X23501] :
      ( ( X23494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23496,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23496,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23495),X23494))) )
      & ( X23494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23498),X23494))
        | X23495 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23494),X23497)),X23498)
        | hBOOL(hAPP(X23496,X23497))
        | ~ hBOOL(hAPP(X23496,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23495),X23494))) )
      & ( X23499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_3(X23499,X23500,X23501)),X23499))
        | X23499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( X23500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23499),esk154_3(X23499,X23500,X23501))),esk155_3(X23499,X23500,X23501))
        | X23499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( ~ hBOOL(hAPP(X23501,esk154_3(X23499,X23500,X23501)))
        | X23499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( X23499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_3(X23499,X23500,X23501)),X23499))
        | ~ hBOOL(hAPP(X23501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( X23500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23499),esk154_3(X23499,X23500,X23501))),esk155_3(X23499,X23500,X23501))
        | ~ hBOOL(hAPP(X23501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) )
      & ( ~ hBOOL(hAPP(X23501,esk154_3(X23499,X23500,X23501)))
        | ~ hBOOL(hAPP(X23501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23501,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23500),X23499))) ) ),
    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_split__div])])])])])]) ).

fof(i_0_8215,plain,
    ! [X19232,X19233,X19234] :
      ( ~ class_Orderings_Olinorder(X19234)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19234),X19233))
      | X19232 = c_Orderings_Obot__class_Obot(tc_fun(X19234,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19234,tc_HOL_Obool)),X19232),X19233))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X19234),c_Big__Operators_Olattice_OSup__fin(X19234,c_Orderings_Oord__class_Omax(X19234),X19232)),c_Big__Operators_Olattice_OSup__fin(X19234,c_Orderings_Oord__class_Omax(X19234),X19233)) = c_Big__Operators_Olattice_OSup__fin(X19234,c_Orderings_Oord__class_Omax(X19234),X19233) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).

fof(i_0_8216,plain,
    ! [X19229,X19230,X19231] :
      ( ~ class_Orderings_Olinorder(X19231)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19231),X19230))
      | X19229 = c_Orderings_Obot__class_Obot(tc_fun(X19231,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19231,tc_HOL_Obool)),X19229),X19230))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X19231),c_Big__Operators_Olattice_OInf__fin(X19231,c_Orderings_Oord__class_Omin(X19231),X19229)),c_Big__Operators_Olattice_OInf__fin(X19231,c_Orderings_Oord__class_Omin(X19231),X19230)) = c_Big__Operators_Olattice_OInf__fin(X19231,c_Orderings_Oord__class_Omin(X19231),X19230) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).

cnf(i_0_8217,plain,
    hAPP(c_List_Orotate(X1,hAPP(c_Nat_OSuc,X2)),X3) = hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_5716]) ).

fof(i_0_8218,plain,
    ! [X18016,X18017,X18018,X18019,X18020,X18021] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18021,X18020,X18019)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18021),X18018))
      | hBOOL(hAPP(hAPP(c_member(X18021),X18017),X18018))
      | hAPP(hAPP(c_Finite__Set_Ofold(X18021,X18020,X18019),X18016),hAPP(hAPP(c_Set_Oinsert(X18021),X18017),X18018)) = hAPP(hAPP(c_Finite__Set_Ofold(X18021,X18020,X18019),hAPP(hAPP(X18019,X18017),X18016)),X18018) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5717])]) ).

cnf(i_0_8219,plain,
    ( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X3
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_5718]) ).

fof(i_0_8220,plain,
    ! [X25111,X25112] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25112,tc_HOL_Obool),tc_HOL_Obool)),X25111),hAPP(c_Set_OPow(X25112),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25112,tc_HOL_Obool),X25111)))),
    inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).

fof(i_0_8221,plain,
    ! [X20479,X20480,X20481,X20482] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20482),X20481),X20480))
      | ~ hBOOL(hAPP(hAPP(c_member(X20482),X20481),X20479))
      | hBOOL(hAPP(hAPP(c_member(X20482),X20481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20482,tc_HOL_Obool)),X20480),X20479))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).

fof(i_0_8222,plain,
    ! [X23199,X23200,X23201,X23202] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23201),X23200))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23202),X23199),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23200),hAPP(c_Nat_OSuc,X23201))) = c_Groups_Ozero__class_Ozero(X23202)
        | ~ class_Groups_Ocomm__monoid__add(X23202) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23201),X23200))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23202),X23199),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23200),hAPP(c_Nat_OSuc,X23201))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23202),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23202),X23199),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23200),X23201))),hAPP(X23199,X23201))
        | ~ class_Groups_Ocomm__monoid__add(X23202) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5719])])]) ).

fof(i_0_8223,plain,
    ! [X27059,X27060,X27061,X27062,X27063,X27064] :
      ( ( hBOOL(hAPP(X27064,hAPP(c_Product__Type_Ofst(X27060,X27059),hAPP(hAPP(c_Product__Type_OPair(X27060,X27059),X27063),X27061))))
        | ~ hBOOL(hAPP(X27062,X27061))
        | ~ hBOOL(hAPP(X27064,X27063)) )
      & ( hBOOL(hAPP(X27062,hAPP(c_Product__Type_Osnd(X27060,X27059),hAPP(hAPP(c_Product__Type_OPair(X27060,X27059),X27063),X27061))))
        | ~ hBOOL(hAPP(X27062,X27061))
        | ~ hBOOL(hAPP(X27064,X27063)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).

fof(i_0_8224,plain,
    ! [X21525,X21526,X21527,X21528,X21529,X21530] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21530)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21529,tc_fun(X21528,X21530)),X21527),X21526),X21525) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21529,X21530),X21527),hAPP(hAPP(c_COMBC(X21529,X21528,X21530),X21526),X21525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).

fof(i_0_8225,plain,
    ! [X21352,X21353,X21354,X21355,X21356,X21357] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21357)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21356,tc_fun(X21355,X21357)),X21354),X21353),X21352) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21356,X21357),X21354),hAPP(hAPP(c_COMBC(X21356,X21355,X21357),X21353),X21352)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).

fof(i_0_8226,plain,
    ! [X19586,X19587,X19588] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),X19587))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19588,tc_HOL_Obool)),X19587),X19586))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),X19586))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19588,tc_HOL_Obool)),X19587),X19586))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),X19587))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),X19586))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X19588),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19588,tc_HOL_Obool)),X19587),X19586))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).

fof(i_0_8227,plain,
    ! [X19345,X19346,X19347,X19348] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19348,tc_HOL_Obool)),X19347),X19346),X19345))
      | hBOOL(hAPP(X19347,X19345))
      | hBOOL(hAPP(X19346,X19345)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5720])]) ).

fof(i_0_8228,plain,
    ! [X20901,X20902,X20903] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20903,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20903,tc_HOL_Obool)),X20902),X20901)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20903,tc_HOL_Obool)),X20902),X20901)) = X20902,
    inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).

fof(i_0_8229,plain,
    ! [X31401,X31402,X31403] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31403,tc_HOL_Obool)),X31402),X31401))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X31403),tc_HOL_Obool)),c_List_Olistsp(X31403,X31402)),c_List_Olistsp(X31403,X31401))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).

fof(i_0_8230,plain,
    ! [X29730,X29731,X29732] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29732,tc_HOL_Obool)),X29731),X29730))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X29732),tc_HOL_Obool)),c_List_Olists(X29732,X29731)),c_List_Olists(X29732,X29730))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).

fof(i_0_8231,plain,
    ! [X23896,X23897,X23898,X23899] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23897),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23899),X23896),X23898)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23899),X23897),X23898)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23898),c_Groups_Ozero__class_Ozero(X23899)))
        | ~ class_Fields_Olinordered__field(X23899) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23899),X23897),X23898)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23897),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23899),X23896),X23898)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23899),X23898),c_Groups_Ozero__class_Ozero(X23899)))
        | ~ class_Fields_Olinordered__field(X23899) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).

fof(i_0_8232,plain,
    ! [X23964,X23965,X23966,X23967] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23967),X23965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23967),X23964),X23966)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23967),X23964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23967),X23965),X23966)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23967),X23966),c_Groups_Ozero__class_Ozero(X23967)))
        | ~ class_Fields_Olinordered__field(X23967) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23967),X23964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23967),X23965),X23966)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23967),X23965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23967),X23964),X23966)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23967),X23966),c_Groups_Ozero__class_Ozero(X23967)))
        | ~ class_Fields_Olinordered__field(X23967) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).

fof(i_0_8233,plain,
    ! [X33429,X33430] :
      ( ( ~ c_Predicate_Osymp(X33430,X33429)
        | c_Relation_Osym(X33430,hAPP(c_Set_OCollect(tc_prod(X33430,X33430)),hAPP(c_Product__Type_Oprod_Oprod__case(X33430,X33430,tc_HOL_Obool),X33429))) )
      & ( ~ c_Relation_Osym(X33430,hAPP(c_Set_OCollect(tc_prod(X33430,X33430)),hAPP(c_Product__Type_Oprod_Oprod__case(X33430,X33430,tc_HOL_Obool),X33429)))
        | c_Predicate_Osymp(X33430,X33429) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symp__def])]) ).

fof(i_0_8234,plain,
    ! [X33317,X33318] :
      ( ( ~ c_Predicate_Otransp(X33318,X33317)
        | c_Relation_Otrans(X33318,hAPP(c_Set_OCollect(tc_prod(X33318,X33318)),hAPP(c_Product__Type_Oprod_Oprod__case(X33318,X33318,tc_HOL_Obool),X33317))) )
      & ( ~ c_Relation_Otrans(X33318,hAPP(c_Set_OCollect(tc_prod(X33318,X33318)),hAPP(c_Product__Type_Oprod_Oprod__case(X33318,X33318,tc_HOL_Obool),X33317)))
        | c_Predicate_Otransp(X33318,X33317) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transp__def])]) ).

fof(i_0_8235,plain,
    ! [X28173,X28174] :
      ( ( ~ c_Wellfounded_OwfP(X28174,X28173)
        | c_Wellfounded_Owf(X28174,hAPP(c_Set_OCollect(tc_prod(X28174,X28174)),hAPP(c_Product__Type_Oprod_Oprod__case(X28174,X28174,tc_HOL_Obool),X28173))) )
      & ( ~ c_Wellfounded_Owf(X28174,hAPP(c_Set_OCollect(tc_prod(X28174,X28174)),hAPP(c_Product__Type_Oprod_Oprod__case(X28174,X28174,tc_HOL_Obool),X28173)))
        | c_Wellfounded_OwfP(X28174,X28173) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).

fof(i_0_8236,plain,
    ! [X23311,X23312] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23311),X23312)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23311),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23312)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23311),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23311),X23312)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23312)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).

cnf(i_0_8237,plain,
    ( c_List_OdropWhile(X3,X1,X2) = c_List_Olist_ONil(X3)
    | ~ hBOOL(hAPP(X1,esk442_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5669]) ).

fof(i_0_8238,plain,
    ! [X27794,X27795,X27796,X27797,X27798,X27799] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27796,X27799),X27795),hAPP(c_COMBK(tc_fun(X27799,tc_HOL_Obool),X27796),X27797)) != hAPP(hAPP(c_Product__Type_OSigma(X27796,X27799),X27794),hAPP(c_COMBK(tc_fun(X27799,tc_HOL_Obool),X27796),X27797))
        | X27795 = X27794
        | ~ hBOOL(hAPP(hAPP(c_member(X27799),X27798),X27797)) )
      & ( X27795 != X27794
        | hAPP(hAPP(c_Product__Type_OSigma(X27796,X27799),X27795),hAPP(c_COMBK(tc_fun(X27799,tc_HOL_Obool),X27796),X27797)) = hAPP(hAPP(c_Product__Type_OSigma(X27796,X27799),X27794),hAPP(c_COMBK(tc_fun(X27799,tc_HOL_Obool),X27796),X27797))
        | ~ hBOOL(hAPP(hAPP(c_member(X27799),X27798),X27797)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).

fof(i_0_8239,plain,
    ! [X24800,X24801] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24801))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24801),X24800)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24801,X24800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24801),X24800) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).

fof(i_0_8240,plain,
    ! [X28328,X28329] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28329,tc_HOL_Obool)),esk328_2(X28328,X28329)),hAPP(c_Relation_OImage(X28329,X28329,X28328),esk328_2(X28328,X28329))))
        | c_Wellfounded_Owf(X28329,X28328) )
      & ( esk328_2(X28328,X28329) != c_Orderings_Obot__class_Obot(tc_fun(X28329,tc_HOL_Obool))
        | c_Wellfounded_Owf(X28329,X28328) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).

fof(i_0_8241,plain,
    ! [X26644,X26645,X26646,X26647,X26648] :
      ( ~ hBOOL(hAPP(hAPP(X26648,X26647),X26646))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26645,X26644,tc_HOL_Obool),X26648),hAPP(hAPP(c_Product__Type_OPair(X26645,X26644),X26647),X26646))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).

fof(i_0_8242,plain,
    ! [X26639,X26640,X26641,X26642,X26643] :
      ( ~ hBOOL(hAPP(hAPP(X26643,X26642),X26641))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26640,X26639,tc_HOL_Obool),X26643),hAPP(hAPP(c_Product__Type_OPair(X26640,X26639),X26642),X26641))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).

fof(i_0_8243,plain,
    ! [X23309,X23310] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23309),X23310)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23309))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23309))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23309),X23310)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])]) ).

fof(i_0_8244,plain,
    ! [X19887,X19888,X19889] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19889),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19888),X19887)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19889),X19887)),X19888)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19889),X19887)),X19888))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19889),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19888),X19887))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).

fof(i_0_8245,plain,
    ! [X20171,X20172,X20173] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20173),X20172)),X20171))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20173),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20171),X20172))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20173),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20171),X20172)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20173),X20172)),X20171)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).

fof(i_0_8246,plain,
    ! [X19852,X19853,X19854] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19854),X19853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19854,tc_HOL_Obool)),X19853),X19852))
      | hAPP(c_Finite__Set_Ocard(X19854),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19854,tc_HOL_Obool)),X19852),X19853)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19854),X19852)),hAPP(c_Finite__Set_Ocard(X19854),X19853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).

fof(i_0_8247,plain,
    ! [X28777,X28778,X28779,X28780,X28781] :
      ( ~ c_Finite__Set_Ofolding__idem(X28781,X28780,X28779,X28778)
      | hAPP(c_Fun_Ocomp(X28780,X28780,X28780,hAPP(X28779,X28777)),hAPP(X28779,X28777)) = hAPP(X28779,X28777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).

cnf(i_0_8248,plain,
    c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_5721]) ).

fof(i_0_8249,plain,
    ! [X25891,X25892,X25893] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25893)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25892)),X25891)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25892)),X25891) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25892)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25892)),X25891)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25893)),X25891)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25893))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25892)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25892)),X25891)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25893),X25892))),X25891)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25893))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5722])])]) ).

cnf(i_0_8250,plain,
    c_Transitive__Closure_Otrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_5723]) ).

cnf(i_0_8251,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3,X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Oupt(X3,X4)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5724]) ).

cnf(i_0_8252,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Oupt(X3,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3,X4)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5725]) ).

fof(i_0_8253,plain,
    ! [X27250,X27251,X27252] : hAPP(c_Relation_OField(X27252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27252,X27252),tc_HOL_Obool)),X27251),X27250)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27252,tc_HOL_Obool)),hAPP(c_Relation_OField(X27252),X27251)),hAPP(c_Relation_OField(X27252),X27250)),
    inference(variable_rename,[status(thm)],[fact_Field__Un]) ).

fof(i_0_8254,plain,
    ! [X31550,X31551,X31552,X31553] : hAPP(c_List_Oset(tc_prod(X31553,X31552)),c_Enum_Oproduct(X31553,X31552,X31551,X31550)) = hAPP(hAPP(c_Product__Type_OSigma(X31553,X31552),hAPP(c_List_Oset(X31553),X31551)),hAPP(c_COMBK(tc_fun(X31552,tc_HOL_Obool),X31553),hAPP(c_List_Oset(X31552),X31550))),
    inference(variable_rename,[status(thm)],[fact_product__list__set]) ).

fof(i_0_8255,plain,
    ! [X31296,X31297,X31298,X31299,X31300] :
      ( ( hAPP(hAPP(c_List_Omap(tc_prod(X31300,X31298),X31300),c_Product__Type_Ofst(X31300,X31298)),X31296) = X31299
        | hAPP(hAPP(c_List_Ozip(X31300,X31298),X31299),X31297) != X31296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31300)),X31299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31298)),X31297) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X31300,X31298),X31298),c_Product__Type_Osnd(X31300,X31298)),X31296) = X31297
        | hAPP(hAPP(c_List_Ozip(X31300,X31298),X31299),X31297) != X31296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31300)),X31299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31298)),X31297) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X31300,X31298),X31300),c_Product__Type_Ofst(X31300,X31298)),X31296) != X31299
        | hAPP(hAPP(c_List_Omap(tc_prod(X31300,X31298),X31298),c_Product__Type_Osnd(X31300,X31298)),X31296) != X31297
        | hAPP(hAPP(c_List_Ozip(X31300,X31298),X31299),X31297) = X31296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31300)),X31299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31298)),X31297) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).

fof(i_0_8256,plain,
    ! [X20461,X20462,X20463,X20464] :
      ( ( hBOOL(hAPP(X20463,X20461))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20464,tc_HOL_Obool)),X20463),X20462),X20461)) )
      & ( hBOOL(hAPP(X20462,X20461))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20464,tc_HOL_Obool)),X20463),X20462),X20461)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5726])])]) ).

fof(i_0_8257,plain,
    ! [X20524,X20525,X20526,X20527] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20527,tc_HOL_Obool)),X20526),X20525),X20524))
      | hBOOL(hAPP(X20526,X20524)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).

fof(i_0_8258,plain,
    ! [X20528,X20529,X20530,X20531] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20531,tc_HOL_Obool)),X20530),X20529),X20528))
      | hBOOL(hAPP(X20529,X20528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).

cnf(i_0_8259,plain,
    hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate1(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_5727]) ).

fof(i_0_8260,plain,
    ! [X29713,X29714,X29715,X29716,X29717,X29718] :
      ( ( hBOOL(hAPP(hAPP(X29717,X29716),X29714))
        | ~ c_List_Olistrelp(X29718,X29717,hAPP(hAPP(c_List_Olist_OCons(X29718),X29716),X29715),hAPP(hAPP(c_List_Olist_OCons(X29718),X29714),X29713)) )
      & ( c_List_Olistrelp(X29718,X29717,X29715,X29713)
        | ~ c_List_Olistrelp(X29718,X29717,hAPP(hAPP(c_List_Olist_OCons(X29718),X29716),X29715),hAPP(hAPP(c_List_Olist_OCons(X29718),X29714),X29713)) )
      & ( ~ hBOOL(hAPP(hAPP(X29717,X29716),X29714))
        | ~ c_List_Olistrelp(X29718,X29717,X29715,X29713)
        | c_List_Olistrelp(X29718,X29717,hAPP(hAPP(c_List_Olist_OCons(X29718),X29716),X29715),hAPP(hAPP(c_List_Olist_OCons(X29718),X29714),X29713)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).

fof(i_0_8261,plain,
    ! [X29707,X29708,X29709,X29710,X29711,X29712] :
      ( ~ hBOOL(hAPP(hAPP(X29712,X29711),X29710))
      | ~ c_List_Olistrelp(X29709,X29712,X29708,X29707)
      | c_List_Olistrelp(X29709,X29712,hAPP(hAPP(c_List_Olist_OCons(X29709),X29711),X29708),hAPP(hAPP(c_List_Olist_OCons(X29709),X29710),X29707)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).

cnf(i_0_8262,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5728]) ).

fof(i_0_8263,plain,
    ! [X28244] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X28244),c_Int_OInteg))
      | X28244 = hAPP(c_Int_ORep__Integ,esk314_1(X28244)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).

fof(i_0_8264,plain,
    ! [X25623,X25624,X25625] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25625,tc_HOL_Obool)),esk253_3(X25623,X25624,X25625)),X25624))
        | hBOOL(hAPP(hAPP(c_member(X25625),X25623),c_Complete__Lattice_OInf__class_OInf(tc_fun(X25625,tc_HOL_Obool),X25624))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25625),X25623),esk253_3(X25623,X25624,X25625)))
        | hBOOL(hAPP(hAPP(c_member(X25625),X25623),c_Complete__Lattice_OInf__class_OInf(tc_fun(X25625,tc_HOL_Obool),X25624))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).

fof(i_0_8265,plain,
    ! [X31000,X31001,X31002,X31005,X31006,X31007,X31008,X31009] :
      ( ( X31001 = hAPP(hAPP(c_List_Olist_OCons(X31002),esk418_3(X31000,X31001,X31002)),esk419_3(X31000,X31001,X31002))
        | X31001 = c_List_Olist_ONil(X31002)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31002)),X31001),c_List_Olists(X31002,X31000))) )
      & ( hBOOL(hAPP(hAPP(c_member(X31002),esk418_3(X31000,X31001,X31002)),X31000))
        | X31001 = c_List_Olist_ONil(X31002)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31002)),X31001),c_List_Olists(X31002,X31000))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31002)),esk419_3(X31000,X31001,X31002)),c_List_Olists(X31002,X31000)))
        | X31001 = c_List_Olist_ONil(X31002)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31002)),X31001),c_List_Olists(X31002,X31000))) )
      & ( X31006 != c_List_Olist_ONil(X31007)
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31007)),X31006),c_List_Olists(X31007,X31005))) )
      & ( X31006 != hAPP(hAPP(c_List_Olist_OCons(X31007),X31008),X31009)
        | ~ hBOOL(hAPP(hAPP(c_member(X31007),X31008),X31005))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31007)),X31009),c_List_Olists(X31007,X31005)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31007)),X31006),c_List_Olists(X31007,X31005))) ) ),
    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_lists_Osimps])])])])])]) ).

fof(i_0_8266,plain,
    ! [X32958,X32959,X32960,X32961] :
      ( ( X32960 = X32958
        | ~ hBOOL(hAPP(hAPP(c_member(X32961),X32960),hAPP(c_List_Oset(X32961),c_List_Oreplicate(X32961,X32959,X32958)))) )
      & ( X32959 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32961),X32960),hAPP(c_List_Oset(X32961),c_List_Oreplicate(X32961,X32959,X32958)))) )
      & ( X32960 != X32958
        | X32959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_member(X32961),X32960),hAPP(c_List_Oset(X32961),c_List_Oreplicate(X32961,X32959,X32958)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])]) ).

fof(i_0_8267,plain,
    ! [X21047,X21048,X21049,X21050,X21051] :
      ( ~ c_Finite__Set_Ofolding__one(X21051,X21050,X21049)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21051),X21048))
      | X21048 = c_Orderings_Obot__class_Obot(tc_fun(X21051,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21051),X21047))
      | X21047 = c_Orderings_Obot__class_Obot(tc_fun(X21051,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21051,tc_HOL_Obool)),X21048),X21047) != c_Orderings_Obot__class_Obot(tc_fun(X21051,tc_HOL_Obool))
      | hAPP(X21049,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21051,tc_HOL_Obool)),X21048),X21047)) = hAPP(hAPP(X21050,hAPP(X21049,X21048)),hAPP(X21049,X21047)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).

fof(i_0_8268,plain,
    ! [X24689,X24690,X24691,X24692] :
      ( ~ class_Divides_Osemiring__div(X24692)
      | c_Divides_Odiv__class_Omod(X24692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24692),X24691),X24690),X24689) = c_Divides_Odiv__class_Omod(X24692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24692),c_Divides_Odiv__class_Omod(X24692,X24691,X24689)),c_Divides_Odiv__class_Omod(X24692,X24690,X24689)),X24689) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).

fof(i_0_8269,plain,
    ! [X24637,X24638,X24639,X24640] :
      ( ~ class_Divides_Osemiring__div(X24640)
      | c_Divides_Odiv__class_Omod(X24640,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24640),X24639),X24638),X24637) = c_Divides_Odiv__class_Omod(X24640,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24640),c_Divides_Odiv__class_Omod(X24640,X24639,X24637)),c_Divides_Odiv__class_Omod(X24640,X24638,X24637)),X24637) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).

fof(i_0_8270,plain,
    ! [X24603,X24604,X24605,X24606] :
      ( ~ class_Divides_Oring__div(X24606)
      | c_Divides_Odiv__class_Omod(X24606,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24606),X24605),X24604),X24603) = c_Divides_Odiv__class_Omod(X24606,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24606),c_Divides_Odiv__class_Omod(X24606,X24605,X24603)),c_Divides_Odiv__class_Omod(X24606,X24604,X24603)),X24603) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).

fof(i_0_8271,plain,
    ! [X20419,X20420,X20421] :
      ( ~ class_Rings_Olinordered__semidom(X20421)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20421),c_Groups_Oone__class_Oone(X20421)),X20420))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20421),c_Groups_Oone__class_Oone(X20421)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20421),X20420),hAPP(hAPP(c_Power_Opower__class_Opower(X20421),X20420),X20419)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).

fof(i_0_8272,plain,
    ! [X22298,X22299] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22299),X22298),X22298)),c_Groups_Ozero__class_Ozero(X22299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),X22298),c_Groups_Ozero__class_Ozero(X22299)))
        | ~ class_Groups_Olinordered__ab__group__add(X22299) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),X22298),c_Groups_Ozero__class_Ozero(X22299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22299),X22298),X22298)),c_Groups_Ozero__class_Ozero(X22299)))
        | ~ class_Groups_Olinordered__ab__group__add(X22299) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])]) ).

fof(i_0_8273,plain,
    ! [X22739,X22740] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22740),X22739),X22739)),c_Groups_Ozero__class_Ozero(X22740)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22740),X22739),c_Groups_Ozero__class_Ozero(X22740)))
        | ~ class_Rings_Olinordered__idom(X22740) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22740),X22739),c_Groups_Ozero__class_Ozero(X22740)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22740),X22739),X22739)),c_Groups_Ozero__class_Ozero(X22740)))
        | ~ class_Rings_Olinordered__idom(X22740) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_8274,plain,
    ! [X22233,X22234] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22234),X22233),X22233)),c_Groups_Ozero__class_Ozero(X22234)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22234),X22233),c_Groups_Ozero__class_Ozero(X22234)))
        | ~ class_Groups_Olinordered__ab__group__add(X22234) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22234),X22233),c_Groups_Ozero__class_Ozero(X22234)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22234),X22233),X22233)),c_Groups_Ozero__class_Ozero(X22234)))
        | ~ class_Groups_Olinordered__ab__group__add(X22234) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).

fof(i_0_8275,plain,
    ! [X25501,X25502] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk246_2(X25501,X25502)),X25502))
        | c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X25501),X25502) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25501),esk246_2(X25501,X25502)))
        | c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X25501),X25502) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat])])])]) ).

fof(i_0_8276,plain,
    ! [X21465,X21466,X21467,X21468] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21468),X21467),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21468,tc_HOL_Obool),X21466)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X21468,tc_HOL_Obool)),X21465),X21466))
      | hBOOL(hAPP(hAPP(c_member(X21468),X21467),X21465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).

fof(i_0_8277,plain,
    ! [X21461,X21462,X21463,X21464] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21464),X21463),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21464,tc_HOL_Obool),X21462)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X21464,tc_HOL_Obool)),X21461),X21462))
      | hBOOL(hAPP(hAPP(c_member(X21464),X21463),X21461)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).

fof(i_0_8278,plain,
    ! [X26375,X26376] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26376))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26376),X26375)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26376),X26375) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial])]) ).

fof(i_0_8279,plain,
    ! [X22023,X22024] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X22024,X22023)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X22024,X22023),tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X22023),c_Orderings_Otop__class_Otop(tc_fun(X22023,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22024),c_Orderings_Otop__class_Otop(tc_fun(X22024,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_8280,plain,
    ! [X19334,X19335,X19336] :
      ( ~ class_Orderings_Olinorder(X19336)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19336),X19335))
      | X19335 = c_Orderings_Obot__class_Obot(tc_fun(X19336,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19336),X19334))
      | X19334 = c_Orderings_Obot__class_Obot(tc_fun(X19336,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X19336,c_Orderings_Oord__class_Omin(X19336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19336,tc_HOL_Obool)),X19335),X19334)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19336),c_Big__Operators_Olattice_OInf__fin(X19336,c_Orderings_Oord__class_Omin(X19336),X19335)),c_Big__Operators_Olattice_OInf__fin(X19336,c_Orderings_Oord__class_Omin(X19336),X19334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).

fof(i_0_8281,plain,
    ! [X19331,X19332,X19333] :
      ( ~ class_Orderings_Olinorder(X19333)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19333),X19332))
      | X19332 = c_Orderings_Obot__class_Obot(tc_fun(X19333,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19333),X19331))
      | X19331 = c_Orderings_Obot__class_Obot(tc_fun(X19333,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X19333,c_Orderings_Oord__class_Omax(X19333),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19333,tc_HOL_Obool)),X19332),X19331)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19333),c_Big__Operators_Olattice_OSup__fin(X19333,c_Orderings_Oord__class_Omax(X19333),X19332)),c_Big__Operators_Olattice_OSup__fin(X19333,c_Orderings_Oord__class_Omax(X19333),X19331)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).

fof(i_0_8282,plain,
    ! [X17299,X17300,X17301,X17302] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17302),X17301),X17300))
      | hBOOL(hAPP(hAPP(c_member(X17302),X17301),X17299))
      | hBOOL(hAPP(hAPP(c_member(X17302),X17301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17302,tc_HOL_Obool)),X17300),X17299))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5729])]) ).

fof(i_0_8283,plain,
    ! [X22825,X22826,X22827] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22827),X22826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22825))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22825),X22827)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22825),X22826))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).

fof(i_0_8284,plain,
    ! [X22492,X22493,X22494] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22494),X22493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22492))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22494),X22492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22493),X22492))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).

fof(i_0_8285,plain,
    ! [X22495,X22496,X22497] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22497),X22496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22495))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22495),X22497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22495),X22496))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).

fof(i_0_8286,plain,
    ! [X23361,X23362,X23363] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23363),X23362))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23361))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23363),X23361)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23362),X23361))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).

fof(i_0_8287,plain,
    ! [X23476,X23477,X23478] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23478),X23477))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23476),X23477)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23476),X23478))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).

fof(i_0_8288,plain,
    ! [X31247,X31248,X31249] :
      ( ( ~ c_Fun_Oinj__on(tc_List_Olist(X31249),tc_List_Olist(X31248),hAPP(c_List_Omap(X31249,X31248),X31247),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31249),tc_HOL_Obool)))
        | c_Fun_Oinj__on(X31249,X31248,X31247,c_Orderings_Otop__class_Otop(tc_fun(X31249,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X31249,X31248,X31247,c_Orderings_Otop__class_Otop(tc_fun(X31249,tc_HOL_Obool)))
        | c_Fun_Oinj__on(tc_List_Olist(X31249),tc_List_Olist(X31248),hAPP(c_List_Omap(X31249,X31248),X31247),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31249),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).

fof(i_0_8289,plain,
    ! [X31244,X31245,X31246] :
      ( ~ c_Fun_Oinj__on(tc_List_Olist(X31246),tc_List_Olist(X31245),hAPP(c_List_Omap(X31246,X31245),X31244),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31246),tc_HOL_Obool)))
      | c_Fun_Oinj__on(X31246,X31245,X31244,c_Orderings_Otop__class_Otop(tc_fun(X31246,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).

fof(i_0_8290,plain,
    ! [X17808,X17809,X17810,X17811] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17811,tc_HOL_Obool)),X17810),X17809))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17811,tc_HOL_Obool)),X17810),hAPP(hAPP(c_Set_Oinsert(X17811),X17808),X17809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_8291,plain,
    ! [X32872,X32873,X32874,X32875] : hAPP(hAPP(c_List_Oappend(X32875),c_List_Oreplicate(X32875,X32874,X32873)),hAPP(hAPP(c_List_Olist_OCons(X32875),X32873),X32872)) = hAPP(hAPP(c_List_Olist_OCons(X32875),X32873),hAPP(hAPP(c_List_Oappend(X32875),c_List_Oreplicate(X32875,X32874,X32873)),X32872)),
    inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(i_0_8292,plain,
    ! [X21864,X21865,X21866,X21867,X21868] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21868,tc_fun(X21867,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X21868),X21866),X21865)),X21864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21867,tc_HOL_Obool)),hAPP(X21864,X21866)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21868,tc_fun(X21867,tc_HOL_Obool)),X21865),X21864)),
    inference(variable_rename,[status(thm)],[fact_INT__insert]) ).

fof(i_0_8293,plain,
    ! [X21163,X21164,X21165,X21166,X21167] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21167,tc_fun(X21166,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X21167),X21165),X21164)),X21163) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21166,tc_HOL_Obool)),hAPP(X21163,X21165)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21167,tc_fun(X21166,tc_HOL_Obool)),X21164),X21163)),
    inference(variable_rename,[status(thm)],[fact_UN__insert]) ).

fof(i_0_8294,plain,
    ! [X21002,X21003,X21004,X21005] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21004),X21002),hAPP(c_Finite__Set_Ofold1(X21004,c_Lattices_Osemilattice__inf__class_Oinf(X21004)),X21003)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21004),X21005),X21003))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21004),X21002),X21005))
        | X21003 = c_Orderings_Obot__class_Obot(tc_fun(X21004,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21004),X21003))
        | ~ class_Lattices_Osemilattice__inf(X21004) )
      & ( hBOOL(hAPP(hAPP(c_member(X21004),esk91_3(X21002,X21003,X21004)),X21003))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21004),X21002),hAPP(c_Finite__Set_Ofold1(X21004,c_Lattices_Osemilattice__inf__class_Oinf(X21004)),X21003)))
        | X21003 = c_Orderings_Obot__class_Obot(tc_fun(X21004,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21004),X21003))
        | ~ class_Lattices_Osemilattice__inf(X21004) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21004),X21002),esk91_3(X21002,X21003,X21004)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21004),X21002),hAPP(c_Finite__Set_Ofold1(X21004,c_Lattices_Osemilattice__inf__class_Oinf(X21004)),X21003)))
        | X21003 = c_Orderings_Obot__class_Obot(tc_fun(X21004,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21004),X21003))
        | ~ class_Lattices_Osemilattice__inf(X21004) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__fold1__iff])])])])]) ).

fof(i_0_8295,plain,
    ! [X19056,X19057,X19058,X19059] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19058),X19056),hAPP(c_Finite__Set_Ofold1(X19058,c_Orderings_Oord__class_Omin(X19058)),X19057)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19058),X19059),X19057))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19058),X19056),X19059))
        | X19057 = c_Orderings_Obot__class_Obot(tc_fun(X19058,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19058),X19057))
        | ~ class_Orderings_Olinorder(X19058) )
      & ( hBOOL(hAPP(hAPP(c_member(X19058),esk43_3(X19056,X19057,X19058)),X19057))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19058),X19056),hAPP(c_Finite__Set_Ofold1(X19058,c_Orderings_Oord__class_Omin(X19058)),X19057)))
        | X19057 = c_Orderings_Obot__class_Obot(tc_fun(X19058,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19058),X19057))
        | ~ class_Orderings_Olinorder(X19058) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19058),X19056),esk43_3(X19056,X19057,X19058)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19058),X19056),hAPP(c_Finite__Set_Ofold1(X19058,c_Orderings_Oord__class_Omin(X19058)),X19057)))
        | X19057 = c_Orderings_Obot__class_Obot(tc_fun(X19058,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19058),X19057))
        | ~ class_Orderings_Olinorder(X19058) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff])])])])]) ).

fof(i_0_8296,plain,
    ! [X19042,X19043,X19044,X19045] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19044),X19042),hAPP(c_Finite__Set_Ofold1(X19044,c_Orderings_Oord__class_Omin(X19044)),X19043)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19044),X19045),X19043))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19044),X19042),X19045))
        | X19043 = c_Orderings_Obot__class_Obot(tc_fun(X19044,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19044),X19043))
        | ~ class_Orderings_Olinorder(X19044) )
      & ( hBOOL(hAPP(hAPP(c_member(X19044),esk41_3(X19042,X19043,X19044)),X19043))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19044),X19042),hAPP(c_Finite__Set_Ofold1(X19044,c_Orderings_Oord__class_Omin(X19044)),X19043)))
        | X19043 = c_Orderings_Obot__class_Obot(tc_fun(X19044,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19044),X19043))
        | ~ class_Orderings_Olinorder(X19044) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19044),X19042),esk41_3(X19042,X19043,X19044)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19044),X19042),hAPP(c_Finite__Set_Ofold1(X19044,c_Orderings_Oord__class_Omin(X19044)),X19043)))
        | X19043 = c_Orderings_Obot__class_Obot(tc_fun(X19044,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19044),X19043))
        | ~ class_Orderings_Olinorder(X19044) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff])])])])]) ).

fof(i_0_8297,plain,
    ! [X32435,X32436,X32437,X32438,X32439] : c_List_Omaps(X32439,X32438,X32437,hAPP(hAPP(c_List_Olist_OCons(X32439),X32436),X32435)) = hAPP(hAPP(c_List_Oappend(X32438),hAPP(X32437,X32436)),c_List_Omaps(X32439,X32438,X32437,X32435)),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).

cnf(i_0_8298,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk427_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | c_List_Oconcat(X1,X2) = c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5664]) ).

cnf(i_0_8299,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk428_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | c_List_Olist_ONil(X1) = c_List_Oconcat(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5665]) ).

fof(i_0_8300,plain,
    ! [X22372,X22373,X22374] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22374),X22373),X22372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22374),X22373),X22372)),c_Groups_Ozero__class_Ozero(X22374)))
        | ~ class_Groups_Oordered__ab__group__add(X22374) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22374),X22373),X22372)),c_Groups_Ozero__class_Ozero(X22374)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22374),X22373),X22372))
        | ~ class_Groups_Oordered__ab__group__add(X22374) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(i_0_8301,plain,
    ! [X22369,X22370,X22371] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22371),X22370),X22369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22371),X22370),X22369)),c_Groups_Ozero__class_Ozero(X22371)))
        | ~ class_Groups_Oordered__ab__group__add(X22371) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22371),X22370),X22369)),c_Groups_Ozero__class_Ozero(X22371)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22371),X22370),X22369))
        | ~ class_Groups_Oordered__ab__group__add(X22371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).

fof(i_0_8302,plain,
    ! [X23364,X23365,X23366] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23366),X23365))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23364),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23365),X23364)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23366),X23364))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).

cnf(i_0_8303,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4)) = hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_5730]) ).

cnf(i_0_8304,plain,
    c_Code__Numeral_OSuc__code__numeral(X1) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))),
    inference(split_conjunct,[status(thm)],[i_0_5731]) ).

fof(i_0_8305,plain,
    ! [X29894,X29895,X29896] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29896),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29895)),X29894)))
      | hBOOL(hAPP(hAPP(c_member(X29895),hAPP(hAPP(c_List_Onth(X29895),X29894),X29896)),hAPP(c_List_Oset(X29895),X29894))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).

fof(i_0_8306,plain,
    ! [X22624,X22625] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22624))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22625),X22624))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).

fof(i_0_8307,plain,
    ! [X22622,X22623] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22622))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22622),X22623))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).

fof(i_0_8308,plain,
    ! [X22726,X22727] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22727),X22726))
      | hAPP(c_Finite__Set_Ocard(X22727),X22726) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X22727,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X22727),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22726) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_8309,plain,
    ! [X22724,X22725] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22725),X22724))
        | hAPP(c_Finite__Set_Ocard(X22725),X22724) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X22725,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X22725),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22724) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22725),X22724))
        | hAPP(c_Finite__Set_Ocard(X22725),X22724) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5732])]) ).

fof(i_0_8310,plain,
    ! [X23917,X23918,X23919,X23920] :
      ( ~ class_Fields_Ofield(X23920)
      | X23919 = c_Groups_Ozero__class_Ozero(X23920)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23920),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23920),X23918),X23919)),X23917) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23920),X23918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23920),X23919),X23917))),X23919) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).

fof(i_0_8311,plain,
    ! [X23921,X23922,X23923,X23924] :
      ( ~ class_Fields_Ofield__inverse__zero(X23924)
      | X23923 = c_Groups_Ozero__class_Ozero(X23924)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23924),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23924),X23922),X23923)),X23921) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23924),X23922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23924),X23921),X23923))),X23923) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).

fof(i_0_8312,plain,
    ! [X23938,X23939,X23940,X23941] :
      ( ~ class_Fields_Ofield(X23941)
      | X23940 = c_Groups_Ozero__class_Ozero(X23941)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23941),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23941),X23939),X23940)),X23938) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23941),X23939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23941),X23940),X23938))),X23940) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).

fof(i_0_8313,plain,
    ! [X29897,X29898,X29899,X29901,X29902,X29903,X29904] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk394_3(X29897,X29898,X29899)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29899)),X29897)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29899),X29898),hAPP(c_List_Oset(X29899),X29897))) )
      & ( hAPP(hAPP(c_List_Onth(X29899),X29897),esk394_3(X29897,X29898,X29899)) = X29898
        | ~ hBOOL(hAPP(hAPP(c_member(X29899),X29898),hAPP(c_List_Oset(X29899),X29897))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29904),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29903)),X29901)))
        | hAPP(hAPP(c_List_Onth(X29903),X29901),X29904) != X29902
        | hBOOL(hAPP(hAPP(c_member(X29903),X29902),hAPP(c_List_Oset(X29903),X29901))) ) ),
    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_in__set__conv__nth])])])])])]) ).

fof(i_0_8314,plain,
    ! [X23047,X23048,X23049,X23050] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23050),X23049))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23048),X23047))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23050),X23048)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23049),X23047))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_8315,plain,
    ! [X20053,X20054,X20055,X20056] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20056),X20055))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20054),X20053))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20056),X20054)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20055),X20053))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_8316,plain,
    ! [X19873,X19874,X19875] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19875),X19874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19873),X19875))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19875),X19873)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19874),X19873))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).

fof(i_0_8317,plain,
    ! [X19879,X19880,X19881] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19881),X19880))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19881),X19879))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19879),X19880)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19879),X19881))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).

fof(i_0_8318,plain,
    ! [X19971,X19972,X19973,X19974] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19974),X19973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19972),X19971))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19974),X19972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19973),X19971))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).

fof(i_0_8319,plain,
    ! [X19924,X19925,X19926,X19927] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19927),X19926))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19925),X19924))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19927),X19925)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19926),X19924))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_8320,plain,
    ! [X18600,X18601,X18602,X18603,X18604] :
      ( ~ class_Rings_Ocomm__semiring__1(X18604)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),X18603),X18602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),X18601),X18600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),X18601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18604),X18603),X18602)),X18600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).

fof(i_0_8321,plain,
    ! [X22774,X22775,X22776] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22776,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X22776),X22775)),hAPP(c_SetInterval_Oord__class_OlessThan(X22776),X22774)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22776),X22775),X22774))
        | ~ class_Orderings_Olinorder(X22776) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22776),X22775),X22774))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22776,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X22776),X22775)),hAPP(c_SetInterval_Oord__class_OlessThan(X22776),X22774)))
        | ~ class_Orderings_Olinorder(X22776) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).

fof(i_0_8322,plain,
    ! [X24309,X24310,X24311] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24311,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24311),X24310)),hAPP(c_SetInterval_Oord__class_OatMost(X24311),X24309)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24311),X24310),X24309))
        | ~ class_Orderings_Oorder(X24311) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24311),X24310),X24309))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24311,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24311),X24310)),hAPP(c_SetInterval_Oord__class_OatMost(X24311),X24309)))
        | ~ class_Orderings_Oorder(X24311) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).

fof(i_0_8323,plain,
    ! [X22771,X22772,X22773] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22773,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X22773),X22772)),hAPP(c_SetInterval_Oord__class_OlessThan(X22773),X22771)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22773),X22772),X22771))
        | ~ class_Orderings_Olinorder(X22773) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22773),X22772),X22771))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22773,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X22773),X22772)),hAPP(c_SetInterval_Oord__class_OlessThan(X22773),X22771)))
        | ~ class_Orderings_Olinorder(X22773) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).

fof(i_0_8324,plain,
    ! [X24306,X24307,X24308] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24308),X24307)),hAPP(c_SetInterval_Oord__class_OatLeast(X24308),X24306)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24308),X24306),X24307))
        | ~ class_Orderings_Oorder(X24308) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24308),X24306),X24307))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24308),X24307)),hAPP(c_SetInterval_Oord__class_OatLeast(X24308),X24306)))
        | ~ class_Orderings_Oorder(X24308) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).

fof(i_0_8325,plain,
    ! [X24073,X24074,X24075] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24075,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24075),X24074)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24075),X24073)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24075),X24073),X24074))
        | ~ class_Orderings_Olinorder(X24075) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24075),X24073),X24074))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24075,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24075),X24074)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24075),X24073)))
        | ~ class_Orderings_Olinorder(X24075) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).

cnf(i_0_8326,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5733]) ).

fof(i_0_8327,plain,
    ! [X23810,X23811,X23812] :
      ( ~ class_Fields_Olinordered__field(X23812)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23812),X23811),c_Groups_Ozero__class_Ozero(X23812)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23812),c_Groups_Ozero__class_Ozero(X23812)),X23810))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23812),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23812),X23811),X23810)),c_Groups_Ozero__class_Ozero(X23812))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_8328,plain,
    ! [X23807,X23808,X23809] :
      ( ~ class_Fields_Olinordered__field(X23809)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23809),c_Groups_Ozero__class_Ozero(X23809)),X23808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23809),X23807),c_Groups_Ozero__class_Ozero(X23809)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23809),X23808),X23807)),c_Groups_Ozero__class_Ozero(X23809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_8329,plain,
    ! [X22343,X22344,X22345] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22345)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22345),X22344),c_Groups_Ozero__class_Ozero(X22345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22345),c_Groups_Ozero__class_Ozero(X22345)),X22343))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22345),X22344),X22343)),c_Groups_Ozero__class_Ozero(X22345))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_8330,plain,
    ! [X22327,X22328,X22329] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22329)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22329),c_Groups_Ozero__class_Ozero(X22329)),X22328))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22329),X22327),c_Groups_Ozero__class_Ozero(X22329)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22329),X22328),X22327)),c_Groups_Ozero__class_Ozero(X22329))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_8331,plain,
    ! [X22330,X22331,X22332] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22332)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22332),c_Groups_Ozero__class_Ozero(X22332)),X22331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22332),X22330),c_Groups_Ozero__class_Ozero(X22332)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22332),X22330),X22331)),c_Groups_Ozero__class_Ozero(X22332))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_8332,plain,
    ! [X23848,X23849,X23850] :
      ( ~ class_Fields_Olinordered__field(X23850)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23850),c_Groups_Ozero__class_Ozero(X23850)),X23849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23850),X23848),c_Groups_Ozero__class_Ozero(X23850)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23850),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23850),X23849),X23848)),c_Groups_Ozero__class_Ozero(X23850))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_8333,plain,
    ! [X23866,X23867,X23868] :
      ( ~ class_Fields_Olinordered__field(X23868)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23868),X23867),c_Groups_Ozero__class_Ozero(X23868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23868),c_Groups_Ozero__class_Ozero(X23868)),X23866))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23868),X23867),X23866)),c_Groups_Ozero__class_Ozero(X23868))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_8334,plain,
    ! [X22293,X22294,X22295] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),c_Groups_Ozero__class_Ozero(X22295)),X22294))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22293),c_Groups_Ozero__class_Ozero(X22295)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22295),X22294),X22293)),c_Groups_Ozero__class_Ozero(X22295)))
        | ~ class_Rings_Oordered__cancel__semiring(X22295) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),c_Groups_Ozero__class_Ozero(X22295)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),c_Groups_Ozero__class_Ozero(X22295)),X22293))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22295),X22294),X22293)),c_Groups_Ozero__class_Ozero(X22295)))
        | ~ class_Rings_Oordered__cancel__semiring(X22295) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_8335,plain,
    ! [X22254,X22255,X22256] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22256)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22256),X22255),c_Groups_Ozero__class_Ozero(X22256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22256),c_Groups_Ozero__class_Ozero(X22256)),X22254))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22256),X22255),X22254)),c_Groups_Ozero__class_Ozero(X22256))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_8336,plain,
    ! [X22248,X22249,X22250] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22250)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22250),c_Groups_Ozero__class_Ozero(X22250)),X22249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22250),X22248),c_Groups_Ozero__class_Ozero(X22250)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22250),X22249),X22248)),c_Groups_Ozero__class_Ozero(X22250))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_8337,plain,
    ! [X22251,X22252,X22253] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22253)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22253),c_Groups_Ozero__class_Ozero(X22253)),X22252))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22253),X22251),c_Groups_Ozero__class_Ozero(X22253)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22253),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22253),X22251),X22252)),c_Groups_Ozero__class_Ozero(X22253))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_8338,plain,
    ! [X29808,X29809,X29810] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29810,tc_HOL_Obool)),hAPP(c_List_Oset(X29810),X29809)),hAPP(c_List_Oset(X29810),hAPP(hAPP(c_List_Olist_OCons(X29810),X29808),X29809)))),
    inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).

fof(i_0_8339,plain,
    ! [X33969,X33970,X33971,X33972,X33973] : c_Lazy__Sequence_Omap(X33973,X33972,X33971,c_Lazy__Sequence_Olazy__sequence_OInsert(X33973,X33970,X33969)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33972,hAPP(X33971,X33970),c_Lazy__Sequence_Omap(X33973,X33972,X33971,X33969)),
    inference(variable_rename,[status(thm)],[fact__06]) ).

fof(i_0_8340,plain,
    ! [X31831,X31832,X31833,X31834] : c_List_Otranspose(X31834,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31833),tc_List_Olist(X31834)),hAPP(c_List_Omap(X31833,X31834),X31832)),X31831)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31833),tc_List_Olist(X31834)),hAPP(c_List_Omap(X31833,X31834),X31832)),c_List_Otranspose(X31833,X31831)),
    inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).

cnf(i_0_8341,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5734]) ).

cnf(i_0_8342,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5735]) ).

fof(i_0_8343,plain,
    ! [X34065,X34066,X34067,X34068] :
      ( ~ class_Rings_Ocomm__semiring__1(X34068)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34068),X34067),X34066)),X34065))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34068),X34067),X34065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).

fof(i_0_8344,plain,
    ! [X34069,X34070,X34071,X34072] :
      ( ~ class_Rings_Ocomm__semiring__1(X34072)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34072),X34071),X34070)),X34069))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34072),X34070),X34069)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).

fof(i_0_8345,plain,
    ! [X18929,X18930,X18931,X18932] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),X18931),X18929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18932),X18931),X18930)),X18929))
        | ~ class_Orderings_Olinorder(X18932) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),X18930),X18929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18932),X18931),X18930)),X18929))
        | ~ class_Orderings_Olinorder(X18932) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),X18931),X18929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),X18930),X18929))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18932),X18931),X18930)),X18929))
        | ~ class_Orderings_Olinorder(X18932) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).

fof(i_0_8346,plain,
    ! [X19547,X19548,X19549,X19550] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19550),X19549),X19547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19550),X19549),X19548)),X19547))
        | ~ class_Lattices_Osemilattice__sup(X19550) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19550),X19548),X19547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19550),X19549),X19548)),X19547))
        | ~ class_Lattices_Osemilattice__sup(X19550) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5736])])]) ).

fof(i_0_8347,plain,
    ! [X19516,X19517,X19518,X19519] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),X19518),X19516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19519),X19518),X19517)),X19516))
        | ~ class_Lattices_Osemilattice__sup(X19519) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),X19517),X19516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19519),X19518),X19517)),X19516))
        | ~ class_Lattices_Osemilattice__sup(X19519) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),X19518),X19516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),X19517),X19516))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19519),X19518),X19517)),X19516))
        | ~ class_Lattices_Osemilattice__sup(X19519) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).

fof(i_0_8348,plain,
    ! [X18838,X18839,X18840,X18841] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),X18840),X18838))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18841),X18840),X18839)),X18838))
        | ~ class_Orderings_Olinorder(X18841) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),X18839),X18838))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18841),X18840),X18839)),X18838))
        | ~ class_Orderings_Olinorder(X18841) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),X18840),X18838))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),X18839),X18838))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18841),X18840),X18839)),X18838))
        | ~ class_Orderings_Olinorder(X18841) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).

fof(i_0_8349,plain,
    ! [X18807,X18808,X18809,X18810] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),X18809),X18807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18810),X18809),X18808)),X18807))
        | ~ class_Orderings_Olinorder(X18810) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),X18808),X18807))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18810),X18809),X18808)),X18807))
        | ~ class_Orderings_Olinorder(X18810) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5737])])]) ).

fof(i_0_8350,plain,
    ! [X30153,X30154,X30155,X30156] :
      ( ( hAPP(hAPP(c_List_Onth(X30156),X30155),X30154) != hAPP(hAPP(c_List_Onth(X30156),X30155),X30153)
        | X30154 = X30153
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30156)),X30155)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30154),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30156)),X30155)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30156),X30155)) )
      & ( X30154 != X30153
        | hAPP(hAPP(c_List_Onth(X30156),X30155),X30154) = hAPP(hAPP(c_List_Onth(X30156),X30155),X30153)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30156)),X30155)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30154),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30156)),X30155)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30156),X30155)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).

fof(i_0_8351,plain,
    ! [X30145,X30146,X30147,X30148,X30149,X30150] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30146),X30145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30146)),X30145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30148),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30146)),X30145)))
        | X30147 = X30148
        | hAPP(hAPP(c_List_Onth(X30146),X30145),X30147) != hAPP(hAPP(c_List_Onth(X30146),X30145),X30148) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk401_2(X30149,X30150)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30150)),X30149)))
        | hBOOL(hAPP(c_List_Odistinct(X30150),X30149)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk402_2(X30149,X30150)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30150)),X30149)))
        | hBOOL(hAPP(c_List_Odistinct(X30150),X30149)) )
      & ( esk401_2(X30149,X30150) != esk402_2(X30149,X30150)
        | hBOOL(hAPP(c_List_Odistinct(X30150),X30149)) )
      & ( hAPP(hAPP(c_List_Onth(X30150),X30149),esk401_2(X30149,X30150)) = hAPP(hAPP(c_List_Onth(X30150),X30149),esk402_2(X30149,X30150))
        | hBOOL(hAPP(c_List_Odistinct(X30150),X30149)) ) ),
    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_distinct__conv__nth])])])])])]) ).

fof(i_0_8352,plain,
    ! [X31230,X31231,X31232,X31233] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X31232),X31230))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31233),hAPP(hAPP(c_List_Omap(X31232,X31233),X31231),X31230))) )
      & ( c_Fun_Oinj__on(X31232,X31233,X31231,hAPP(c_List_Oset(X31232),X31230))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31233),hAPP(hAPP(c_List_Omap(X31232,X31233),X31231),X31230))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31232),X31230))
        | ~ c_Fun_Oinj__on(X31232,X31233,X31231,hAPP(c_List_Oset(X31232),X31230))
        | hBOOL(hAPP(c_List_Odistinct(X31233),hAPP(hAPP(c_List_Omap(X31232,X31233),X31231),X31230))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).

fof(i_0_8353,plain,
    ! [X19207,X19208] :
      ( ~ class_Orderings_Olinorder(X19208)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19208),X19207))
      | X19207 = c_Orderings_Obot__class_Obot(tc_fun(X19208,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19208),c_Big__Operators_Olattice_OInf__fin(X19208,c_Orderings_Oord__class_Omin(X19208),X19207)),c_Big__Operators_Olattice_OSup__fin(X19208,c_Orderings_Oord__class_Omax(X19208),X19207))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).

fof(i_0_8354,plain,
    ! [X17755,X17756,X17757,X17758,X17759] :
      ( ~ c_Fun_Oinj__on(X17759,X17758,X17757,X17756)
      | c_Fun_Oinj__on(X17759,X17758,X17757,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17759,tc_HOL_Obool)),X17756),X17755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).

fof(i_0_8355,plain,
    ! [X33015,X33016,X33017,X33018] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33018,X33017),c_Lazy__Sequence_Olazy__sequence_OInsert(X33018,X33016,X33015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33017,X33016)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33018,X33017),X33015))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I2_J]) ).

cnf(i_0_8356,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5738]) ).

cnf(i_0_8357,plain,
    ( X2 = X4
    | hBOOL(hAPP(hAPP(c_List_Omember(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5739]) ).

cnf(i_0_8358,plain,
    c_List_Omember(X1) = c_List_Oset(X1),
    inference(split_conjunct,[status(thm)],[i_0_5740]) ).

fof(i_0_8359,plain,
    ! [X17943,X17944,X17945,X17946,X17947,X17948] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17948,X17947,X17946)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17948),X17945))
      | hAPP(hAPP(c_Finite__Set_Ofold(X17948,X17947,X17946),X17944),hAPP(hAPP(c_Set_Oinsert(X17948),X17943),X17945)) = hAPP(hAPP(c_Finite__Set_Ofold(X17948,X17947,X17946),hAPP(hAPP(X17946,X17943),X17944)),X17945) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).

fof(i_0_8360,plain,
    ! [X17382,X17383,X17384] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17384),X17383),X17382))
      | hAPP(hAPP(c_Set_Oinsert(X17384),X17383),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17384,tc_HOL_Obool)),X17382),hAPP(hAPP(c_Set_Oinsert(X17384),X17383),c_Orderings_Obot__class_Obot(tc_fun(X17384,tc_HOL_Obool))))) = X17382 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).

fof(i_0_8361,plain,
    ! [X19366,X19367] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19367),c_Orderings_Otop__class_Otop(tc_fun(X19367,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19366),c_Orderings_Otop__class_Otop(tc_fun(X19366,tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X19367,X19366)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X19367,X19366),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_8362,plain,
    ! [X19364,X19365] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19365),c_Orderings_Otop__class_Otop(tc_fun(X19365,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X19365,X19364)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X19365,X19364),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19364),c_Orderings_Otop__class_Otop(tc_fun(X19364,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X19365,X19364)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X19365,X19364),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19365),c_Orderings_Otop__class_Otop(tc_fun(X19365,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19364),c_Orderings_Otop__class_Otop(tc_fun(X19364,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X19365,X19364)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X19365,X19364),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])]) ).

fof(i_0_8363,plain,
    ! [X24233,X24234,X24235,X24236] :
      ( ~ class_Groups_Ocomm__monoid__add(X24236)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24235),X24234))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24236),X24233),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24235,X24234)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24236),hAPP(X24233,X24235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24236),X24233),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24235),X24234))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).

fof(i_0_8364,plain,
    ! [X20701,X20702,X20703,X20704,X20705] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20705),hAPP(X20704,X20703)),X20702))
      | hBOOL(hAPP(hAPP(c_member(X20701),X20703),hAPP(c_Set_Ovimage(X20701,X20705,X20704),X20702))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).

cnf(i_0_8365,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(c_List_Orotate(X2,X3),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5741]) ).

fof(i_0_8366,plain,
    ! [X32030,X32031,X32032] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32032,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32032,X32032,c_COMBI(X32032)),X32031),X32030))
        | c_List_Olinorder__class_Osorted(X32032,X32030)
        | ~ class_Orderings_Olinorder(X32032) )
      & ( ~ c_List_Olinorder__class_Osorted(X32032,X32030)
        | c_List_Olinorder__class_Osorted(X32032,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32032,X32032,c_COMBI(X32032)),X32031),X32030))
        | ~ class_Orderings_Olinorder(X32032) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).

fof(i_0_8367,plain,
    ! [X23189,X23190,X23191,X23192] :
      ( ~ class_Groups_Ocomm__monoid__add(X23192)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23191),X23190))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23192),X23189),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23191),X23190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23192),hAPP(X23189,X23191)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23192),X23189),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23191)),X23190))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).

fof(i_0_8368,plain,
    ! [X17662,X17663,X17664] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17662,tc_HOL_Obool)),X17664),X17663))
        | X17664 != X17663 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17662,tc_HOL_Obool)),X17663),X17664))
        | X17664 != X17663 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17662,tc_HOL_Obool)),X17664),X17663))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17662,tc_HOL_Obool)),X17663),X17664))
        | X17664 = X17663 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_8369,plain,
    ! [X17562,X17563,X17564] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17564,tc_HOL_Obool)),X17563),X17562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17564,tc_HOL_Obool)),X17562),X17563))
      | X17563 = X17562 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_8370,plain,
    ! [X32220,X32221,X32222] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32222),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32221)),X32220)))
      | hAPP(hAPP(c_List_Onth(X32221),hAPP(c_List_Orev(X32221),X32220)),X32222) = hAPP(hAPP(c_List_Onth(X32221),X32220),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32221)),X32220)),hAPP(c_Nat_OSuc,X32222))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).

fof(i_0_8371,plain,
    ! [X21833,X21834,X21835,X21836,X21837] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21837),X21836),X21835))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21834,tc_HOL_Obool)),hAPP(X21833,X21836)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21837,tc_fun(X21834,tc_HOL_Obool)),X21835),X21833)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21837,tc_fun(X21834,tc_HOL_Obool)),X21835),X21833) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).

fof(i_0_8372,plain,
    ! [X21385,X21386,X21387,X21388,X21389] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21389),X21388),X21387))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21386,tc_HOL_Obool)),hAPP(X21385,X21388)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21389,tc_fun(X21386,tc_HOL_Obool)),X21387),X21385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21389,tc_fun(X21386,tc_HOL_Obool)),X21387),X21385) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).

fof(i_0_8373,plain,
    ! [X30045,X30046,X30047,X30048,X30049] : hAPP(hAPP(c_List_Olist__update(X30049,hAPP(hAPP(c_List_Olist__update(X30049,X30048),X30047),X30046)),X30047),X30045) = hAPP(hAPP(c_List_Olist__update(X30049,X30048),X30047),X30045),
    inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).

fof(i_0_8374,plain,
    ! [X22821,X22822] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X22822)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22821))),
    inference(variable_rename,[status(thm)],[fact_negative__zless]) ).

fof(i_0_8375,plain,
    ! [X22303,X22304,X22305] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22305)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22305),X22304),c_Groups_Ozero__class_Ozero(X22305)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22305),X22303),c_Groups_Ozero__class_Ozero(X22305)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22305),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22305),X22304),X22303)),c_Groups_Ozero__class_Ozero(X22305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_8376,plain,
    ! [X22522,X22523,X22524] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22524)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22524),X22523),c_Groups_Ozero__class_Ozero(X22524)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22524),X22522),c_Groups_Ozero__class_Ozero(X22524)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22524),X22523),X22522)),c_Groups_Ozero__class_Ozero(X22524))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_8377,plain,
    ! [X22525,X22526,X22527] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22527),X22526),c_Groups_Ozero__class_Ozero(X22527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22527),X22525),c_Groups_Ozero__class_Ozero(X22527)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22527),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22527),X22526),X22525)),c_Groups_Ozero__class_Ozero(X22527))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_8378,plain,
    ! [X22216,X22217,X22218] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22218)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22218),X22217),c_Groups_Ozero__class_Ozero(X22218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22218),X22216),c_Groups_Ozero__class_Ozero(X22218)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22218),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22218),X22217),X22216)),c_Groups_Ozero__class_Ozero(X22218))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_8379,plain,
    ! [X26504,X26505,X26506] :
      ( ~ class_Rings_Osemiring__1(X26506)
      | ~ hBOOL(hAPP(hAPP(c_member(X26506),X26505),c_Nat_Osemiring__1__class_ONats(X26506)))
      | ~ hBOOL(hAPP(hAPP(c_member(X26506),X26504),c_Nat_Osemiring__1__class_ONats(X26506)))
      | hBOOL(hAPP(hAPP(c_member(X26506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26506),X26505),X26504)),c_Nat_Osemiring__1__class_ONats(X26506))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).

fof(i_0_8380,plain,
    ! [X22936,X22937,X22938] :
      ( ~ class_Rings_Oring__1(X22938)
      | ~ hBOOL(hAPP(hAPP(c_member(X22938),X22937),c_Int_Oring__1__class_OInts(X22938)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22938),X22936),c_Int_Oring__1__class_OInts(X22938)))
      | hBOOL(hAPP(hAPP(c_member(X22938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22938),X22937),X22936)),c_Int_Oring__1__class_OInts(X22938))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).

fof(i_0_8381,plain,
    ! [X26501,X26502,X26503] :
      ( ~ class_Rings_Osemiring__1(X26503)
      | ~ hBOOL(hAPP(hAPP(c_member(X26503),X26502),c_Nat_Osemiring__1__class_ONats(X26503)))
      | ~ hBOOL(hAPP(hAPP(c_member(X26503),X26501),c_Nat_Osemiring__1__class_ONats(X26503)))
      | hBOOL(hAPP(hAPP(c_member(X26503),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26503),X26502),X26501)),c_Nat_Osemiring__1__class_ONats(X26503))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).

fof(i_0_8382,plain,
    ! [X22933,X22934,X22935] :
      ( ~ class_Rings_Oring__1(X22935)
      | ~ hBOOL(hAPP(hAPP(c_member(X22935),X22934),c_Int_Oring__1__class_OInts(X22935)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22935),X22933),c_Int_Oring__1__class_OInts(X22935)))
      | hBOOL(hAPP(hAPP(c_member(X22935),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22935),X22934),X22933)),c_Int_Oring__1__class_OInts(X22935))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_8383,plain,
    ! [X22939,X22940,X22941] :
      ( ~ class_Rings_Oring__1(X22941)
      | ~ hBOOL(hAPP(hAPP(c_member(X22941),X22940),c_Int_Oring__1__class_OInts(X22941)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22941),X22939),c_Int_Oring__1__class_OInts(X22941)))
      | hBOOL(hAPP(hAPP(c_member(X22941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22941),X22940),X22939)),c_Int_Oring__1__class_OInts(X22941))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).

fof(i_0_8384,plain,
    ! [X31301,X31302,X31303] : c_List_Olist_Olist__size(X31303,X31302,X31301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X31303,tc_Nat_Onat),X31302),X31301))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31303)),X31301)),
    inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(i_0_8385,plain,
    ! [X19804,X19805] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19805),c_Orderings_Otop__class_Otop(tc_fun(X19805,tc_HOL_Obool))))
      | ~ c_Fun_Oinj__on(X19805,X19805,X19804,c_Orderings_Otop__class_Otop(tc_fun(X19805,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19805,X19805,X19804),c_Orderings_Otop__class_Otop(tc_fun(X19805,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19805,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_8386,plain,
    ! [X31254,X31255,X31256,X31257] :
      ( ~ class_Rings_Osemiring__1(X31257)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31257),hAPP(hAPP(c_List_Omap(X31256,X31257),hAPP(c_COMBK(X31257,X31256),X31255)),X31254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X31257),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X31257),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31256)),X31254))),X31255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).

fof(i_0_8387,plain,
    ! [X20371,X20372,X20373] :
      ( ~ class_Rings_Oring__1(X20373)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20373),hAPP(c_Groups_Ouminus__class_Ouminus(X20373),X20372)),X20371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20373),hAPP(hAPP(c_Power_Opower__class_Opower(X20373),hAPP(c_Groups_Ouminus__class_Ouminus(X20373),c_Groups_Oone__class_Oone(X20373))),X20371)),hAPP(hAPP(c_Power_Opower__class_Opower(X20373),X20372),X20371)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).

fof(i_0_8388,plain,
    ! [X19717,X19718,X19719,X19720] : hBOOL(hAPP(hAPP(c_member(X19720),hAPP(X19719,X19718)),hAPP(c_Set_Oimage(X19717,X19720,X19719),c_Orderings_Otop__class_Otop(tc_fun(X19717,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_8389,plain,
    ! [X25718,X25719,X25720,X25721] :
      ( ~ class_Int_Onumber(X25721)
      | ~ class_Rings_Osemiring(X25721)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25721),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25721),X25720),X25719)),hAPP(c_Int_Onumber__class_Onumber__of(X25721),X25718)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25721),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25721),X25720),hAPP(c_Int_Onumber__class_Onumber__of(X25721),X25718))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25721),X25719),hAPP(c_Int_Onumber__class_Onumber__of(X25721),X25718))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_8390,plain,
    ! [X25726,X25727,X25728,X25729] :
      ( ~ class_Int_Onumber(X25729)
      | ~ class_Rings_Oring(X25729)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25729),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25729),X25728),X25727)),hAPP(c_Int_Onumber__class_Onumber__of(X25729),X25726)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25729),X25728),hAPP(c_Int_Onumber__class_Onumber__of(X25729),X25726))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25729),X25727),hAPP(c_Int_Onumber__class_Onumber__of(X25729),X25726))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).

fof(i_0_8391,plain,
    ! [X22009,X22010,X22011] :
      ( ~ class_Lattices_Olattice(X22011)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22011),X22010))
      | X22010 = c_Orderings_Obot__class_Obot(tc_fun(X22011,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22011),X22009))
      | X22009 = c_Orderings_Obot__class_Obot(tc_fun(X22011,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22011,tc_HOL_Obool)),X22010),X22009) != c_Orderings_Obot__class_Obot(tc_fun(X22011,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X22011,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22011,tc_HOL_Obool)),X22010),X22009)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22011),c_Big__Operators_Olattice__class_OInf__fin(X22011,X22010)),c_Big__Operators_Olattice__class_OInf__fin(X22011,X22009)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).

fof(i_0_8392,plain,
    ! [X21104,X21105,X21106] :
      ( ~ class_Lattices_Olattice(X21106)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21106),X21105))
      | X21105 = c_Orderings_Obot__class_Obot(tc_fun(X21106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21106),X21104))
      | X21104 = c_Orderings_Obot__class_Obot(tc_fun(X21106,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21106,tc_HOL_Obool)),X21105),X21104) != c_Orderings_Obot__class_Obot(tc_fun(X21106,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X21106,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21106,tc_HOL_Obool)),X21105),X21104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21106),c_Big__Operators_Olattice__class_OSup__fin(X21106,X21105)),c_Big__Operators_Olattice__class_OSup__fin(X21106,X21104)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).

fof(i_0_8393,plain,
    ! [X21110,X21111,X21112] :
      ( ~ class_Orderings_Olinorder(X21112)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21112),X21111))
      | X21111 = c_Orderings_Obot__class_Obot(tc_fun(X21112,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21112),X21110))
      | X21110 = c_Orderings_Obot__class_Obot(tc_fun(X21112,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21112,tc_HOL_Obool)),X21111),X21110) != c_Orderings_Obot__class_Obot(tc_fun(X21112,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X21112,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21112,tc_HOL_Obool)),X21111),X21110)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21112),c_Big__Operators_Olinorder__class_OMin(X21112,X21111)),c_Big__Operators_Olinorder__class_OMin(X21112,X21110)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).

fof(i_0_8394,plain,
    ! [X21116,X21117,X21118] :
      ( ~ class_Orderings_Olinorder(X21118)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21118),X21117))
      | X21117 = c_Orderings_Obot__class_Obot(tc_fun(X21118,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21118),X21116))
      | X21116 = c_Orderings_Obot__class_Obot(tc_fun(X21118,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21118,tc_HOL_Obool)),X21117),X21116) != c_Orderings_Obot__class_Obot(tc_fun(X21118,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X21118,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21118,tc_HOL_Obool)),X21117),X21116)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X21118),c_Big__Operators_Olinorder__class_OMax(X21118,X21117)),c_Big__Operators_Olinorder__class_OMax(X21118,X21116)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).

fof(i_0_8395,plain,
    ! [X18417,X18418,X18419,X18420] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18420),X18419),X18418))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18420),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18420),X18419),X18417)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18420),X18418),X18417))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_8396,plain,
    ! [X18421,X18422,X18423,X18424] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18424)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18424),X18423),X18422))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18424),X18421),X18423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18424),X18421),X18422))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_8397,plain,
    ! [X18086,X18087,X18088,X18089] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18089)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18089),X18088),X18087))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18089),X18088),X18086)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18089),X18087),X18086))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_8398,plain,
    ! [X18082,X18083,X18084,X18085] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18085)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18085),X18084),X18083))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18085),X18082),X18084)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18085),X18082),X18083))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_8399,plain,
    ! [X19858,X19859,X19860] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19860)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19860),X19859))
      | X19859 = c_Orderings_Obot__class_Obot(tc_fun(X19860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19860),X19858))
      | X19858 = c_Orderings_Obot__class_Obot(tc_fun(X19860,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X19860,c_Groups_Otimes__class_Otimes(X19860)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19860,tc_HOL_Obool)),X19859),X19858)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19860),hAPP(c_Finite__Set_Ofold1(X19860,c_Groups_Otimes__class_Otimes(X19860)),X19859)),hAPP(c_Finite__Set_Ofold1(X19860,c_Groups_Otimes__class_Otimes(X19860)),X19858)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).

fof(i_0_8400,plain,
    ! [X32211,X32212,X32213] : hAPP(c_List_Orev(X32213),hAPP(hAPP(c_List_Odrop(X32213),X32212),X32211)) = hAPP(hAPP(c_List_Otake(X32213),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32213)),X32211)),X32212)),hAPP(c_List_Orev(X32213),X32211)),
    inference(variable_rename,[status(thm)],[fact_rev__drop]) ).

fof(i_0_8401,plain,
    ! [X32214,X32215,X32216] : hAPP(c_List_Orev(X32216),hAPP(hAPP(c_List_Otake(X32216),X32215),X32214)) = hAPP(hAPP(c_List_Odrop(X32216),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32216)),X32214)),X32215)),hAPP(c_List_Orev(X32216),X32214)),
    inference(variable_rename,[status(thm)],[fact_rev__take]) ).

fof(i_0_8402,plain,
    ! [X24253,X24254,X24255] :
      ( ~ class_Orderings_Olinorder(X24255)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),X24253))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24255,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24255),X24254),c_Orderings_Obot__class_Obot(tc_fun(X24255,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X24255,X24254,X24253)) = c_SetInterval_Oord__class_OatLeastAtMost(X24255,X24254,X24253) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).

fof(i_0_8403,plain,
    ! [X19076,X19077] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19077,tc_HOL_Obool)),X19076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19077,tc_HOL_Obool)),X19076)))
        | X19076 = c_Orderings_Obot__class_Obot(tc_fun(X19077,tc_HOL_Obool)) )
      & ( X19076 != c_Orderings_Obot__class_Obot(tc_fun(X19077,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19077,tc_HOL_Obool)),X19076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19077,tc_HOL_Obool)),X19076))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).

fof(i_0_8404,plain,
    ! [X25965,X25966,X25967] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25967),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25966)),X25965)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25967),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25966)),X25965)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25967),X25966))),X25965) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5742])]) ).

fof(i_0_8405,plain,
    ! [X26827,X26828] : c_Divides_Opdivmod(X26828,X26827) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26828)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26827))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26828),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26827))),
    inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).

fof(i_0_8406,plain,
    ! [X25095,X25096,X25097] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25097,tc_HOL_Obool)),X25096),X25095))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25097,tc_HOL_Obool)),X25096),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25097,tc_HOL_Obool),X25095))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).

fof(i_0_8407,plain,
    ! [X19674,X19675,X19676,X19677] : hAPP(c_Finite__Set_Ofold__image(X19677,X19676,X19675),X19674) = c_Finite__Set_Ofold(X19676,X19677,hAPP(hAPP(c_COMBB(X19677,tc_fun(X19677,X19677),X19676),X19675),X19674)),
    inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).

fof(i_0_8408,plain,
    ! [X24554,X24555] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24555)),X24554) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24555),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X24555)),X24554),
    inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).

fof(i_0_8409,plain,
    ! [X27244,X27245] : hAPP(c_Relation_OField(X27245),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X27245,X27245),tc_HOL_Obool),X27244)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X27245,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X27245,X27245),tc_HOL_Obool),tc_fun(X27245,tc_HOL_Obool),c_Relation_OField(X27245)),X27244)),
    inference(variable_rename,[status(thm)],[fact_Field__Union]) ).

fof(i_0_8410,plain,
    ! [X19706,X19707,X19708] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19708,tc_HOL_Obool)),X19707),X19706))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19708,tc_HOL_Obool)),X19707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19708,tc_HOL_Obool)),X19706),X19707)) = X19706 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).

fof(i_0_8411,plain,
    ! [X31012,X31013,X31014] :
      ( ~ c_Fun_Oinj__on(X31014,X31013,X31012,c_Orderings_Otop__class_Otop(tc_fun(X31014,tc_HOL_Obool)))
      | c_Fun_Oinj__on(tc_List_Olist(X31014),tc_List_Olist(X31013),hAPP(c_List_Omap(X31014,X31013),X31012),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31014),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).

fof(i_0_8412,plain,
    ! [X20920,X20921,X20922] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20922,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20922,tc_HOL_Obool)),X20921),X20920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20922,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20922,tc_HOL_Obool)),X20921)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20922,tc_HOL_Obool)),X20920)),
    inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).

fof(i_0_8413,plain,
    ! [X20923,X20924,X20925] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20925,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20925,tc_HOL_Obool)),X20924),X20923)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20925,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20925,tc_HOL_Obool)),X20924)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20925,tc_HOL_Obool)),X20923)),
    inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).

fof(i_0_8414,plain,
    ! [X28747,X28748,X28749,X28750,X28751] :
      ( ( hBOOL(hAPP(hAPP(X28750,X28748),X28747))
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28751,X28750,X28749),X28748),X28747)) )
      & ( hBOOL(hAPP(X28749,X28747))
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28751,X28750,X28749),X28748),X28747)) )
      & ( ~ hBOOL(hAPP(hAPP(X28750,X28748),X28747))
        | ~ hBOOL(hAPP(X28749,X28747))
        | hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28751,X28750,X28749),X28748),X28747)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_peek__and__def])])]) ).

fof(i_0_8415,plain,
    ! [X32828,X32829,X32830,X32831,X32832] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32832,X32831,X32830),X32829),X32828))
        | hBOOL(hAPP(hAPP(X32830,X32828),X32829)) )
      & ( ~ hBOOL(hAPP(hAPP(X32830,X32828),X32829))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32832,X32831,X32830),X32829),X32828)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])]) ).

fof(i_0_8416,plain,
    ! [X32823,X32824,X32825,X32826,X32827] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32827,X32826,X32825),X32824),X32823))
        | hBOOL(hAPP(hAPP(X32825,X32823),X32824)) )
      & ( ~ hBOOL(hAPP(hAPP(X32825,X32823),X32824))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32827,X32826,X32825),X32824),X32823)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])]) ).

fof(i_0_8417,plain,
    ! [X32813,X32814,X32815,X32816,X32817] :
      ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32817,X32816,X32815),X32814),X32813))
      | hBOOL(hAPP(hAPP(X32815,X32813),X32814)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])]) ).

fof(i_0_8418,plain,
    ! [X20519,X20520,X20521,X20522,X20523] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X20523,X20522,X20521),X20520),X20519))
        | hBOOL(hAPP(X20520,hAPP(X20521,X20519))) )
      & ( ~ hBOOL(hAPP(X20520,hAPP(X20521,X20519)))
        | hBOOL(hAPP(hAPP(c_Set_Ovimage(X20523,X20522,X20521),X20520),X20519)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).

fof(i_0_8419,plain,
    ! [X21745,X21746,X21747,X21749] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21747),esk111_3(X21745,X21746,X21747)),X21746))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),c_Complete__Lattice_OInf__class_OInf(X21747,X21746)),X21745))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21747)
        | ~ class_Orderings_Olinorder(X21747) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),esk111_3(X21745,X21746,X21747)),X21745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),c_Complete__Lattice_OInf__class_OInf(X21747,X21746)),X21745))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21747)
        | ~ class_Orderings_Olinorder(X21747) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21747),X21749),X21746))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),X21749),X21745))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),c_Complete__Lattice_OInf__class_OInf(X21747,X21746)),X21745))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21747)
        | ~ class_Orderings_Olinorder(X21747) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__less__iff])])])])]) ).

fof(i_0_8420,plain,
    ! [X25752,X25753,X25754,X25755] :
      ( ~ class_Int_Onumber__ring(X25755)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25755),hAPP(c_Int_Onumber__class_Onumber__of(X25755),X25754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25755),hAPP(c_Int_Onumber__class_Onumber__of(X25755),X25753)),X25752)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25755),hAPP(c_Int_Onumber__class_Onumber__of(X25755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25754),X25753))),X25752) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_8421,plain,
    ! [X25742,X25743,X25744,X25745] :
      ( ~ class_Int_Onumber__ring(X25745)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25745),hAPP(c_Int_Onumber__class_Onumber__of(X25745),X25744)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25745),hAPP(c_Int_Onumber__class_Onumber__of(X25745),X25743)),X25742)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25745),hAPP(c_Int_Onumber__class_Onumber__of(X25745),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25744),X25743))),X25742) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_8422,plain,
    ! [X25790,X25791,X25792,X25793] :
      ( ~ class_Int_Onumber__ring(X25793)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25793),hAPP(c_Int_Onumber__class_Onumber__of(X25793),X25792)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25793),hAPP(c_Int_Onumber__class_Onumber__of(X25793),X25791)),X25790)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25793),hAPP(c_Int_Onumber__class_Onumber__of(X25793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25792),X25791))),X25790) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).

fof(i_0_8423,plain,
    ! [X23274,X23275,X23276] :
      ( ~ class_Orderings_Olinorder(X23276)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23276),X23275),X23274))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23276,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23276),X23275),c_Orderings_Obot__class_Obot(tc_fun(X23276,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X23276,X23275,X23274)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23276,X23275),X23274) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).

fof(i_0_8424,plain,
    ! [X31219,X31220,X31221,X31222,X31223] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31222)),X31221)))
      | hAPP(hAPP(c_List_Onth(X31220),hAPP(hAPP(c_List_Omap(X31222,X31220),X31219),X31221)),X31223) = hAPP(X31219,hAPP(hAPP(c_List_Onth(X31222),X31221),X31223)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).

fof(i_0_8425,plain,
    ! [X26967,X26968] :
      ( ( X26967 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26968,X26967) = X26968
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26968),X26967))) )
      & ( X26967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26968,X26967) = c_Nitpick_Onat__gcd(X26967,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26968,X26967))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26968),X26967))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).

fof(i_0_8426,plain,
    ! [X24949,X24950,X24951,X24952] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24952,tc_HOL_Obool)),X24951),X24950))
      | ~ hBOOL(hAPP(hAPP(c_member(X24952),X24949),X24951))
      | hBOOL(hAPP(hAPP(c_member(X24952),X24949),c_Complete__Lattice_OSup__class_OSup(tc_fun(X24952,tc_HOL_Obool),X24950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).

fof(i_0_8427,plain,
    ! [X22336,X22337,X22338] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22338)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22338),c_Groups_Ozero__class_Ozero(X22338)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22338),X22337),X22336)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22338),c_Groups_Ozero__class_Ozero(X22338)),X22336))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22338),c_Groups_Ozero__class_Ozero(X22338)),X22337)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_8428,plain,
    ! [X22333,X22334,X22335] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22335)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22335),c_Groups_Ozero__class_Ozero(X22335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22335),X22334),X22333)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22335),c_Groups_Ozero__class_Ozero(X22335)),X22334))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22335),c_Groups_Ozero__class_Ozero(X22335)),X22333)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

fof(i_0_8429,plain,
    ! [X32590,X32591,X32592,X32595,X32596,X32597,X32598,X32599] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32592),X32591),hAPP(c_List_Oset(X32592),X32590)))
        | X32590 = hAPP(hAPP(c_List_Oappend(X32592),esk474_3(X32590,X32591,X32592)),hAPP(hAPP(c_List_Olist_OCons(X32592),X32591),esk475_3(X32590,X32591,X32592))) )
      & ( X32595 != hAPP(hAPP(c_List_Oappend(X32597),X32598),hAPP(hAPP(c_List_Olist_OCons(X32597),X32596),X32599))
        | hBOOL(hAPP(hAPP(c_member(X32597),X32596),hAPP(c_List_Oset(X32597),X32595))) ) ),
    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_in__set__conv__decomp])])])])]) ).

fof(i_0_8430,plain,
    ! [X33418,X33419] : c_Relation_Osym(X33419,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33419,X33419),tc_HOL_Obool)),X33418),hAPP(c_Relation_Oconverse(X33419,X33419),X33418))),
    inference(variable_rename,[status(thm)],[fact_sym__Int__converse]) ).

fof(i_0_8431,plain,
    ! [X33412,X33413] : c_Relation_Osym(X33413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33413,X33413),tc_HOL_Obool)),X33412),hAPP(c_Relation_Oconverse(X33413,X33413),X33412))),
    inference(variable_rename,[status(thm)],[fact_sym__Un__converse]) ).

fof(i_0_8432,plain,
    ! [X21085,X21086,X21087] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21087),X21086))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21087),X21085))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21087,tc_HOL_Obool)),X21086),X21085) != c_Orderings_Obot__class_Obot(tc_fun(X21087,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(X21087),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21087,tc_HOL_Obool)),X21086),X21085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21087),X21086)),hAPP(c_Finite__Set_Ocard(X21087),X21085)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).

fof(i_0_8433,plain,
    ! [X24494,X24495] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24495)),X24494) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X24495)),X24494),
    inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).

fof(i_0_8434,plain,
    ! [X30339,X30340,X30341] :
      ( ~ class_Orderings_Olinorder(X30341)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30341),X30340))
      | c_List_Olinorder__class_Osorted__list__of__set(X30341,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30341,tc_HOL_Obool)),X30340),hAPP(hAPP(c_Set_Oinsert(X30341),X30339),c_Orderings_Obot__class_Obot(tc_fun(X30341,tc_HOL_Obool))))) = c_List_Oremove1(X30341,X30339,c_List_Olinorder__class_Osorted__list__of__set(X30341,X30340)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).

fof(i_0_8435,plain,
    ! [X19489,X19490] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X19490,X19489)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X19490,X19489),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X19489),c_Orderings_Otop__class_Otop(tc_fun(X19489,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_8436,plain,
    ! [X31744,X31745,X31746,X31747,X31748] :
      ( ~ class_Orderings_Olinorder(X31748)
      | hAPP(c_List_Ofilter(X31747,X31746),c_List_Olinorder__class_Osort__key(X31747,X31748,X31745,X31744)) = c_List_Olinorder__class_Osort__key(X31747,X31748,X31745,hAPP(c_List_Ofilter(X31747,X31746),X31744)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])]) ).

fof(i_0_8437,plain,
    ! [X24522,X24523,X24524] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24524,tc_HOL_Obool)),X24523),hAPP(c_Set_OPow(X24524),X24522)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24524,tc_HOL_Obool)),X24523),X24522)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24524,tc_HOL_Obool)),X24523),X24522))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24524,tc_HOL_Obool)),X24523),hAPP(c_Set_OPow(X24524),X24522))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).

fof(i_0_8438,plain,
    ! [X24519,X24520,X24521] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24521,tc_HOL_Obool)),X24520),hAPP(c_Set_OPow(X24521),X24519)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24521,tc_HOL_Obool)),X24520),X24519)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).

fof(i_0_8439,plain,
    ! [X25188,X25189] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25189)),X25188)))
        | X25189 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X25188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X25189 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25189)),X25188))) )
      & ( X25188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25189)),X25188))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).

fof(i_0_8440,plain,
    ! [X24211,X24212,X24213,X24214] :
      ( ~ class_Orderings_Olinorder(X24214)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24214),X24213),X24212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24214),X24212),X24211))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24214,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24214,X24213,X24212)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24214,X24212,X24211)) = c_SetInterval_Oord__class_OatLeastAtMost(X24214,X24213,X24211) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).

fof(i_0_8441,plain,
    ! [X23468,X23469,X23470,X23471] :
      ( ~ class_Orderings_Olinorder(X23471)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23471),X23470),X23469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23471),X23469),X23468))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23471,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23471,X23470,X23469)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23471,X23469,X23468)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23471,X23470,X23468) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).

fof(i_0_8442,plain,
    ! [X23552,X23553,X23554,X23555] :
      ( ~ class_Orderings_Olinorder(X23555)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23555),X23554),X23553))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23555),X23553),X23552))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23555,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23555,X23554,X23553)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23555,X23553,X23552)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23555,X23554,X23552) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).

fof(i_0_8443,plain,
    ! [X24260,X24261,X24262,X24263] :
      ( ~ class_Orderings_Olinorder(X24263)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24263),X24262),X24261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24263),X24261),X24260))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24263,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24263,X24262,X24261)),c_SetInterval_Oord__class_OatLeastAtMost(X24263,X24261,X24260)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X24263,X24262,X24260) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).

fof(i_0_8444,plain,
    ! [X19600,X19601,X19602] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19602,tc_HOL_Obool)),X19601),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19602,tc_HOL_Obool)),X19601),X19600))),
    inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).

fof(i_0_8445,plain,
    ! [X19603,X19604,X19605] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19605,tc_HOL_Obool)),X19604),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19605,tc_HOL_Obool)),X19603),X19604))),
    inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).

fof(i_0_8446,plain,
    ! [X28943,X28944,X28945] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28945,X28945)),X28944),X28943))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28945,X28945)),X28944),c_Transitive__Closure_Ortrancl(X28945,X28943))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).

fof(i_0_8447,plain,
    ! [X23548,X23549,X23550,X23551] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23551),X23550))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23549),X23548))
      | hAPP(c_Finite__Set_Ocard(tc_sum(X23551,X23549)),c_Sum__Type_OPlus(X23551,X23549,X23550,X23548)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X23551),X23550)),hAPP(c_Finite__Set_Ocard(X23549),X23548)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_8448,plain,
    ! [X23431,X23432,X23433,X23434] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23434),X23433))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23432),X23431))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X23434,X23432)),c_Sum__Type_OPlus(X23434,X23432,X23433,X23431)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X23434),X23433)),hAPP(c_Finite__Set_Ocard(X23432),X23431)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23434),X23433))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X23434,X23432)),c_Sum__Type_OPlus(X23434,X23432,X23433,X23431)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23432),X23431))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X23434,X23432)),c_Sum__Type_OPlus(X23434,X23432,X23433,X23431)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if])])]) ).

fof(i_0_8449,plain,
    ! [X19538,X19539,X19540,X19541] :
      ( ~ class_Lattices_Osemilattice__sup(X19541)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19541),X19540),X19539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19541),X19538),X19539))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19541),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19541),X19540),X19538)),X19539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).

fof(i_0_8450,plain,
    ! [X19534,X19535,X19536,X19537] :
      ( ~ class_Lattices_Osemilattice__sup(X19537)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19537),X19536),X19535))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19537),X19534),X19535))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19537),X19536),X19534)),X19535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).

fof(i_0_8451,plain,
    ! [X18820,X18821,X18822,X18823] :
      ( ~ class_Orderings_Olinorder(X18823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18823),X18822),X18821))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18823),X18820),X18821))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18823),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18823),X18822),X18820)),X18821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).

fof(i_0_8452,plain,
    ! [X18816,X18817,X18818,X18819] :
      ( ~ class_Orderings_Olinorder(X18819)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18819),X18818),X18817))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18819),X18816),X18817))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18819),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18819),X18818),X18816)),X18817)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).

fof(i_0_8453,plain,
    ! [X20506,X20507,X20508,X20509] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20509,tc_HOL_Obool)),X20508),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20509,tc_HOL_Obool)),X20507),X20506)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20509,tc_HOL_Obool)),X20507),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20509,tc_HOL_Obool)),X20508),X20506)),
    inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).

fof(i_0_8454,plain,
    ! [X19382,X19383,X19384,X19385] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19385,tc_HOL_Obool)),X19384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19385,tc_HOL_Obool)),X19383),X19382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19385,tc_HOL_Obool)),X19383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19385,tc_HOL_Obool)),X19384),X19382)),
    inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).

fof(i_0_8455,plain,
    ! [X19632,X19633,X19634] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19634,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19634,tc_HOL_Obool)),X19633),X19632)),X19632) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19634,tc_HOL_Obool)),X19633),X19632),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(i_0_8456,plain,
    ! [X17306,X17307,X17308] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17308,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17308,tc_HOL_Obool)),X17307),X17306)),X17306) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17308,tc_HOL_Obool)),X17307),X17306),
    inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).

cnf(i_0_8457,plain,
    ( hAPP(c_List_Orotate(X1,X3),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_5743]) ).

fof(i_0_8458,plain,
    ! [X17101,X17102,X17103,X17104,X17105] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17105),X17104),X17103))
      | hBOOL(hAPP(hAPP(c_member(X17102),hAPP(X17101,X17104)),hAPP(c_Set_Oimage(X17105,X17102,X17101),X17103))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_8459,plain,
    ! [X16968,X16969,X16970,X16971] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16971,X16970,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16971)),X16969),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16971),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16971,X16970,X16968)
      | c_Hoare__Mirabelle_Ohoare__derivs(X16971,X16970,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16971)),X16969),X16968)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).

fof(i_0_8460,plain,
    ! [X18104,X18105,X18106,X18107,X18108] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18108,X18107,X18106)
      | c_Finite__Set_Ofun__left__comm(X18105,X18107,hAPP(hAPP(c_COMBB(X18108,tc_fun(X18107,X18107),X18105),X18106),X18104)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).

fof(i_0_8461,plain,
    ! [X17488,X17489,X17490,X17491,X17492] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17492,X17491,X17490)
      | c_Finite__Set_Ofun__left__comm__idem(X17489,X17491,hAPP(hAPP(c_COMBB(X17492,tc_fun(X17491,X17491),X17489),X17490),X17488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).

fof(i_0_8462,plain,
    ! [X20874,X20875,X20876,X20877] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20877),X20876),X20875))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20877,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20877),X20876),X20874)),X20875) = hAPP(hAPP(c_Set_Oinsert(X20877),X20876),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20877,tc_HOL_Obool)),X20874),X20875)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).

fof(i_0_8463,plain,
    ! [X20858,X20859,X20860,X20861] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20861),X20860),X20859))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20861,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20861),X20860),X20858)),X20859) = hAPP(hAPP(c_Set_Oinsert(X20861),X20860),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20861,tc_HOL_Obool)),X20858),X20859)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20861),X20860),X20859))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20861,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20861),X20860),X20858)),X20859) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20861,tc_HOL_Obool)),X20858),X20859) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5744])]) ).

fof(i_0_8464,plain,
    ! [X19735,X19736,X19737,X19738,X19739] :
      ( ( hAPP(c_Set_Oimage(X19739,X19738,X19737),X19736) != hAPP(c_Set_Oimage(X19739,X19738,X19737),X19735)
        | X19736 = X19735
        | ~ c_Fun_Oinj__on(X19739,X19738,X19737,c_Orderings_Otop__class_Otop(tc_fun(X19739,tc_HOL_Obool))) )
      & ( X19736 != X19735
        | hAPP(c_Set_Oimage(X19739,X19738,X19737),X19736) = hAPP(c_Set_Oimage(X19739,X19738,X19737),X19735)
        | ~ c_Fun_Oinj__on(X19739,X19738,X19737,c_Orderings_Otop__class_Otop(tc_fun(X19739,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff])])]) ).

fof(i_0_8465,plain,
    ! [X28409,X28410,X28411,X28412,X28413,X28414,X28415] :
      ( hAPP(c_Fun_Ocomp(X28415,X28414,X28413,X28412),X28411) != X28410
      | hAPP(X28412,hAPP(X28411,X28409)) = hAPP(X28410,X28409) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).

fof(i_0_8466,plain,
    ! [X22867] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X22867)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).

fof(i_0_8467,plain,
    ! [X30677,X30678,X30679] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30679),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30678)),X30677)))
      | hAPP(hAPP(c_List_Olist_OCons(X30678),hAPP(hAPP(c_List_Onth(X30678),X30677),X30679)),hAPP(hAPP(c_List_Odrop(X30678),hAPP(c_Nat_OSuc,X30679)),X30677)) = hAPP(hAPP(c_List_Odrop(X30678),X30679),X30677) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).

fof(i_0_8468,plain,
    ! [X20590,X20591,X20592,X20593] : hAPP(c_Set_Oimage(X20593,X20592,X20591),hAPP(c_Set_Ovimage(X20593,X20592,X20591),X20590)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20592,tc_HOL_Obool)),X20590),hAPP(c_Set_Oimage(X20593,X20592,X20591),c_Orderings_Otop__class_Otop(tc_fun(X20593,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).

fof(i_0_8469,plain,
    ! [X23077,X23078] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23078),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23077))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23078),X23077)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23078),X23077))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23078),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23077)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

fof(i_0_8470,plain,
    ! [X24256,X24257,X24258,X24259] :
      ( ~ class_Orderings_Olinorder(X24259)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24259),X24258),X24257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24259),X24257),X24256))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24259,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24259,X24258,X24257)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24259,X24257,X24256)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24259,X24258),X24256) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).

fof(i_0_8471,plain,
    ! [X23198] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23198))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23198))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23198)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23198)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).

fof(i_0_8472,plain,
    ! [X19709,X19710,X19711] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19711),X19710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19711,tc_HOL_Obool)),X19709),X19710))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19711),X19709)),hAPP(c_Finite__Set_Ocard(X19711),X19710))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_8473,plain,
    ! [X19681,X19682,X19683] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19683),X19682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19683,tc_HOL_Obool)),X19681),X19682))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19683),X19681)),hAPP(c_Finite__Set_Ocard(X19683),X19682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_8474,plain,
    ! [X19570,X19571,X19572,X19573] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19573),X19572),X19571))
      | hBOOL(hAPP(hAPP(c_member(X19573),X19572),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19573,tc_HOL_Obool)),X19571),X19570))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).

fof(i_0_8475,plain,
    ! [X19359,X19360,X19361,X19362] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19362),X19361),X19360))
        | hBOOL(hAPP(hAPP(c_member(X19362),X19361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19362,tc_HOL_Obool)),X19359),X19360))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19362),X19361),X19359))
        | hBOOL(hAPP(hAPP(c_member(X19362),X19361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19362,tc_HOL_Obool)),X19359),X19360))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5745])])]) ).

fof(i_0_8476,plain,
    ! [X19574,X19575,X19576,X19577] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19577),X19576),X19575))
      | hBOOL(hAPP(hAPP(c_member(X19577),X19576),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19577,tc_HOL_Obool)),X19574),X19575))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).

fof(i_0_8477,plain,
    ! [X19806,X19807] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19807),c_Orderings_Otop__class_Otop(tc_fun(X19807,tc_HOL_Obool))))
      | hAPP(c_Set_Oimage(X19807,X19807,X19806),c_Orderings_Otop__class_Otop(tc_fun(X19807,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19807,tc_HOL_Obool))
      | c_Fun_Oinj__on(X19807,X19807,X19806,c_Orderings_Otop__class_Otop(tc_fun(X19807,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_8478,plain,
    ! [X25076,X25077,X25078] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),X25077),X25076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),hAPP(c_Groups_Oabs__class_Oabs(X25078),X25077)),X25076))
        | ~ class_Rings_Olinordered__idom(X25078) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),hAPP(c_Groups_Ouminus__class_Ouminus(X25078),X25077)),X25076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),hAPP(c_Groups_Oabs__class_Oabs(X25078),X25077)),X25076))
        | ~ class_Rings_Olinordered__idom(X25078) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),X25077),X25076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),hAPP(c_Groups_Ouminus__class_Ouminus(X25078),X25077)),X25076))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25078),hAPP(c_Groups_Oabs__class_Oabs(X25078),X25077)),X25076))
        | ~ class_Rings_Olinordered__idom(X25078) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).

fof(i_0_8479,plain,
    ! [X25071,X25072,X25073] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),X25072),X25071))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),hAPP(c_Groups_Oabs__class_Oabs(X25073),X25072)),X25071))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25073) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),hAPP(c_Groups_Ouminus__class_Ouminus(X25073),X25072)),X25071))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),hAPP(c_Groups_Oabs__class_Oabs(X25073),X25072)),X25071))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25073) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),X25072),X25071))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),hAPP(c_Groups_Ouminus__class_Ouminus(X25073),X25072)),X25071))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25073),hAPP(c_Groups_Oabs__class_Oabs(X25073),X25072)),X25071))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25073) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).

fof(i_0_8480,plain,
    ! [X25068,X25069,X25070] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25070)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25070),X25069),X25068))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25070),hAPP(c_Groups_Ouminus__class_Ouminus(X25070),X25069)),X25068))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25070),hAPP(c_Groups_Oabs__class_Oabs(X25070),X25069)),X25068)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).

fof(i_0_8481,plain,
    ! [X29746,X29747,X29748] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29748)),X29747),c_Wellfounded_Oacc(tc_List_Olist(X29748),c_List_Olistrel1(X29748,X29746))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29748)),X29747),c_List_Olists(X29748,c_Wellfounded_Oacc(X29748,X29746)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).

fof(i_0_8482,plain,
    ! [X22310,X22311] :
      ( ~ class_Rings_Olinordered__ring(X22311)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22311),X22310),X22310)),c_Groups_Ozero__class_Ozero(X22311))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5746])]) ).

fof(i_0_8483,plain,
    ! [X20962,X20963,X20964,X20965] :
      ( ~ c_Fun_Oinj__on(X20965,X20964,X20963,c_Orderings_Otop__class_Otop(tc_fun(X20965,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X20965,X20964,X20963),hAPP(c_Set_Oimage(X20965,X20964,X20963),X20962)) = X20962 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).

fof(i_0_8484,plain,
    ! [X23417,X23418,X23419,X23420] :
      ( ~ class_Orderings_Olinorder(X23420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23420),X23419),X23418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23420),X23418),X23417))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23420,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23420,X23419,X23418)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23420,X23418),X23417)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23420,X23419,X23417) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).

fof(i_0_8485,plain,
    ! [X23377,X23378,X23379,X23380] :
      ( ~ class_Divides_Osemiring__div(X23380)
      | X23379 = c_Groups_Ozero__class_Ozero(X23380)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23380),X23378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23380),X23379),X23377))),X23379) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23380),X23377),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23380),X23378),X23379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).

fof(i_0_8486,plain,
    ! [X23381,X23382,X23383,X23384] :
      ( ~ class_Divides_Osemiring__div(X23384)
      | X23383 = c_Groups_Ozero__class_Ozero(X23384)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23384),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23384),X23382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23384),X23381),X23383))),X23383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23384),X23381),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23384),X23382),X23383)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).

fof(i_0_8487,plain,
    ! [X23929,X23930,X23931,X23932] :
      ( ~ class_Fields_Ofield__inverse__zero(X23932)
      | X23931 = c_Groups_Ozero__class_Ozero(X23932)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23932),X23930),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23932),X23929),X23931)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23932),X23929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23932),X23930),X23931))),X23931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).

fof(i_0_8488,plain,
    ! [X28040,X28041,X28042,X28043] :
      ( ~ class_Groups_Ocomm__monoid__mult(X28043)
      | ~ c_Fun_Oinj__on(X28042,X28043,X28041,X28040)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28042,X28043),X28041),X28040) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28043,X28043),c_Fun_Oid(X28043)),hAPP(c_Set_Oimage(X28042,X28043,X28041),X28040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).

fof(i_0_8489,plain,
    ! [X28036,X28037,X28038,X28039] :
      ( ~ class_Groups_Ocomm__monoid__add(X28039)
      | ~ c_Fun_Oinj__on(X28038,X28039,X28037,X28036)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28038,X28039),X28037),X28036) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28039,X28039),c_Fun_Oid(X28039)),hAPP(c_Set_Oimage(X28038,X28039,X28037),X28036)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).

fof(i_0_8490,plain,
    ! [X27510,X27511] :
      ( ( ~ c_Wellfounded_Owf(X27511,X27510)
        | c_Wellfounded_Owf(X27511,hAPP(hAPP(c_Relation_Orel__comp(X27511,X27511,X27511),X27510),X27510)) )
      & ( ~ c_Wellfounded_Owf(X27511,hAPP(hAPP(c_Relation_Orel__comp(X27511,X27511,X27511),X27510),X27510))
        | c_Wellfounded_Owf(X27511,X27510) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).

fof(i_0_8491,plain,
    ! [X25565,X25566,X25567] :
      ( X25567 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25566,X25566),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X25566,X25566),tc_HOL_Obool)),X25567),X25565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).

fof(i_0_8492,plain,
    ! [X30519,X30520,X30521] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X30521),X30520))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30521),hAPP(hAPP(c_List_Oappend(X30521),X30520),X30519))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30521),X30519))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30521),hAPP(hAPP(c_List_Oappend(X30521),X30520),X30519))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30521,tc_HOL_Obool)),hAPP(c_List_Oset(X30521),X30520)),hAPP(c_List_Oset(X30521),X30519)) = c_Orderings_Obot__class_Obot(tc_fun(X30521,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30521),hAPP(hAPP(c_List_Oappend(X30521),X30520),X30519))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30521),X30520))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30521),X30519))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30521,tc_HOL_Obool)),hAPP(c_List_Oset(X30521),X30520)),hAPP(c_List_Oset(X30521),X30519)) != c_Orderings_Obot__class_Obot(tc_fun(X30521,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X30521),hAPP(hAPP(c_List_Oappend(X30521),X30520),X30519))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).

fof(i_0_8493,plain,
    ! [X30865,X30866,X30867] :
      ( ~ class_Orderings_Olinorder(X30867)
      | c_Big__Operators_Olattice_OInf__fin(X30867,c_Orderings_Oord__class_Omin(X30867),hAPP(c_List_Oset(X30867),hAPP(hAPP(c_List_Olist_OCons(X30867),X30866),X30865))) = hAPP(c_List_Ofoldl(X30867,X30867,c_Orderings_Oord__class_Omin(X30867),X30866),X30865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])]) ).

fof(i_0_8494,plain,
    ! [X30868,X30869,X30870] :
      ( ~ class_Orderings_Olinorder(X30870)
      | c_Big__Operators_Olattice_OSup__fin(X30870,c_Orderings_Oord__class_Omax(X30870),hAPP(c_List_Oset(X30870),hAPP(hAPP(c_List_Olist_OCons(X30870),X30869),X30868))) = hAPP(c_List_Ofoldl(X30870,X30870,c_Orderings_Oord__class_Omax(X30870),X30869),X30868) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])]) ).

fof(i_0_8495,plain,
    ! [X24241,X24242,X24243,X24244] :
      ( ~ class_Groups_Ocomm__monoid__add(X24244)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24243),X24242))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24244),X24241),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24243,X24242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24244),hAPP(X24241,X24243)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24244),X24241),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X24243,X24242))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).

fof(i_0_8496,plain,
    ! [X29352,X29353,X29354] : hAPP(hAPP(c_Nat_Ocompow(X29354,X29354),hAPP(c_Nat_OSuc,X29353)),X29352) = hAPP(c_Fun_Ocomp(X29354,X29354,X29354,X29352),hAPP(hAPP(c_Nat_Ocompow(X29354,X29354),X29353),X29352)),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(i_0_8497,plain,
    ! [X29873,X29874,X29875,X29876,X29877] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29877),X29876),hAPP(c_List_Oset(X29877),X29875)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29874),hAPP(X29873,X29876)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29874),c_List_Olist_Olist__size(X29877,X29873,X29875))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).

fof(i_0_8498,plain,
    ! [X29878,X29879,X29880,X29881,X29882] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29882),X29881),hAPP(c_List_Oset(X29882),X29880)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29879),hAPP(X29878,X29881)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29879),c_List_Olist_Olist__size(X29882,X29878,X29880))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).

fof(i_0_8499,plain,
    ! [X29991,X29992] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29992),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X29991)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X29991),X29992)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29991))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).

fof(i_0_8500,plain,
    ! [X23535,X23536] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23536),X23535))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23535),X23536) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23535),X23536)),X23536)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).

fof(i_0_8501,plain,
    ! [X29743,X29744,X29745] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29745)),X29744),c_List_Olists(X29745,c_Wellfounded_Oacc(X29745,X29743))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29745)),X29744),c_Wellfounded_Oacc(tc_List_Olist(X29745),c_List_Olistrel1(X29745,X29743)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).

cnf(i_0_8502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5747]) ).

cnf(i_0_8503,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5748]) ).

fof(i_0_8504,plain,
    ! [X22967,X22968] :
      ( ~ class_Rings_Osemiring__1(X22968)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22968),X22967) = c_Nat_Osemiring__1__class_Oof__nat__aux(X22968,hAPP(hAPP(c_COMBC(X22968,X22968,X22968),c_Groups_Oplus__class_Oplus(X22968)),c_Groups_Oone__class_Oone(X22968)),X22967,c_Groups_Ozero__class_Ozero(X22968)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).

fof(i_0_8505,plain,
    ! [X29554,X29555,X29556,X29557] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29557)),X29556)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29557)),X29555)))
      | X29556 != hAPP(hAPP(c_List_Olist_OCons(X29557),X29554),X29555) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).

fof(i_0_8506,plain,
    ! [X24496,X24497,X24498] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24498,tc_HOL_Obool)),X24497),X24496))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X24498,tc_HOL_Obool)),X24497),hAPP(c_Set_OPow(X24498),X24496))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).

fof(i_0_8507,plain,
    ! [X21750,X21751,X21752,X21753,X21754] : hAPP(hAPP(c_Power_Opower_Opower(X21754,X21753,X21752),X21751),hAPP(c_Nat_OSuc,X21750)) = hAPP(hAPP(X21752,X21751),hAPP(hAPP(c_Power_Opower_Opower(X21754,X21753,X21752),X21751),X21750)),
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(i_0_8508,plain,
    ! [X18244,X18245,X18246] :
      ( ~ class_Orderings_Olinorder(X18246)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18246,tc_HOL_Obool)),X18245),X18244))
      | X18245 = c_Orderings_Obot__class_Obot(tc_fun(X18246,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18246),X18244))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18246),c_Big__Operators_Olinorder__class_OMin(X18246,X18244)),c_Big__Operators_Olinorder__class_OMin(X18246,X18245))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).

fof(i_0_8509,plain,
    ! [X18241,X18242,X18243] :
      ( ~ class_Orderings_Olinorder(X18243)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18243,tc_HOL_Obool)),X18242),X18241))
      | X18242 = c_Orderings_Obot__class_Obot(tc_fun(X18243,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18243),X18241))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18243),c_Big__Operators_Olinorder__class_OMax(X18243,X18242)),c_Big__Operators_Olinorder__class_OMax(X18243,X18241))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).

fof(i_0_8510,plain,
    ! [X23069,X23070] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23070),X23069))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23070),X23069)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23070),X23069)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23070),X23069)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).

fof(i_0_8511,plain,
    ! [X17017,X17018,X17019] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17019),X17018),hAPP(hAPP(c_Set_Oinsert(X17019),X17017),c_Orderings_Obot__class_Obot(tc_fun(X17019,tc_HOL_Obool)))))
      | X17018 = X17017 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).

fof(i_0_8512,plain,
    ! [X17014,X17015,X17016] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17016),X17015),hAPP(hAPP(c_Set_Oinsert(X17016),X17014),c_Orderings_Obot__class_Obot(tc_fun(X17016,tc_HOL_Obool)))))
        | X17015 = X17014 )
      & ( X17015 != X17014
        | hBOOL(hAPP(hAPP(c_member(X17016),X17015),hAPP(hAPP(c_Set_Oinsert(X17016),X17014),c_Orderings_Obot__class_Obot(tc_fun(X17016,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).

fof(i_0_8513,plain,
    ! [X19721,X19722,X19723,X19724,X19725] :
      ( X19725 != hAPP(X19724,X19723)
      | hBOOL(hAPP(hAPP(c_member(X19722),X19725),hAPP(c_Set_Oimage(X19721,X19722,X19724),c_Orderings_Otop__class_Otop(tc_fun(X19721,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_8514,plain,
    ! [X27971,X27972,X27973,X27974] :
      ( ( X27974 != c_Orderings_Obot__class_Obot(tc_fun(X27973,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27973,X27972),X27972,c_Product__Type_Osnd(X27973,X27972)),hAPP(hAPP(c_Product__Type_OSigma(X27973,X27972),X27974),hAPP(c_COMBK(tc_fun(X27972,tc_HOL_Obool),X27973),X27971))) = c_Orderings_Obot__class_Obot(tc_fun(X27972,tc_HOL_Obool)) )
      & ( X27974 = c_Orderings_Obot__class_Obot(tc_fun(X27973,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27973,X27972),X27972,c_Product__Type_Osnd(X27973,X27972)),hAPP(hAPP(c_Product__Type_OSigma(X27973,X27972),X27974),hAPP(c_COMBK(tc_fun(X27972,tc_HOL_Obool),X27973),X27971))) = X27971 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).

fof(i_0_8515,plain,
    ! [X27967,X27968,X27969,X27970] :
      ( ( X27970 != c_Orderings_Obot__class_Obot(tc_fun(X27969,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27968,X27969),X27968,c_Product__Type_Ofst(X27968,X27969)),hAPP(hAPP(c_Product__Type_OSigma(X27968,X27969),X27967),hAPP(c_COMBK(tc_fun(X27969,tc_HOL_Obool),X27968),X27970))) = c_Orderings_Obot__class_Obot(tc_fun(X27968,tc_HOL_Obool)) )
      & ( X27970 = c_Orderings_Obot__class_Obot(tc_fun(X27969,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27968,X27969),X27968,c_Product__Type_Ofst(X27968,X27969)),hAPP(hAPP(c_Product__Type_OSigma(X27968,X27969),X27967),hAPP(c_COMBK(tc_fun(X27969,tc_HOL_Obool),X27968),X27970))) = X27967 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).

fof(i_0_8516,plain,
    ! [X17122,X17123,X17124,X17125,X17126] :
      ( ( X17125 = X17122
        | X17125 = X17123
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) )
      & ( X17124 = X17123
        | X17125 = X17123
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) )
      & ( X17125 = X17122
        | X17124 = X17122
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) )
      & ( X17124 = X17123
        | X17124 = X17122
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) )
      & ( X17125 != X17123
        | X17124 != X17122
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) )
      & ( X17125 != X17122
        | X17124 != X17123
        | hAPP(hAPP(c_Set_Oinsert(X17126),X17125),hAPP(hAPP(c_Set_Oinsert(X17126),X17124),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17126),X17123),hAPP(hAPP(c_Set_Oinsert(X17126),X17122),c_Orderings_Obot__class_Obot(tc_fun(X17126,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).

fof(i_0_8517,plain,
    ! [X30082,X30083,X30084,X30085,X30086] :
      ( ( X30086 != X30083
        | hAPP(hAPP(c_List_Onth(X30085),hAPP(hAPP(c_List_Olist__update(X30085,X30084),X30086),X30082)),X30083) = X30082
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30086),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30085)),X30084))) )
      & ( X30086 = X30083
        | hAPP(hAPP(c_List_Onth(X30085),hAPP(hAPP(c_List_Olist__update(X30085,X30084),X30086),X30082)),X30083) = hAPP(hAPP(c_List_Onth(X30085),X30084),X30083)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30086),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30085)),X30084))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).

fof(i_0_8518,plain,
    ! [X20046,X20047,X20048] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20048),X20047)),X20046))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20048),X20046)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_8519,plain,
    ! [X19934,X19935,X19936] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19936),X19934))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19936),X19935)),X19934)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19935),X19934))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19936),X19935)),X19934)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5749])])]) ).

fof(i_0_8520,plain,
    ! [X19931,X19932,X19933] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19933),X19932)),X19931))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19933),X19931)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_8521,plain,
    ! [X19928,X19929,X19930] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19930),X19929)),X19928))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19929),X19928)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_8522,plain,
    ! [X22619,X22620] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22620))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22620),hAPP(c_Nat_OSuc,X22619))),X22620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).

fof(i_0_8523,plain,
    ! [X24193,X24194,X24195,X24196] :
      ( ~ class_Orderings_Olinorder(X24196)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24196),X24195),X24194))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24196),X24194),X24193))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24196,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24196,X24195),X24194)),c_SetInterval_Oord__class_OatLeastAtMost(X24196,X24194,X24193)) = c_SetInterval_Oord__class_OatLeastAtMost(X24196,X24195,X24193) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).

fof(i_0_8524,plain,
    ! [X23098,X23099,X23100] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23100),X23099))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23099),X23098)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23100),X23099)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23099),X23098))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).

fof(i_0_8525,plain,
    ! [X17353,X17354,X17355] : hAPP(hAPP(c_Set_Oinsert(X17355),X17354),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17355,tc_HOL_Obool)),X17353),hAPP(hAPP(c_Set_Oinsert(X17355),X17354),c_Orderings_Obot__class_Obot(tc_fun(X17355,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X17355),X17354),X17353),
    inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).

cnf(i_0_8526,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5750]) ).

cnf(i_0_8527,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5751]) ).

cnf(i_0_8528,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5752]) ).

cnf(i_0_8529,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5753]) ).

cnf(i_0_8530,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5754]) ).

cnf(i_0_8531,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5576]) ).

fof(i_0_8532,plain,
    ! [X19678,X19679,X19680] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19680),X19679))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X19680),X19679)),hAPP(c_Finite__Set_Ocard(X19680),hAPP(hAPP(c_Set_Oinsert(X19680),X19678),X19679)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_8533,plain,
    ! [X22873,X22874,X22875] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22874)),X22873)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22875),X22874))),X22873),
    inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).

fof(i_0_8534,plain,
    ! [X25027,X25028,X25029,X25031] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25029),esk220_3(X25027,X25028,X25029)),X25027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25029),X25028),c_Complete__Lattice_OSup__class_OSup(X25029,X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25029)
        | ~ class_Orderings_Olinorder(X25029) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25029),X25028),esk220_3(X25027,X25028,X25029)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25029),X25028),c_Complete__Lattice_OSup__class_OSup(X25029,X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25029)
        | ~ class_Orderings_Olinorder(X25029) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25029),X25031),X25027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25029),X25028),X25031))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25029),X25028),c_Complete__Lattice_OSup__class_OSup(X25029,X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25029)
        | ~ class_Orderings_Olinorder(X25029) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Sup__iff])])])])]) ).

fof(i_0_8535,plain,
    ! [X23995] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X23995))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23995)))
        | ~ c_Nat__Transfer_Onat__set(X23995) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23995)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X23995))
        | ~ c_Nat__Transfer_Onat__set(X23995) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J])])]) ).

cnf(i_0_8536,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5755]) ).

fof(i_0_8537,plain,
    ! [X23704,X23705] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23705)),hAPP(c_Int_Onat,X23704)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23705),X23704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23705)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23705),X23704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23705)),hAPP(c_Int_Onat,X23704)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23705)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).

fof(i_0_8538,plain,
    ! [X23678,X23679] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23679)),hAPP(c_Int_Onat,X23678)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23679),X23678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23679)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23679),X23678))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23679)),hAPP(c_Int_Onat,X23678)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23679)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).

fof(i_0_8539,plain,
    ! [X23425,X23426,X23427] :
      ( ~ class_Orderings_Olinorder(X23427)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23427),X23426),X23425))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23427,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23427,X23426,X23425)),hAPP(hAPP(c_Set_Oinsert(X23427),X23425),c_Orderings_Obot__class_Obot(tc_fun(X23427,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23427,X23426,X23425) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).

fof(i_0_8540,plain,
    ! [X17349,X17350,X17351,X17352] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17352),X17351),X17350))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17352,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17352),X17351),X17349)),X17350) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17352,tc_HOL_Obool)),X17349),X17350) )
      & ( hBOOL(hAPP(hAPP(c_member(X17352),X17351),X17350))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17352,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17352),X17351),X17349)),X17350) = hAPP(hAPP(c_Set_Oinsert(X17352),X17351),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17352,tc_HOL_Obool)),X17349),X17350)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5756])]) ).

fof(i_0_8541,plain,
    ! [X18666,X18667,X18668] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18668),esk38_3(X18666,X18667,X18668)),X18667))
        | ~ hBOOL(hAPP(hAPP(c_member(X18668),X18666),X18667))
        | c_Big__Operators_Olinorder__class_OMin(X18668,X18667) = X18666
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18668),X18667))
        | ~ class_Orderings_Olinorder(X18668) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18668),X18666),esk38_3(X18666,X18667,X18668)))
        | ~ hBOOL(hAPP(hAPP(c_member(X18668),X18666),X18667))
        | c_Big__Operators_Olinorder__class_OMin(X18668,X18667) = X18666
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18668),X18667))
        | ~ class_Orderings_Olinorder(X18668) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).

fof(i_0_8542,plain,
    ! [X31166,X31167,X31168,X31169,X31170] : hAPP(hAPP(c_List_Omap(X31170,X31169),X31168),hAPP(hAPP(c_List_Oappend(X31170),X31167),X31166)) = hAPP(hAPP(c_List_Oappend(X31169),hAPP(hAPP(c_List_Omap(X31170,X31169),X31168),X31167)),hAPP(hAPP(c_List_Omap(X31170,X31169),X31168),X31166)),
    inference(variable_rename,[status(thm)],[fact_map__append]) ).

fof(i_0_8543,plain,
    ! [X25218,X25219] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25219,tc_HOL_Obool)),esk226_2(X25218,X25219)),X25218))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25219),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25219,tc_HOL_Obool),X25218)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25219,tc_HOL_Obool)),X25218)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25219),esk226_2(X25218,X25219)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25219),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25219,tc_HOL_Obool),X25218)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25219,tc_HOL_Obool)),X25218)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).

fof(i_0_8544,plain,
    ! [X23372,X23373] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23373))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23372))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23373),X23372)),X23373)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).

fof(i_0_8545,plain,
    ! [X23486,X23487] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23487))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23486))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23486),X23487)),X23486)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).

fof(i_0_8546,plain,
    ! [X22482,X22483] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22482))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22482),X22483)),X22482)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).

cnf(i_0_8547,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5757]) ).

cnf(i_0_8548,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5758]) ).

fof(i_0_8549,plain,
    ! [X20744,X20745,X20746,X20747] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20747),X20746),X20745)),hAPP(hAPP(c_Set_Oinsert(X20747),X20746),X20744)) = hAPP(hAPP(c_Set_Oinsert(X20747),X20746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20747,tc_HOL_Obool)),X20745),X20744)),
    inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).

fof(i_0_8550,plain,
    ! [X23307,X23308] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23307))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23308),X23307)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])]) ).

fof(i_0_8551,plain,
    ! [X23348,X23349] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23349))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23349),X23348)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])]) ).

fof(i_0_8552,plain,
    ! [X23354,X23355] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23355),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23354))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23355),X23354)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])]) ).

fof(i_0_8553,plain,
    ! [X34154,X34155,X34156,X34157] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),c_Divides_Odiv__class_Omod(X34157,X34154,X34155)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),X34154))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),X34155))
        | ~ class_Divides_Osemiring__div(X34157) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),X34154))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),c_Divides_Odiv__class_Omod(X34157,X34154,X34155)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34157),X34156),X34155))
        | ~ class_Divides_Osemiring__div(X34157) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).

fof(i_0_8554,plain,
    ! [X34142,X34143,X34144,X34145] :
      ( ~ class_Divides_Osemiring__div(X34145)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34145),X34144),c_Divides_Odiv__class_Omod(X34145,X34143,X34142)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34145),X34144),X34142))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34145),X34144),X34143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).

fof(i_0_8555,plain,
    ! [X24752,X24753,X24754] :
      ( ~ class_Divides_Osemiring__div(X24754)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24754),c_Divides_Odiv__class_Omod(X24754,X24753,X24752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24754),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24754),X24753),X24752)),X24752)) = X24753 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).

fof(i_0_8556,plain,
    ! [X23798,X23799,X23800] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23799),c_Groups_Ozero__class_Ozero(X23800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23799))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23798),c_Groups_Ozero__class_Ozero(X23800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23799))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23799),c_Groups_Ozero__class_Ozero(X23800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23798),c_Groups_Ozero__class_Ozero(X23800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23799))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),X23798))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23799),c_Groups_Ozero__class_Ozero(X23800)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),X23798),c_Groups_Ozero__class_Ozero(X23800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23800),c_Groups_Ozero__class_Ozero(X23800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23800),X23799),X23798)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23800) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_8557,plain,
    ! [X23784,X23785,X23786] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23785),c_Groups_Ozero__class_Ozero(X23786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23784),c_Groups_Ozero__class_Ozero(X23786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23785),c_Groups_Ozero__class_Ozero(X23786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23784),c_Groups_Ozero__class_Ozero(X23786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),X23784))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23785),c_Groups_Ozero__class_Ozero(X23786)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),X23784),c_Groups_Ozero__class_Ozero(X23786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23786),c_Groups_Ozero__class_Ozero(X23786)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23786),X23785),X23784)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X23786) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_8558,plain,
    ! [X22239,X22240,X22241] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22240),c_Groups_Ozero__class_Ozero(X22241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22240))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22239),c_Groups_Ozero__class_Ozero(X22241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22240))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22240),c_Groups_Ozero__class_Ozero(X22241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22239))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22239),c_Groups_Ozero__class_Ozero(X22241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22239))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22240))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),X22239))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22240),c_Groups_Ozero__class_Ozero(X22241)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),X22239),c_Groups_Ozero__class_Ozero(X22241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22241),c_Groups_Ozero__class_Ozero(X22241)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22241),X22240),X22239)))
        | ~ class_Rings_Olinordered__ring__strict(X22241) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_8559,plain,
    ! [X33157,X33158,X33159,X33160,X33161,X33162,X33163] :
      ( ( ~ c_List_Oall__interval__int(X33159,X33158,X33157)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X33160),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X33158,X33157)))
        | hBOOL(hAPP(X33159,X33160)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk504_3(X33161,X33162,X33163)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X33162,X33161)))
        | c_List_Oall__interval__int(X33163,X33162,X33161) )
      & ( ~ hBOOL(hAPP(X33163,esk504_3(X33161,X33162,X33163)))
        | c_List_Oall__interval__int(X33163,X33162,X33161) ) ),
    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_all__interval__int__def])])])])])]) ).

cnf(i_0_8560,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5702]) ).

cnf(i_0_8561,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5703]) ).

fof(i_0_8562,plain,
    ! [X23044,X23045,X23046] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23046),X23045))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23046),X23044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23045),X23044))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_8563,plain,
    ! [X20057,X20058,X20059] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20059),X20058))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20059),X20057)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20058),X20057))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

cnf(i_0_8564,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5704]) ).

cnf(i_0_8565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5705]) ).

fof(i_0_8566,plain,
    ! [X23059,X23060,X23061] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23061),X23060))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23059),X23061)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23059),X23060))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_8567,plain,
    ! [X23446,X23447,X23448] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23448),X23447))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23448),X23446)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23447),X23446))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).

fof(i_0_8568,plain,
    ! [X19978,X19979,X19980] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19980),X19979))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19980),X19978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19979),X19978))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).

fof(i_0_8569,plain,
    ! [X19975,X19976,X19977] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19977),X19976))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19975),X19977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19975),X19976))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).

fof(i_0_8570,plain,
    ! [X19916,X19917,X19918] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19918),X19917))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19918),X19916)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19917),X19916))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_8571,plain,
    ! [X20162,X20163,X20164] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20164),X20163))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20164),X20162)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20163),X20162))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).

fof(i_0_8572,plain,
    ! [X20165,X20166,X20167] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20167),X20166))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20165),X20166)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20165),X20167))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).

fof(i_0_8573,plain,
    ! [X30856,X30857,X30858] :
      ( ~ class_Lattices_Olattice(X30858)
      | c_Big__Operators_Olattice__class_OInf__fin(X30858,hAPP(c_List_Oset(X30858),hAPP(hAPP(c_List_Olist_OCons(X30858),X30857),X30856))) = hAPP(c_List_Ofoldl(X30858,X30858,c_Lattices_Osemilattice__inf__class_Oinf(X30858),X30857),X30856) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).

fof(i_0_8574,plain,
    ! [X30853,X30854,X30855] :
      ( ~ class_Lattices_Olattice(X30855)
      | c_Big__Operators_Olattice__class_OSup__fin(X30855,hAPP(c_List_Oset(X30855),hAPP(hAPP(c_List_Olist_OCons(X30855),X30854),X30853))) = hAPP(c_List_Ofoldl(X30855,X30855,c_Lattices_Osemilattice__sup__class_Osup(X30855),X30854),X30853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).

fof(i_0_8575,plain,
    ! [X30859,X30860,X30861] :
      ( ~ class_Orderings_Olinorder(X30861)
      | c_Big__Operators_Olinorder__class_OMin(X30861,hAPP(c_List_Oset(X30861),hAPP(hAPP(c_List_Olist_OCons(X30861),X30860),X30859))) = hAPP(c_List_Ofoldl(X30861,X30861,c_Orderings_Oord__class_Omin(X30861),X30860),X30859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).

fof(i_0_8576,plain,
    ! [X30862,X30863,X30864] :
      ( ~ class_Orderings_Olinorder(X30864)
      | c_Big__Operators_Olinorder__class_OMax(X30864,hAPP(c_List_Oset(X30864),hAPP(hAPP(c_List_Olist_OCons(X30864),X30863),X30862))) = hAPP(c_List_Ofoldl(X30864,X30864,c_Orderings_Oord__class_Omax(X30864),X30863),X30862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).

fof(i_0_8577,plain,
    ! [X21945,X21946,X21947] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21947),X21946))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21946),X21947))),X21945) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21946)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21947),X21945)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).

fof(i_0_8578,plain,
    ! [X24755,X24756,X24757] :
      ( ~ class_Divides_Osemiring__div(X24757)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24757),X24756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24757),X24755),X24756))),c_Divides_Odiv__class_Omod(X24757,X24755,X24756)) = X24755 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).

cnf(i_0_8579,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5759]) ).

fof(i_0_8580,plain,
    ! [X30065,X30066,X30067,X30068,X30069] : hAPP(hAPP(c_List_Olist__update(X30069,hAPP(hAPP(c_List_Olist_OCons(X30069),X30068),X30067)),hAPP(c_Nat_OSuc,X30066)),X30065) = hAPP(hAPP(c_List_Olist_OCons(X30069),X30068),hAPP(hAPP(c_List_Olist__update(X30069,X30067),X30066),X30065)),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(i_0_8581,plain,
    ! [X33080,X33081,X33082,X33083,X33084,X33085] :
      ( ( X33083 = X33081
        | c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33083,X33082) != c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33081,X33080) )
      & ( X33082 = X33080
        | c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33083,X33082) != c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33081,X33080) )
      & ( X33083 != X33081
        | X33082 != X33080
        | c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33083,X33082) = c_Nitpick_Opair__box_OPairBox(X33085,X33084,X33081,X33080) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).

fof(i_0_8582,plain,
    ! [X20490,X20491,X20492,X20493,X20494,X20495] :
      ( hAPP(X20495,X20494) != X20493
      | ~ hBOOL(hAPP(hAPP(c_member(X20492),X20493),X20491))
      | hBOOL(hAPP(hAPP(c_member(X20490),X20494),hAPP(c_Set_Ovimage(X20490,X20492,X20495),X20491))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).

fof(i_0_8583,plain,
    ! [X16984,X16985,X16986,X16987,X16988,X16989] :
      ( X16989 != hAPP(X16988,X16987)
      | ~ hBOOL(hAPP(hAPP(c_member(X16986),X16987),X16985))
      | hBOOL(hAPP(hAPP(c_member(X16984),X16989),hAPP(c_Set_Oimage(X16986,X16984,X16988),X16985))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_8584,plain,
    ! [X17095,X17096,X17097,X17098,X17099,X17100] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17100),X17099),X17098))
      | X17097 != hAPP(X17096,X17099)
      | hBOOL(hAPP(hAPP(c_member(X17095),X17097),hAPP(c_Set_Oimage(X17100,X17095,X17096),X17098))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_8585,plain,
    ! [X17743,X17744,X17745,X17746,X17747,X17748] :
      ( ( hAPP(X17746,X17744) != hAPP(X17746,X17743)
        | X17744 = X17743
        | ~ hBOOL(hAPP(hAPP(c_member(X17748),X17743),X17745))
        | ~ hBOOL(hAPP(hAPP(c_member(X17748),X17744),X17745))
        | ~ c_Fun_Oinj__on(X17748,X17747,X17746,X17745) )
      & ( X17744 != X17743
        | hAPP(X17746,X17744) = hAPP(X17746,X17743)
        | ~ hBOOL(hAPP(hAPP(c_member(X17748),X17743),X17745))
        | ~ hBOOL(hAPP(hAPP(c_member(X17748),X17744),X17745))
        | ~ c_Fun_Oinj__on(X17748,X17747,X17746,X17745) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_8586,plain,
    ! [X17749,X17750,X17751,X17752,X17753,X17754] :
      ( ~ c_Fun_Oinj__on(X17754,X17753,X17752,X17751)
      | X17750 = X17749
      | ~ hBOOL(hAPP(hAPP(c_member(X17754),X17750),X17751))
      | ~ hBOOL(hAPP(hAPP(c_member(X17754),X17749),X17751))
      | hAPP(X17752,X17750) != hAPP(X17752,X17749) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_8587,plain,
    ! [X17737,X17738,X17739,X17740,X17741,X17742] :
      ( ~ c_Fun_Oinj__on(X17742,X17741,X17740,X17739)
      | hAPP(X17740,X17738) != hAPP(X17740,X17737)
      | ~ hBOOL(hAPP(hAPP(c_member(X17742),X17738),X17739))
      | ~ hBOOL(hAPP(hAPP(c_member(X17742),X17737),X17739))
      | X17738 = X17737 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_8588,plain,
    ! [X23492,X23493] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23492),X23493))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23492),X23493) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23493)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23492),X23493))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23492),X23493) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23492),X23493)),X23493))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23493)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5760])])]) ).

fof(i_0_8589,plain,
    ! [X23490,X23491] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23491))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23490),X23491))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23490),X23491) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23490),X23491)),X23491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5761])]) ).

fof(i_0_8590,plain,
    ! [X23343,X23344] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23343),X23344))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23344),X23343)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23344)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23344),X23343)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23344)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23343),X23344))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23343))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23344),X23343)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23344)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).

fof(i_0_8591,plain,
    ! [X32582,X32583,X32584,X32586,X32587,X32588,X32589] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk473_3(X32582,X32583,X32584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32584)),X32582)))
        | ~ c_List_Olist__ex(X32584,X32583,X32582) )
      & ( hBOOL(hAPP(X32583,hAPP(hAPP(c_List_Onth(X32584),X32582),esk473_3(X32582,X32583,X32584))))
        | ~ c_List_Olist__ex(X32584,X32583,X32582) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32588)),X32586)))
        | ~ hBOOL(hAPP(X32587,hAPP(hAPP(c_List_Onth(X32588),X32586),X32589)))
        | c_List_Olist__ex(X32588,X32587,X32586) ) ),
    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_list__ex__length])])])])])]) ).

fof(i_0_8592,plain,
    ! [X17960,X17961,X17962,X17963,X17964] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17964,X17963,X17962)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17964),X17961))
      | X17960 = c_Orderings_Obot__class_Obot(tc_fun(X17964,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17964,tc_HOL_Obool)),X17960),X17961))
      | hAPP(hAPP(X17963,hAPP(X17962,X17960)),hAPP(X17962,X17961)) = hAPP(X17962,X17961) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).

fof(i_0_8593,plain,
    ! [X33451,X33452,X33454,X33455,X33456,X33457,X33458,X33459,X33462] :
      ( ( hBOOL(hAPP(hAPP(X33451,esk523_1(X33451)),esk523_1(X33451)))
        | ~ c_Equiv__Relations_Opart__equivp(X33452,X33451) )
      & ( hBOOL(hAPP(hAPP(X33451,X33454),X33454))
        | ~ hBOOL(hAPP(hAPP(X33451,X33454),X33455))
        | ~ c_Equiv__Relations_Opart__equivp(X33452,X33451) )
      & ( hBOOL(hAPP(hAPP(X33451,X33455),X33455))
        | ~ hBOOL(hAPP(hAPP(X33451,X33454),X33455))
        | ~ c_Equiv__Relations_Opart__equivp(X33452,X33451) )
      & ( hAPP(X33451,X33454) = hAPP(X33451,X33455)
        | ~ hBOOL(hAPP(hAPP(X33451,X33454),X33455))
        | ~ c_Equiv__Relations_Opart__equivp(X33452,X33451) )
      & ( ~ hBOOL(hAPP(hAPP(X33451,X33456),X33456))
        | ~ hBOOL(hAPP(hAPP(X33451,X33457),X33457))
        | hAPP(X33451,X33456) != hAPP(X33451,X33457)
        | hBOOL(hAPP(hAPP(X33451,X33456),X33457))
        | ~ c_Equiv__Relations_Opart__equivp(X33452,X33451) )
      & ( ~ hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk525_1(X33458)))
        | ~ hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk524_1(X33458)))
        | ~ hBOOL(hAPP(hAPP(X33458,esk525_1(X33458)),esk525_1(X33458)))
        | hAPP(X33458,esk524_1(X33458)) != hAPP(X33458,esk525_1(X33458))
        | ~ hBOOL(hAPP(hAPP(X33458,X33459),X33459))
        | c_Equiv__Relations_Opart__equivp(X33462,X33458) )
      & ( hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk524_1(X33458)))
        | hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk525_1(X33458)))
        | ~ hBOOL(hAPP(hAPP(X33458,X33459),X33459))
        | c_Equiv__Relations_Opart__equivp(X33462,X33458) )
      & ( hBOOL(hAPP(hAPP(X33458,esk525_1(X33458)),esk525_1(X33458)))
        | hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk525_1(X33458)))
        | ~ hBOOL(hAPP(hAPP(X33458,X33459),X33459))
        | c_Equiv__Relations_Opart__equivp(X33462,X33458) )
      & ( hAPP(X33458,esk524_1(X33458)) = hAPP(X33458,esk525_1(X33458))
        | hBOOL(hAPP(hAPP(X33458,esk524_1(X33458)),esk525_1(X33458)))
        | ~ hBOOL(hAPP(hAPP(X33458,X33459),X33459))
        | c_Equiv__Relations_Opart__equivp(X33462,X33458) ) ),
    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_part__equivp__def])])])])])]) ).

fof(i_0_8594,plain,
    ! [X29182,X29183,X29184] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X29184,X29184,X29184),hAPP(c_Relation_Oconverse(X29184,X29184),X29183)),X29183) != X29183
      | hAPP(c_Relation_ODomain(X29184,X29184),X29183) != X29182
      | c_Equiv__Relations_Oequiv(X29184,X29182,X29183) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).

fof(i_0_8595,plain,
    ! [X32896,X32897,X32898,X32899,X32900,X32901] : hAPP(hAPP(c_List_Ozip(X32901,X32900),c_List_Oreplicate(X32901,X32899,X32898)),c_List_Oreplicate(X32900,X32897,X32896)) = c_List_Oreplicate(tc_prod(X32901,X32900),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X32899),X32897),hAPP(hAPP(c_Product__Type_OPair(X32901,X32900),X32898),X32896)),
    inference(variable_rename,[status(thm)],[fact_zip__replicate]) ).

fof(i_0_8596,plain,
    ! [X25576,X25577,X25578] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X25578,X25577,X25576)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X25577)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X25576))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I13_J]) ).

fof(i_0_8597,plain,
    ! [X17619,X17620,X17621,X17622,X17623] :
      ( ~ class_Orderings_Oord(X17623)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17622,X17623)),X17621),X17620))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17623),hAPP(X17621,X17619)),hAPP(X17620,X17619))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_8598,plain,
    ! [X17577,X17578,X17579,X17580,X17581] :
      ( ~ class_Orderings_Oord(X17581)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17580,X17581)),X17579),X17578))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17581),hAPP(X17579,X17577)),hAPP(X17578,X17577))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_8599,plain,
    ! [X31141,X31142,X31143,X31144,X31145] :
      ( hAPP(hAPP(c_List_Omap(X31145,X31144),X31143),X31142) != hAPP(hAPP(c_List_Omap(X31145,X31144),X31143),X31141)
      | ~ c_Fun_Oinj__on(X31145,X31144,X31143,c_Orderings_Otop__class_Otop(tc_fun(X31145,tc_HOL_Obool)))
      | X31142 = X31141 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).

fof(i_0_8600,plain,
    ! [X31136,X31137,X31138,X31139,X31140] :
      ( ( hAPP(hAPP(c_List_Omap(X31140,X31139),X31138),X31137) != hAPP(hAPP(c_List_Omap(X31140,X31139),X31138),X31136)
        | X31137 = X31136
        | ~ c_Fun_Oinj__on(X31140,X31139,X31138,c_Orderings_Otop__class_Otop(tc_fun(X31140,tc_HOL_Obool))) )
      & ( X31137 != X31136
        | hAPP(hAPP(c_List_Omap(X31140,X31139),X31138),X31137) = hAPP(hAPP(c_List_Omap(X31140,X31139),X31138),X31136)
        | ~ c_Fun_Oinj__on(X31140,X31139,X31138,c_Orderings_Otop__class_Otop(tc_fun(X31140,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map])])]) ).

fof(i_0_8601,plain,
    ! [X30091,X30092,X30093,X30094] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30094),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30093)),X30092)))
      | hAPP(hAPP(c_List_Onth(X30093),hAPP(hAPP(c_List_Olist__update(X30093,X30092),X30094),X30091)),X30094) = X30091 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).

fof(i_0_8602,plain,
    ! [X24329,X24330,X24331] :
      ( ~ class_Groups_Ocomm__monoid__add(X24331)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24331),X24330),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24329))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24331),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24331),X24330),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24329))),hAPP(X24330,hAPP(c_Nat_OSuc,X24329))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).

fof(i_0_8603,plain,
    ! [X33393,X33394,X33395] :
      ( ~ c_Relation_Osym(X33395,X33394)
      | ~ c_Relation_Osym(X33395,X33393)
      | c_Relation_Osym(X33395,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33395,X33395),tc_HOL_Obool)),X33394),X33393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Int])]) ).

fof(i_0_8604,plain,
    ! [X33399,X33400,X33401] :
      ( ~ c_Relation_Osym(X33401,X33400)
      | ~ c_Relation_Osym(X33401,X33399)
      | c_Relation_Osym(X33401,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33401,X33401),tc_HOL_Obool)),X33400),X33399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Un])]) ).

fof(i_0_8605,plain,
    ! [X33228,X33229,X33230] :
      ( ~ c_Relation_Otrans(X33230,X33229)
      | ~ c_Relation_Otrans(X33230,X33228)
      | c_Relation_Otrans(X33230,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33230,X33230),tc_HOL_Obool)),X33229),X33228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).

fof(i_0_8606,plain,
    ! [X23127,X23128,X23129,X23130] :
      ( ~ class_Orderings_Olinorder(X23130)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23130),X23129),X23128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23130),X23128),X23127))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23130,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23130,X23129),X23128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23130,X23128),X23127)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23130,X23129),X23127) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).

fof(i_0_8607,plain,
    ! [X30104,X30105] : c_List_Obutlast(X30105,X30104) = hAPP(hAPP(c_List_Otake(X30105),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30105)),X30104)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30104),
    inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).

fof(i_0_8608,plain,
    ! [X20999,X21000,X21001] :
      ( ~ class_Lattices_Osemilattice__inf(X21001)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21001),X21000))
      | ~ hBOOL(hAPP(hAPP(c_member(X21001),X20999),X21000))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21001),hAPP(c_Finite__Set_Ofold1(X21001,c_Lattices_Osemilattice__inf__class_Oinf(X21001)),X21000)),X20999)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).

fof(i_0_8609,plain,
    ! [X19034,X19035,X19036] :
      ( ~ class_Orderings_Olinorder(X19036)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19036),X19035))
      | ~ hBOOL(hAPP(hAPP(c_member(X19036),X19034),X19035))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19036),hAPP(c_Finite__Set_Ofold1(X19036,c_Orderings_Oord__class_Omin(X19036)),X19035)),X19034)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).

fof(i_0_8610,plain,
    ! [X22868] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X22868))))),
    inference(variable_rename,[status(thm)],[i_0_5762]) ).

fof(i_0_8611,plain,
    ! [X32578,X32579,X32580] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32580),esk472_3(X32578,X32579,X32580)),hAPP(c_List_Oset(X32580),X32579)))
        | ~ c_List_Olinorder__class_Osorted(X32580,X32579)
        | c_List_Olinorder__class_Osorted(X32580,hAPP(hAPP(c_List_Olist_OCons(X32580),X32578),X32579))
        | ~ class_Orderings_Olinorder(X32580) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32580),X32578),esk472_3(X32578,X32579,X32580)))
        | ~ c_List_Olinorder__class_Osorted(X32580,X32579)
        | c_List_Olinorder__class_Osorted(X32580,hAPP(hAPP(c_List_Olist_OCons(X32580),X32578),X32579))
        | ~ class_Orderings_Olinorder(X32580) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_OCons])])])]) ).

fof(i_0_8612,plain,
    ! [X32099,X32100,X32101,X32102] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32101),X32102),hAPP(c_List_Oset(X32101),X32099)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32101),X32100),X32102))
        | ~ c_List_Olinorder__class_Osorted(X32101,hAPP(hAPP(c_List_Olist_OCons(X32101),X32100),X32099))
        | ~ class_Orderings_Olinorder(X32101) )
      & ( c_List_Olinorder__class_Osorted(X32101,X32099)
        | ~ c_List_Olinorder__class_Osorted(X32101,hAPP(hAPP(c_List_Olist_OCons(X32101),X32100),X32099))
        | ~ class_Orderings_Olinorder(X32101) )
      & ( hBOOL(hAPP(hAPP(c_member(X32101),esk438_3(X32099,X32100,X32101)),hAPP(c_List_Oset(X32101),X32099)))
        | ~ c_List_Olinorder__class_Osorted(X32101,X32099)
        | c_List_Olinorder__class_Osorted(X32101,hAPP(hAPP(c_List_Olist_OCons(X32101),X32100),X32099))
        | ~ class_Orderings_Olinorder(X32101) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32101),X32100),esk438_3(X32099,X32100,X32101)))
        | ~ c_List_Olinorder__class_Osorted(X32101,X32099)
        | c_List_Olinorder__class_Osorted(X32101,hAPP(hAPP(c_List_Olist_OCons(X32101),X32100),X32099))
        | ~ class_Orderings_Olinorder(X32101) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I2_J])])])])]) ).

fof(i_0_8613,plain,
    ! [X32081,X32082,X32083,X32084] :
      ( ( c_List_Olinorder__class_Osorted(X32083,X32081)
        | ~ c_List_Olinorder__class_Osorted(X32083,hAPP(hAPP(c_List_Olist_OCons(X32083),X32082),X32081))
        | ~ class_Orderings_Olinorder(X32083) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32083),X32084),hAPP(c_List_Oset(X32083),X32081)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32083),X32082),X32084))
        | ~ c_List_Olinorder__class_Osorted(X32083,hAPP(hAPP(c_List_Olist_OCons(X32083),X32082),X32081))
        | ~ class_Orderings_Olinorder(X32083) )
      & ( hBOOL(hAPP(hAPP(c_member(X32083),esk435_3(X32081,X32082,X32083)),hAPP(c_List_Oset(X32083),X32081)))
        | ~ c_List_Olinorder__class_Osorted(X32083,X32081)
        | c_List_Olinorder__class_Osorted(X32083,hAPP(hAPP(c_List_Olist_OCons(X32083),X32082),X32081))
        | ~ class_Orderings_Olinorder(X32083) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32083),X32082),esk435_3(X32081,X32082,X32083)))
        | ~ c_List_Olinorder__class_Osorted(X32083,X32081)
        | c_List_Olinorder__class_Osorted(X32083,hAPP(hAPP(c_List_Olist_OCons(X32083),X32082),X32081))
        | ~ class_Orderings_Olinorder(X32083) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__Cons])])])])]) ).

fof(i_0_8614,plain,
    ! [X23277,X23278] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23277))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23277),X23278)),X23277) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23278),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__power__div__base])]) ).

fof(i_0_8615,plain,
    ! [X23804,X23805,X23806] :
      ( ~ class_Fields_Olinordered__field(X23806)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23806),c_Groups_Ozero__class_Ozero(X23806)),X23805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23806),c_Groups_Ozero__class_Ozero(X23806)),X23804))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23806),c_Groups_Ozero__class_Ozero(X23806)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23806),X23805),X23804))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_8616,plain,
    ! [X22324,X22325,X22326] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22326)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22326),c_Groups_Ozero__class_Ozero(X22326)),X22325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22326),c_Groups_Ozero__class_Ozero(X22326)),X22324))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22326),c_Groups_Ozero__class_Ozero(X22326)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22326),X22325),X22324))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_8617,plain,
    ! [X22300,X22301,X22302] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22302)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22302),c_Groups_Ozero__class_Ozero(X22302)),X22301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22302),c_Groups_Ozero__class_Ozero(X22302)),X22300))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22302),c_Groups_Ozero__class_Ozero(X22302)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22302),X22301),X22300))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_8618,plain,
    ! [X22536,X22537,X22538] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22538)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22538),c_Groups_Ozero__class_Ozero(X22538)),X22537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22538),c_Groups_Ozero__class_Ozero(X22538)),X22536))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22538),c_Groups_Ozero__class_Ozero(X22538)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22538),X22537),X22536))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_8619,plain,
    ! [X22539,X22540,X22541] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22541)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22541),c_Groups_Ozero__class_Ozero(X22541)),X22540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22541),c_Groups_Ozero__class_Ozero(X22541)),X22539))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22541),c_Groups_Ozero__class_Ozero(X22541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22541),X22540),X22539))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_8620,plain,
    ! [X20005,X20006,X20007] :
      ( ~ class_Rings_Olinordered__semidom(X20007)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20007),c_Groups_Oone__class_Oone(X20007)),X20006))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20007),c_Groups_Oone__class_Oone(X20007)),X20005))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20007),c_Groups_Oone__class_Oone(X20007)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20007),X20006),X20005))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_8621,plain,
    ! [X23845,X23846,X23847] :
      ( ~ class_Fields_Olinordered__field(X23847)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23847),c_Groups_Ozero__class_Ozero(X23847)),X23846))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23847),c_Groups_Ozero__class_Ozero(X23847)),X23845))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23847),c_Groups_Ozero__class_Ozero(X23847)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23847),X23846),X23845))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_8622,plain,
    ! [X22245,X22246,X22247] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22247)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22247),c_Groups_Ozero__class_Ozero(X22247)),X22246))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22247),c_Groups_Ozero__class_Ozero(X22247)),X22245))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22247),c_Groups_Ozero__class_Ozero(X22247)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22247),X22246),X22245))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_8623,plain,
    ! [X22290,X22291,X22292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),c_Groups_Ozero__class_Ozero(X22292)),X22291))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),c_Groups_Ozero__class_Ozero(X22292)),X22290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),c_Groups_Ozero__class_Ozero(X22292)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22292),X22291),X22290)))
        | ~ class_Rings_Oordered__ring(X22292) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),X22291),c_Groups_Ozero__class_Ozero(X22292)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),X22290),c_Groups_Ozero__class_Ozero(X22292)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22292),c_Groups_Ozero__class_Ozero(X22292)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22292),X22291),X22290)))
        | ~ class_Rings_Oordered__ring(X22292) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_8624,plain,
    ! [X22230,X22231,X22232] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22232)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22232),c_Groups_Ozero__class_Ozero(X22232)),X22231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22232),c_Groups_Ozero__class_Ozero(X22232)),X22230))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22232),c_Groups_Ozero__class_Ozero(X22232)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22232),X22231),X22230))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_8625,plain,
    ! [X19775,X19776,X19777,X19778] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19778),X19777))
      | hAPP(c_Finite__Set_Ocard(X19776),hAPP(c_Set_Oimage(X19778,X19776,X19775),X19777)) != hAPP(c_Finite__Set_Ocard(X19778),X19777)
      | c_Fun_Oinj__on(X19778,X19776,X19775,X19777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_8626,plain,
    ! [X19771,X19772,X19773,X19774] :
      ( ( ~ c_Fun_Oinj__on(X19774,X19772,X19771,X19773)
        | hAPP(c_Finite__Set_Ocard(X19772),hAPP(c_Set_Oimage(X19774,X19772,X19771),X19773)) = hAPP(c_Finite__Set_Ocard(X19774),X19773)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19774),X19773)) )
      & ( hAPP(c_Finite__Set_Ocard(X19772),hAPP(c_Set_Oimage(X19774,X19772,X19771),X19773)) != hAPP(c_Finite__Set_Ocard(X19774),X19773)
        | c_Fun_Oinj__on(X19774,X19772,X19771,X19773)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19774),X19773)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_8627,plain,
    ! [X19732,X19733,X19734] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19734,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19734,tc_HOL_Obool)),X19733),X19732)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19734,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19734,tc_HOL_Obool)),X19733)),X19732),
    inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).

cnf(i_0_8628,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Relation_OId(X1)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5763]) ).

fof(i_0_8629,plain,
    ! [X22189,X22190,X22191,X22192] :
      ( ~ class_Rings_Olinordered__semidom(X22192)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22192),X22191),X22190) != hAPP(hAPP(c_Power_Opower__class_Opower(X22192),X22189),X22190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22192),c_Groups_Ozero__class_Ozero(X22192)),X22191))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22192),c_Groups_Ozero__class_Ozero(X22192)),X22189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22190))
      | X22191 = X22189 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).

cnf(i_0_8630,plain,
    ( c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5764]) ).

cnf(i_0_8631,plain,
    ( c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5765]) ).

fof(i_0_8632,plain,
    ! [X27804,X27805,X27806,X27807] : hAPP(c_Finite__Set_Ocard(tc_prod(X27807,X27806)),hAPP(hAPP(c_Product__Type_OSigma(X27807,X27806),X27805),hAPP(c_COMBK(tc_fun(X27806,tc_HOL_Obool),X27807),X27804))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27807),X27805)),hAPP(c_Finite__Set_Ocard(X27806),X27804)),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).

fof(i_0_8633,plain,
    ! [X20870,X20871,X20872,X20873] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20873),X20872),X20871))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20873,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20873),X20872),X20870)) = hAPP(hAPP(c_Set_Oinsert(X20873),X20872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20873,tc_HOL_Obool)),X20871),X20870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).

fof(i_0_8634,plain,
    ! [X20854,X20855,X20856,X20857] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20857),X20856),X20855))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20857,tc_HOL_Obool)),X20855),hAPP(hAPP(c_Set_Oinsert(X20857),X20856),X20854)) = hAPP(hAPP(c_Set_Oinsert(X20857),X20856),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20857,tc_HOL_Obool)),X20855),X20854)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20857),X20856),X20855))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20857,tc_HOL_Obool)),X20855),hAPP(hAPP(c_Set_Oinsert(X20857),X20856),X20854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20857,tc_HOL_Obool)),X20855),X20854) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5766])]) ).

fof(i_0_8635,plain,
    ! [X29766,X29767,X29768,X29769,X29770,X29771,X29772] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29766)),X29768) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29766)),X29767)
        | X29768 != X29767 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29769),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29766)),X29768)))
        | hAPP(hAPP(c_List_Onth(X29766),X29768),X29769) = hAPP(hAPP(c_List_Onth(X29766),X29767),X29769)
        | X29768 != X29767 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk389_3(X29770,X29771,X29772)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29770)),X29772)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29770)),X29772) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29770)),X29771)
        | X29772 = X29771 )
      & ( hAPP(hAPP(c_List_Onth(X29770),X29772),esk389_3(X29770,X29771,X29772)) != hAPP(hAPP(c_List_Onth(X29770),X29771),esk389_3(X29770,X29771,X29772))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29770)),X29772) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29770)),X29771)
        | X29772 = X29771 ) ),
    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_list__eq__iff__nth__eq])])])])])]) ).

fof(i_0_8636,plain,
    ! [X28696,X28697,X28698,X28699,X28700,X28701] :
      ( ~ c_Finite__Set_Ofolding(X28701,X28700,X28699,X28698)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28701),X28697))
      | hAPP(hAPP(X28698,X28697),X28696) = hAPP(hAPP(c_Finite__Set_Ofold(X28701,X28700,X28699),X28696),X28697) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).

fof(i_0_8637,plain,
    ! [X17848,X17849,X17850,X17851] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17851,X17850,X17849)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X17851),tc_HOL_Obool)),X17848),X17849))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17851,X17850,X17848) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).

fof(i_0_8638,plain,
    ! [X17844,X17845,X17846,X17847] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17847,X17846,X17845)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X17847),tc_HOL_Obool)),X17846),X17844))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17847,X17844,X17845) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_thin])]) ).

fof(i_0_8639,plain,
    ! [X21149,X21150,X21151,X21152,X21153] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21153)
      | ~ hBOOL(hAPP(hAPP(c_member(X21152),X21151),X21150))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21153),hAPP(X21149,X21151)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21152,X21153),X21150),X21149))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).

fof(i_0_8640,plain,
    ! [X24677,X24678,X24679,X24680] :
      ( ~ class_Divides_Osemiring__div(X24680)
      | c_Divides_Odiv__class_Omod(X24680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24680),c_Divides_Odiv__class_Omod(X24680,X24679,X24678)),X24677),X24678) = c_Divides_Odiv__class_Omod(X24680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24680),X24679),X24677),X24678) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).

fof(i_0_8641,plain,
    ! [X24629,X24630,X24631,X24632] :
      ( ~ class_Divides_Osemiring__div(X24632)
      | c_Divides_Odiv__class_Omod(X24632,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24632),c_Divides_Odiv__class_Omod(X24632,X24631,X24630)),X24629),X24630) = c_Divides_Odiv__class_Omod(X24632,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24632),X24631),X24629),X24630) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).

fof(i_0_8642,plain,
    ! [X24693,X24694,X24695,X24696] :
      ( ~ class_Divides_Osemiring__div(X24696)
      | c_Divides_Odiv__class_Omod(X24696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24696),X24695),X24694),X24693) = c_Divides_Odiv__class_Omod(X24696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24696),c_Divides_Odiv__class_Omod(X24696,X24695,X24693)),X24694),X24693) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).

fof(i_0_8643,plain,
    ! [X24641,X24642,X24643,X24644] :
      ( ~ class_Divides_Osemiring__div(X24644)
      | c_Divides_Odiv__class_Omod(X24644,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24644),X24643),X24642),X24641) = c_Divides_Odiv__class_Omod(X24644,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24644),c_Divides_Odiv__class_Omod(X24644,X24643,X24641)),X24642),X24641) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).

fof(i_0_8644,plain,
    ! [X24607,X24608,X24609,X24610] :
      ( ~ class_Divides_Oring__div(X24610)
      | c_Divides_Odiv__class_Omod(X24610,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24610),X24609),X24608),X24607) = c_Divides_Odiv__class_Omod(X24610,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24610),c_Divides_Odiv__class_Omod(X24610,X24609,X24607)),X24608),X24607) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).

fof(i_0_8645,plain,
    ! [X18459,X18460,X18461] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18461,tc_HOL_Obool)),X18460),X18459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18461,tc_HOL_Obool)),X18460),X18459)) )
      & ( X18460 != X18459
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18461,tc_HOL_Obool)),X18460),X18459)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18461,tc_HOL_Obool)),X18460),X18459))
        | X18460 = X18459
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18461,tc_HOL_Obool)),X18460),X18459)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_8646,plain,
    ! [X18456,X18457,X18458] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18458,tc_HOL_Obool)),X18457),X18456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18458,tc_HOL_Obool)),X18457),X18456))
        | X18457 = X18456 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18458,tc_HOL_Obool)),X18457),X18456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18458,tc_HOL_Obool)),X18457),X18456)) )
      & ( X18457 != X18456
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18458,tc_HOL_Obool)),X18457),X18456)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_8647,plain,
    ! [X19589,X19590,X19591] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19591),X19590))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19591),X19589))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X19591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19591,tc_HOL_Obool)),X19590),X19589))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).

fof(i_0_8648,plain,
    ! [X24543,X24544,X24545] : hAPP(c_Set_OPow(X24545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24545,tc_HOL_Obool)),X24544),X24543)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X24545,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X24545),X24544)),hAPP(c_Set_OPow(X24545),X24543)),
    inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).

fof(i_0_8649,plain,
    ! [X33132,X33133,X33135] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X33133)),X33132))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33133)),X33135),X33132))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33133)),X33135)),esk503_2(X33132,X33133))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__maxlen])])])]) ).

fof(i_0_8650,plain,
    ! [X20187,X20188,X20189,X20190] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20189),X20188))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20189,X20190),X20187),X20188) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20190,X20189,c_Groups_Otimes__class_Otimes(X20190)),X20187),c_Groups_Oone__class_Oone(X20190)),X20188)
        | ~ class_Groups_Ocomm__monoid__mult(X20190) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20189),X20188))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20189,X20190),X20187),X20188) = c_Groups_Oone__class_Oone(X20190)
        | ~ class_Groups_Ocomm__monoid__mult(X20190) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5767])])]) ).

fof(i_0_8651,plain,
    ! [X20191,X20192,X20193,X20194] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20194)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20193),X20192))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20193,X20194),X20191),X20192) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20194,X20193,c_Groups_Otimes__class_Otimes(X20194)),X20191),c_Groups_Oone__class_Oone(X20194)),X20192) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).

fof(i_0_8652,plain,
    ! [X22714,X22715,X22716,X22717] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22716),X22715))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22716,X22717),X22714),X22715) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X22717,X22716,c_Groups_Oplus__class_Oplus(X22717)),X22714),c_Groups_Ozero__class_Ozero(X22717)),X22715)
        | ~ class_Groups_Ocomm__monoid__add(X22717) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22716),X22715))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22716,X22717),X22714),X22715) = c_Groups_Ozero__class_Ozero(X22717)
        | ~ class_Groups_Ocomm__monoid__add(X22717) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5768])])]) ).

fof(i_0_8653,plain,
    ! [X22710,X22711,X22712,X22713] :
      ( ~ class_Groups_Ocomm__monoid__add(X22713)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22712),X22711))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22712,X22713),X22710),X22711) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X22713,X22712,c_Groups_Oplus__class_Oplus(X22713)),X22710),c_Groups_Ozero__class_Ozero(X22713)),X22711) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).

fof(i_0_8654,plain,
    ! [X18453,X18454,X18455] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18455,tc_HOL_Obool)),X18454),X18453))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18455,tc_HOL_Obool)),X18454),X18453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_8655,plain,
    ! [X32931,X32932,X32933,X32934] : hAPP(hAPP(c_List_Oappend(X32934),c_List_Oreplicate(X32934,X32933,X32932)),c_List_Oreplicate(X32934,X32931,X32932)) = hAPP(hAPP(c_List_Oappend(X32934),c_List_Oreplicate(X32934,X32931,X32932)),c_List_Oreplicate(X32934,X32933,X32932)),
    inference(variable_rename,[status(thm)],[fact_append__replicate__commute]) ).

fof(i_0_8656,plain,
    ! [X26915,X26916] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26915),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X26916,X26915) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26916),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26915)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).

fof(i_0_8657,plain,
    ! [X30522,X30523,X30524,X30525] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30525),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30523)))
        | hAPP(hAPP(c_List_Onth(X30524),hAPP(hAPP(c_List_Oappend(X30524),X30523),X30522)),X30525) = hAPP(hAPP(c_List_Onth(X30524),X30523),X30525) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30525),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30523)))
        | hAPP(hAPP(c_List_Onth(X30524),hAPP(hAPP(c_List_Oappend(X30524),X30523),X30522)),X30525) = hAPP(hAPP(c_List_Onth(X30524),X30522),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30525),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30523))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5769])]) ).

fof(i_0_8658,plain,
    ! [X19003,X19004,X19005] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19005),X19004),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19005,tc_HOL_Obool)),X19003)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19005),X19004),X19003)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19005),X19004),X19003))
        | hBOOL(hAPP(hAPP(c_member(X19005),X19004),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19005,tc_HOL_Obool)),X19003))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5770])]) ).

fof(i_0_8659,plain,
    ! [X19000,X19001,X19002] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19002),X19001),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19002,tc_HOL_Obool)),X19000)))
      | ~ hBOOL(hAPP(hAPP(c_member(X19002),X19001),X19000)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5771])]) ).

fof(i_0_8660,plain,
    ! [X18997,X18998,X18999] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18999),X18998),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X18999,tc_HOL_Obool)),X18997)))
      | ~ hBOOL(hAPP(hAPP(c_member(X18999),X18998),X18997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5772])]) ).

fof(i_0_8661,plain,
    ! [X24135,X24136,X24137,X24139,X24140,X24141] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk171_2(X24135,X24136)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24136)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24137),X24136))
        | ~ hBOOL(hAPP(X24135,X24137)) )
      & ( hBOOL(hAPP(X24135,esk171_2(X24135,X24136)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24137),X24136))
        | ~ hBOOL(hAPP(X24135,X24137)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk172_2(X24139,X24140)),X24140))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24141),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24140)))
        | ~ hBOOL(hAPP(X24139,X24141)) )
      & ( hBOOL(hAPP(X24139,esk172_2(X24139,X24140)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24141),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24140)))
        | ~ hBOOL(hAPP(X24139,X24141)) ) ),
    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_ex__nat__less])])])])])]) ).

fof(i_0_8662,plain,
    ! [X30684,X30685,X30686,X30687] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30687) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30686),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30687)),hAPP(hAPP(c_List_Olist_OCons(X30686),X30685),X30684)) = hAPP(hAPP(c_List_Olist_OCons(X30686),X30685),X30684) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30686),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30687)),hAPP(hAPP(c_List_Olist_OCons(X30686),X30685),X30684)) = hAPP(hAPP(c_List_Odrop(X30686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30687)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30684) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).

fof(i_0_8663,plain,
    ! [X28256,X28257] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk317_2(X28256,X28257)),c_Int_OInteg))
        | hBOOL(hAPP(X28257,X28256)) )
      & ( ~ hBOOL(hAPP(X28257,hAPP(c_Int_OAbs__Integ,esk317_2(X28256,X28257))))
        | hBOOL(hAPP(X28257,X28256)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct])])])]) ).

cnf(i_0_8664,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_5773]) ).

fof(i_0_8665,plain,
    ! [X27537,X27538,X27539] :
      ( ~ c_Wellfounded_Owf(X27539,X27538)
      | c_Wellfounded_Owf(X27539,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27539,X27539),tc_HOL_Obool)),X27538),X27537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).

fof(i_0_8666,plain,
    ! [X27534,X27535,X27536] :
      ( ~ c_Wellfounded_Owf(X27536,X27535)
      | c_Wellfounded_Owf(X27536,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27536,X27536),tc_HOL_Obool)),X27534),X27535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).

fof(i_0_8667,plain,
    ! [X27045,X27046] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27046))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27045),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X27046),X27045) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27046),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27045)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).

fof(i_0_8668,plain,
    ! [X30803,X30804] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X30804)
      | X30803 = c_List_Olist_ONil(X30804)
      | hAPP(c_Finite__Set_Ofold1(X30804,c_Groups_Otimes__class_Otimes(X30804)),hAPP(c_List_Oset(X30804),X30803)) = hAPP(c_List_Ofoldl(X30804,X30804,c_Groups_Otimes__class_Otimes(X30804),hAPP(c_List_Ohd(X30804),X30803)),hAPP(c_List_Otl(X30804),X30803)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).

fof(i_0_8669,plain,
    ! [X30619,X30620,X30621,X30622,X30623] : hAPP(hAPP(c_List_Odrop(tc_prod(X30623,X30622)),X30621),hAPP(hAPP(c_List_Ozip(X30623,X30622),X30620),X30619)) = hAPP(hAPP(c_List_Ozip(X30623,X30622),hAPP(hAPP(c_List_Odrop(X30623),X30621),X30620)),hAPP(hAPP(c_List_Odrop(X30622),X30621),X30619)),
    inference(variable_rename,[status(thm)],[fact_drop__zip]) ).

fof(i_0_8670,plain,
    ! [X29929,X29930,X29931,X29932,X29933] : hAPP(hAPP(c_List_Otake(tc_prod(X29933,X29932)),X29931),hAPP(hAPP(c_List_Ozip(X29933,X29932),X29930),X29929)) = hAPP(hAPP(c_List_Ozip(X29933,X29932),hAPP(hAPP(c_List_Otake(X29933),X29931),X29930)),hAPP(hAPP(c_List_Otake(X29932),X29931),X29929)),
    inference(variable_rename,[status(thm)],[fact_take__zip]) ).

fof(i_0_8671,plain,
    ! [X24250,X24251,X24252] :
      ( ~ class_Orderings_Olinorder(X24252)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24252),X24251),X24250))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24252,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24252,X24251),X24250)),hAPP(hAPP(c_Set_Oinsert(X24252),X24250),c_Orderings_Obot__class_Obot(tc_fun(X24252,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X24252,X24251,X24250) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).

fof(i_0_8672,plain,
    ! [X26917,X26918] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26918),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26917),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X26918,X26917) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26918),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26917)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).

fof(i_0_8673,plain,
    ! [X29207,X29208,X29209,X29210,X29211] :
      ( ~ c_Relation_Osingle__valued(X29211,X29210,X29209)
      | ~ c_Relation_Osingle__valued(X29210,X29208,X29207)
      | c_Relation_Osingle__valued(X29211,X29208,hAPP(hAPP(c_Relation_Orel__comp(X29211,X29210,X29208),X29209),X29207)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).

fof(i_0_8674,plain,
    ! [X32207,X32208] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32208),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32208))),c_List_Otranspose(X32208,X32207)))),
    inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).

fof(i_0_8675,plain,
    ! [X23175,X23176,X23177,X23178,X23179] :
      ( ~ class_Orderings_Olinorder(X23179)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23179,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23179,X23178),X23177)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23179,X23176),X23175)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23179,hAPP(hAPP(c_Orderings_Oord__class_Omax(X23179),X23178),X23176)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23179),X23177),X23175)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).

fof(i_0_8676,plain,
    ! [X24201,X24202,X24203,X24204,X24205] :
      ( ~ class_Orderings_Olinorder(X24205)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24205,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24205,X24204,X24203)),c_SetInterval_Oord__class_OatLeastAtMost(X24205,X24202,X24201)) = c_SetInterval_Oord__class_OatLeastAtMost(X24205,hAPP(hAPP(c_Orderings_Oord__class_Omax(X24205),X24204),X24202),hAPP(hAPP(c_Orderings_Oord__class_Omin(X24205),X24203),X24201)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).

fof(i_0_8677,plain,
    ! [X23504,X23505,X23506,X23507,X23508] :
      ( ~ class_Orderings_Olinorder(X23508)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23508,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23508,X23507,X23506)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23508,X23505,X23504)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23508,hAPP(hAPP(c_Orderings_Oord__class_Omax(X23508),X23507),X23505),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23508),X23506),X23504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).

fof(i_0_8678,plain,
    ! [X23395,X23396,X23397,X23398,X23399] :
      ( ~ class_Orderings_Olinorder(X23399)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23399,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23399,X23398,X23397)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23399,X23396,X23395)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23399,hAPP(hAPP(c_Orderings_Oord__class_Omax(X23399),X23398),X23396),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23399),X23397),X23395)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).

fof(i_0_8679,plain,
    ! [X17786,X17787,X17788,X17789] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17789),X17788),X17787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17789,tc_HOL_Obool)),X17787),X17786))
      | hBOOL(hAPP(hAPP(c_member(X17789),X17788),X17786)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_8680,plain,
    ! [X18405,X18406,X18407,X18408] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18408,tc_HOL_Obool)),X18407),X18406))
      | ~ hBOOL(hAPP(hAPP(c_member(X18408),X18405),X18407))
      | hBOOL(hAPP(hAPP(c_member(X18408),X18405),X18406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_8681,plain,
    ! [X17790,X17791,X17792,X17793] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17793,tc_HOL_Obool)),X17792),X17791))
      | ~ hBOOL(hAPP(hAPP(c_member(X17793),X17790),X17792))
      | hBOOL(hAPP(hAPP(c_member(X17793),X17790),X17791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_8682,plain,
    ! [X17782,X17783,X17784,X17785] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17785,tc_HOL_Obool)),X17784),X17783))
      | ~ hBOOL(hAPP(hAPP(c_member(X17785),X17782),X17784))
      | hBOOL(hAPP(hAPP(c_member(X17785),X17782),X17783)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_8683,plain,
    ! [X17565,X17566,X17567,X17568] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17568,tc_HOL_Obool)),X17567),X17566))
      | ~ hBOOL(hAPP(hAPP(c_member(X17568),X17565),X17567))
      | hBOOL(hAPP(hAPP(c_member(X17568),X17565),X17566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_8684,plain,
    ! [X30475,X30476,X30477,X30478] : hAPP(hAPP(c_List_Onth(X30478),hAPP(hAPP(c_List_Oappend(X30478),X30477),hAPP(hAPP(c_List_Olist_OCons(X30478),X30476),X30475))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30478)),X30477)) = X30476,
    inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).

fof(i_0_8685,plain,
    ! [X25739,X25740,X25741] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25741),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25740)),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25739)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25741),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25740)),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25739)) = hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25739)
        | ~ class_Int_Onumber(X25741)
        | ~ class_Orderings_Oord(X25741) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25741),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25740)),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25739)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25741),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25740)),hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25739)) = hAPP(c_Int_Onumber__class_Onumber__of(X25741),X25740)
        | ~ class_Int_Onumber(X25741)
        | ~ class_Orderings_Oord(X25741) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5774])])]) ).

fof(i_0_8686,plain,
    ! [X25736,X25737,X25738] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25738),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25737)),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25736)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25738),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25737)),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25736)) = hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25737)
        | ~ class_Int_Onumber(X25738)
        | ~ class_Orderings_Oord(X25738) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25738),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25737)),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25736)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25738),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25737)),hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25736)) = hAPP(c_Int_Onumber__class_Onumber__of(X25738),X25736)
        | ~ class_Int_Onumber(X25738)
        | ~ class_Orderings_Oord(X25738) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5775])])]) ).

fof(i_0_8687,plain,
    ! [X27047,X27048] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27048),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27047),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X27048),X27047) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27048),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27047)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).

fof(i_0_8688,plain,
    ! [X19895,X19896] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X19896),X19895),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_8689,plain,
    ! [X23339,X23340] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23339),X23340)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23339))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23340)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23339))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23339),X23340)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23340)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_8690,plain,
    ! [X23773,X23774,X23775,X23776,X23777] :
      ( ~ class_Fields_Ofield__inverse__zero(X23777)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23777),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23777),X23776),X23775)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23777),X23774),X23773)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23777),X23776),X23774)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23777),X23775),X23773)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).

fof(i_0_8691,plain,
    ! [X18595,X18596,X18597,X18598,X18599] :
      ( ~ class_Rings_Ocomm__semiring__1(X18599)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),X18598),X18597)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),X18596),X18595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),X18598),X18596)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18599),X18597),X18595)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).

fof(i_0_8692,plain,
    ! [X18571,X18572,X18573,X18574,X18575] :
      ( ~ class_Rings_Ocomm__semiring__1(X18575)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),X18574),X18573)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),X18572),X18571)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),X18574),X18572)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18575),X18573),X18571)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_8693,plain,
    ! [X18605,X18606,X18607,X18608,X18609] :
      ( ~ class_Rings_Ocomm__semiring__1(X18609)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),X18608),X18607)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),X18606),X18605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),X18608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),X18607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18609),X18606),X18605))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).

fof(i_0_8694,plain,
    ! [X32058,X32059,X32060,X32061,X32062] :
      ( ~ class_Orderings_Olinorder(X32062)
      | ~ c_List_Olinorder__class_Osorted(X32062,hAPP(hAPP(c_List_Omap(X32061,X32062),X32060),X32059))
      | c_List_Olinorder__class_Osorted(X32062,hAPP(hAPP(c_List_Omap(X32061,X32062),X32060),c_List_Oremove1(X32061,X32058,X32059))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).

fof(i_0_8695,plain,
    ! [X27759,X27760,X27761] : hAPP(c_Relation_ODomain(X27761,X27760),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X27761,X27760),tc_HOL_Obool),X27759)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X27761,X27760),tc_HOL_Obool),tc_fun(X27761,tc_HOL_Obool)),X27759),c_Relation_ODomain(X27761,X27760)),
    inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).

fof(i_0_8696,plain,
    ! [X27638,X27639,X27640] : hAPP(c_Relation_ORange(X27640,X27639),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X27640,X27639),tc_HOL_Obool),X27638)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X27640,X27639),tc_HOL_Obool),tc_fun(X27639,tc_HOL_Obool)),X27638),c_Relation_ORange(X27640,X27639)),
    inference(variable_rename,[status(thm)],[fact_Range__Union]) ).

fof(i_0_8697,plain,
    ! [X24127,X24128,X24130,X24131,X24132,X24134] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk169_2(X24127,X24128)),X24128))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24130),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24128)))
        | hBOOL(hAPP(X24127,X24130)) )
      & ( ~ hBOOL(hAPP(X24127,esk169_2(X24127,X24128)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24130),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24128)))
        | hBOOL(hAPP(X24127,X24130)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk170_2(X24131,X24132)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24132)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24134),X24132))
        | hBOOL(hAPP(X24131,X24134)) )
      & ( ~ hBOOL(hAPP(X24131,esk170_2(X24131,X24132)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24134),X24132))
        | hBOOL(hAPP(X24131,X24134)) ) ),
    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_all__nat__less])])])])])]) ).

fof(i_0_8698,plain,
    ! [X22945,X22946,X22947] :
      ( ~ class_Rings_Oring__1(X22947)
      | ~ hBOOL(hAPP(hAPP(c_member(X22947),X22946),c_Int_Oring__1__class_OInts(X22947)))
      | hBOOL(hAPP(hAPP(c_member(X22947),hAPP(hAPP(c_Power_Opower__class_Opower(X22947),X22946),X22945)),c_Int_Oring__1__class_OInts(X22947))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).

fof(i_0_8699,plain,
    ! [X25290,X25291] : hAPP(c_Set_OCollect(X25291),hAPP(hAPP(c_COMBC(X25291,tc_fun(X25291,tc_HOL_Obool),tc_HOL_Obool),c_member(X25291)),X25290)) = X25290,
    inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).

fof(i_0_8700,plain,
    ! [X22469,X22470] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22470),X22469))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).

fof(i_0_8701,plain,
    ! [X33941,X33942,X33943,X33944,X33945,X33946,X33947] :
      ( ( ~ c_List_Oall__interval__nat(X33943,X33942,X33941)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33944),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33942),X33941)))
        | hBOOL(hAPP(X33943,X33944)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk567_3(X33945,X33946,X33947)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33946),X33945)))
        | c_List_Oall__interval__nat(X33947,X33946,X33945) )
      & ( ~ hBOOL(hAPP(X33947,esk567_3(X33945,X33946,X33947)))
        | c_List_Oall__interval__nat(X33947,X33946,X33945) ) ),
    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_all__interval__nat__def])])])])])]) ).

fof(i_0_8702,plain,
    ! [X22704,X22705,X22706] :
      ( ~ class_Rings_Olinordered__semidom(X22706)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22706),c_Groups_Oone__class_Oone(X22706)),X22705))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22704))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22706),c_Groups_Oone__class_Oone(X22706)),hAPP(hAPP(c_Power_Opower__class_Opower(X22706),X22705),X22704))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).

fof(i_0_8703,plain,
    ! [X23813,X23814,X23815] :
      ( ~ class_Fields_Olinordered__field(X23815)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23815),X23814),c_Groups_Ozero__class_Ozero(X23815)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23815),X23813),c_Groups_Ozero__class_Ozero(X23815)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23815),c_Groups_Ozero__class_Ozero(X23815)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23815),X23814),X23813))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_8704,plain,
    ! [X22346,X22347,X22348] :
      ( ~ class_Rings_Olinordered__ring__strict(X22348)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22348),X22347),c_Groups_Ozero__class_Ozero(X22348)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22348),X22346),c_Groups_Ozero__class_Ozero(X22348)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22348),c_Groups_Ozero__class_Ozero(X22348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22348),X22347),X22346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_8705,plain,
    ! [X23869,X23870,X23871] :
      ( ~ class_Fields_Olinordered__field(X23871)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23871),X23870),c_Groups_Ozero__class_Ozero(X23871)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23871),X23869),c_Groups_Ozero__class_Ozero(X23871)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23871),c_Groups_Ozero__class_Ozero(X23871)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23871),X23870),X23869))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_8706,plain,
    ! [X22257,X22258,X22259] :
      ( ~ class_Rings_Oordered__ring(X22259)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22259),X22258),c_Groups_Ozero__class_Ozero(X22259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22259),X22257),c_Groups_Ozero__class_Ozero(X22259)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22259),c_Groups_Ozero__class_Ozero(X22259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22259),X22258),X22257))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_8707,plain,
    ! [X22765,X22766,X22767] :
      ( ~ class_Groups_Ocomm__monoid__add(X22767)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X22767),X22766),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22765))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22767),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X22767),X22766),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22765))),hAPP(X22766,X22765)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).

fof(i_0_8708,plain,
    ! [X20071,X20072] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20072),X20071)),X20072)),
    inference(variable_rename,[status(thm)],[i_0_5776]) ).

fof(i_0_8709,plain,
    ! [X20069,X20070] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20070),X20069)),X20069)),
    inference(variable_rename,[status(thm)],[i_0_5777]) ).

fof(i_0_8710,plain,
    ! [X26797,X26798] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26797))
      | c_Divides_OposDivAlg(X26798,X26797) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26798),X26797)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26798,X26797)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).

fof(i_0_8711,plain,
    ! [X23341,X23342] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23341),X23342)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23342),X23341))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23342)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23342),X23341))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23341),X23342)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23342)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).

fof(i_0_8712,plain,
    ! [X27614,X27615] : c_List_Olex(X27615,X27614) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X27615),tc_List_Olist(X27615)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X27615,X27614)),
    inference(variable_rename,[status(thm)],[fact_lex__def]) ).

fof(i_0_8713,plain,
    ! [X30497,X30498,X30499,X30500] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30500),X30499),hAPP(c_List_Oset(X30500),X30498)))
        | c_List_Oremove1(X30500,X30499,hAPP(hAPP(c_List_Oappend(X30500),X30498),X30497)) = hAPP(hAPP(c_List_Oappend(X30500),c_List_Oremove1(X30500,X30499,X30498)),X30497) )
      & ( hBOOL(hAPP(hAPP(c_member(X30500),X30499),hAPP(c_List_Oset(X30500),X30498)))
        | c_List_Oremove1(X30500,X30499,hAPP(hAPP(c_List_Oappend(X30500),X30498),X30497)) = hAPP(hAPP(c_List_Oappend(X30500),X30498),c_List_Oremove1(X30500,X30499,X30497)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5778])]) ).

cnf(i_0_8714,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_5779]) ).

fof(i_0_8715,plain,
    ! [X18933,X18934,X18935,X18936] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18936),X18934),X18933)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),X18934))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),X18933))
        | ~ class_Orderings_Olinorder(X18936) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),X18934))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18936),X18934),X18933)))
        | ~ class_Orderings_Olinorder(X18936) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),X18933))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18936),X18935),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18936),X18934),X18933)))
        | ~ class_Orderings_Olinorder(X18936) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).

fof(i_0_8716,plain,
    ! [X18851,X18852,X18853,X18854] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18854),X18852),X18851)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),X18852))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),X18851))
        | ~ class_Orderings_Olinorder(X18854) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),X18852))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18854),X18852),X18851)))
        | ~ class_Orderings_Olinorder(X18854) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),X18851))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18854),X18853),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18854),X18852),X18851)))
        | ~ class_Orderings_Olinorder(X18854) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).

fof(i_0_8717,plain,
    ! [X18121,X18122,X18123] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18123,X18122,c_Orderings_Obot__class_Obot(tc_fun(X18123,tc_HOL_Obool))),X18121)),
    inference(variable_rename,[status(thm)],[i_0_5780]) ).

fof(i_0_8718,plain,
    ! [X23352,X23353] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23352),X23353)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23352),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23353),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23352),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23352),X23353)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23353),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_8719,plain,
    ! [X31010,X31011] :
      ( X31011 = c_List_Olist_ONil(X31010)
      | c_Random_Oselect__weight(X31010,hAPP(hAPP(c_List_Omap(X31010,tc_prod(tc_Code__Numeral_Ocode__numeral,X31010)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X31010),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X31011)) = c_Random_Oselect(X31010,X31011) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).

fof(i_0_8720,plain,
    ! [X21469,X21470,X21471] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X21470,tc_HOL_Obool)),X21471),X21469))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21470),X21471))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21470),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21470,tc_HOL_Obool),X21469))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).

fof(i_0_8721,plain,
    ! [X25117,X25118,X25119] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),c_Groups_Ozero__class_Ozero(X25119)),X25117))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),c_Groups_Ozero__class_Ozero(X25119)),X25118))
        | hAPP(c_Groups_Oabs__class_Oabs(X25119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),X25118),X25117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25118)),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25117))
        | ~ class_Rings_Oordered__ring__abs(X25119) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),X25117),c_Groups_Ozero__class_Ozero(X25119)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),c_Groups_Ozero__class_Ozero(X25119)),X25118))
        | hAPP(c_Groups_Oabs__class_Oabs(X25119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),X25118),X25117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25118)),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25117))
        | ~ class_Rings_Oordered__ring__abs(X25119) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),c_Groups_Ozero__class_Ozero(X25119)),X25117))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),X25118),c_Groups_Ozero__class_Ozero(X25119)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),X25118),X25117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25118)),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25117))
        | ~ class_Rings_Oordered__ring__abs(X25119) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),X25117),c_Groups_Ozero__class_Ozero(X25119)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25119),X25118),c_Groups_Ozero__class_Ozero(X25119)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),X25118),X25117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25119),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25118)),hAPP(c_Groups_Oabs__class_Oabs(X25119),X25117))
        | ~ class_Rings_Oordered__ring__abs(X25119) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).

cnf(i_0_8722,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5781]) ).

fof(i_0_8723,plain,
    ! [X30009,X30010,X30011] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30011),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30010)),X30009)))
      | c_List_Obutlast(X30010,hAPP(hAPP(c_List_Otake(X30010),X30011),X30009)) = hAPP(hAPP(c_List_Otake(X30010),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30011),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).

fof(i_0_8724,plain,
    ! [X22783,X22784] :
      ( ~ class_Orderings_Oorder(X22784)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22784,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X22784),X22783),c_Orderings_Obot__class_Obot(tc_fun(X22784,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X22784),X22783)) = hAPP(hAPP(c_Set_Oinsert(X22784),X22783),c_Orderings_Obot__class_Obot(tc_fun(X22784,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).

fof(i_0_8725,plain,
    ! [X20726,X20727,X20728,X20729,X20730,X20731,X20732,X20733] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20728,tc_HOL_Obool)),X20727),X20726) != c_Orderings_Obot__class_Obot(tc_fun(X20728,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X20728),X20729),X20727))
        | ~ hBOOL(hAPP(hAPP(c_member(X20728),X20730),X20726))
        | X20729 != X20730 )
      & ( hBOOL(hAPP(hAPP(c_member(X20733),esk89_3(X20731,X20732,X20733)),X20732))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20733,tc_HOL_Obool)),X20732),X20731) = c_Orderings_Obot__class_Obot(tc_fun(X20733,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20733),esk90_3(X20731,X20732,X20733)),X20731))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20733,tc_HOL_Obool)),X20732),X20731) = c_Orderings_Obot__class_Obot(tc_fun(X20733,tc_HOL_Obool)) )
      & ( esk89_3(X20731,X20732,X20733) = esk90_3(X20731,X20732,X20733)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20733,tc_HOL_Obool)),X20732),X20731) = c_Orderings_Obot__class_Obot(tc_fun(X20733,tc_HOL_Obool)) ) ),
    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_disjoint__iff__not__equal])])])])])]) ).

fof(i_0_8726,plain,
    ! [X32106,X32107,X32108] :
      ( ~ class_Orderings_Olinorder(X32108)
      | ~ hBOOL(hAPP(hAPP(c_member(X32108),X32107),hAPP(c_List_Oset(X32108),X32106)))
      | ~ c_List_Olinorder__class_Osorted(X32108,X32106)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32108,X32108,c_COMBI(X32108)),X32107),c_List_Oremove1(X32108,X32107,X32106)) = X32106 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).

fof(i_0_8727,plain,
    ! [X26776,X26777] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26777),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26776))
      | c_Divides_OnegDivAlg(X26777,X26776) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26777),X26776)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26777,X26776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).

fof(i_0_8728,plain,
    ! [X21981,X21982,X21983] :
      ( ~ class_Lattices_Olattice(X21983)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21983),X21982))
      | X21981 = c_Orderings_Obot__class_Obot(tc_fun(X21983,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21983,tc_HOL_Obool)),X21981),X21982))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21983),c_Big__Operators_Olattice__class_OInf__fin(X21983,X21981)),c_Big__Operators_Olattice__class_OInf__fin(X21983,X21982)) = c_Big__Operators_Olattice__class_OInf__fin(X21983,X21982) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).

fof(i_0_8729,plain,
    ! [X20345,X20346,X20347] :
      ( ~ class_Lattices_Olattice(X20347)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20347),X20346))
      | X20345 = c_Orderings_Obot__class_Obot(tc_fun(X20347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20347,tc_HOL_Obool)),X20345),X20346))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20347),c_Big__Operators_Olattice__class_OSup__fin(X20347,X20345)),c_Big__Operators_Olattice__class_OSup__fin(X20347,X20346)) = c_Big__Operators_Olattice__class_OSup__fin(X20347,X20346) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).

fof(i_0_8730,plain,
    ! [X19135,X19136,X19137] :
      ( ~ class_Orderings_Olinorder(X19137)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19137),X19136))
      | X19135 = c_Orderings_Obot__class_Obot(tc_fun(X19137,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19137,tc_HOL_Obool)),X19135),X19136))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X19137),c_Big__Operators_Olinorder__class_OMax(X19137,X19135)),c_Big__Operators_Olinorder__class_OMax(X19137,X19136)) = c_Big__Operators_Olinorder__class_OMax(X19137,X19136) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).

fof(i_0_8731,plain,
    ! [X19138,X19139,X19140] :
      ( ~ class_Orderings_Olinorder(X19140)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19140),X19139))
      | X19138 = c_Orderings_Obot__class_Obot(tc_fun(X19140,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19140,tc_HOL_Obool)),X19138),X19139))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X19140),c_Big__Operators_Olinorder__class_OMin(X19140,X19138)),c_Big__Operators_Olinorder__class_OMin(X19140,X19139)) = c_Big__Operators_Olinorder__class_OMin(X19140,X19139) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).

fof(i_0_8732,plain,
    ! [X24588,X24589,X24590] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24590,X24589)),X24588),X24589) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24590),X24588),X24589),
    inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).

fof(i_0_8733,plain,
    ! [X24591,X24592,X24593] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24593,X24592)),X24591),X24592) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24593),X24591),X24592),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(i_0_8734,plain,
    ! [X21740,X21741,X21742,X21743] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21742),X21741),c_Complete__Lattice_OInf__class_OInf(X21742,X21740)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21742),X21743),X21740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21742),X21741),X21743))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21742) )
      & ( hBOOL(hAPP(hAPP(c_member(X21742),esk110_3(X21740,X21741,X21742)),X21740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21742),X21741),c_Complete__Lattice_OInf__class_OInf(X21742,X21740)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21742) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21742),X21741),esk110_3(X21740,X21741,X21742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21742),X21741),c_Complete__Lattice_OInf__class_OInf(X21742,X21740)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X21742) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Inf__iff])])])])]) ).

fof(i_0_8735,plain,
    ! [X30297,X30298,X30299,X30300] :
      ( ( X30300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X30299),X30300),hAPP(hAPP(c_List_Olist_OCons(X30299),X30298),X30297)) = c_List_Olist_ONil(X30299) )
      & ( X30300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X30299),X30300),hAPP(hAPP(c_List_Olist_OCons(X30299),X30298),X30297)) = hAPP(hAPP(c_List_Olist_OCons(X30299),X30298),hAPP(hAPP(c_List_Otake(X30299),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30300),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30297)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).

fof(i_0_8736,plain,
    ! [X20457,X20458,X20459,X20460] :
      ( ~ hBOOL(hAPP(X20460,X20459))
      | ~ hBOOL(hAPP(X20458,X20459))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20457,tc_HOL_Obool)),X20460),X20458),X20459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).

fof(i_0_8737,plain,
    ! [X33279,X33280,X33281,X33283,X33284,X33285,X33286] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33281),esk514_3(X33279,X33280,X33281)),hAPP(c_List_Oset(X33281),X33279)))
        | ~ c_List_Olist__ex(X33281,X33280,X33279) )
      & ( hBOOL(hAPP(X33280,esk514_3(X33279,X33280,X33281)))
        | ~ c_List_Olist__ex(X33281,X33280,X33279) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33285),X33286),hAPP(c_List_Oset(X33285),X33283)))
        | ~ hBOOL(hAPP(X33284,X33286))
        | c_List_Olist__ex(X33285,X33284,X33283) ) ),
    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_list__ex__iff__raw])])])])])]) ).

fof(i_0_8738,plain,
    ! [X33271,X33272,X33273,X33274,X33275,X33276,X33277] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33273),X33274),hAPP(c_List_Oset(X33273),X33272)))
        | ~ hBOOL(hAPP(X33271,X33274))
        | c_List_Olist__ex(X33273,X33271,X33272) )
      & ( hBOOL(hAPP(hAPP(c_member(X33277),esk513_3(X33275,X33276,X33277)),hAPP(c_List_Oset(X33277),X33276)))
        | ~ c_List_Olist__ex(X33277,X33275,X33276) )
      & ( hBOOL(hAPP(X33275,esk513_3(X33275,X33276,X33277)))
        | ~ c_List_Olist__ex(X33277,X33275,X33276) ) ),
    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_Bex__set__list__ex])])])])])]) ).

fof(i_0_8739,plain,
    ! [X32606,X32607,X32608,X32610,X32611,X32612,X32613] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32608),esk476_3(X32606,X32607,X32608)),hAPP(c_List_Oset(X32608),X32606)))
        | ~ c_List_Olist__ex(X32608,X32607,X32606) )
      & ( hBOOL(hAPP(X32607,esk476_3(X32606,X32607,X32608)))
        | ~ c_List_Olist__ex(X32608,X32607,X32606) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32612),X32613),hAPP(c_List_Oset(X32612),X32610)))
        | ~ hBOOL(hAPP(X32611,X32613))
        | c_List_Olist__ex(X32612,X32611,X32610) ) ),
    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_list__ex__iff])])])])])]) ).

fof(i_0_8740,plain,
    ! [X27330] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X27330)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).

fof(i_0_8741,plain,
    ! [X19822,X19823,X19824,X19825,X19826] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X19826,X19825,X19824)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19826),X19823))
      | X19823 = c_Orderings_Obot__class_Obot(tc_fun(X19826,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19826),X19822))
      | X19822 = c_Orderings_Obot__class_Obot(tc_fun(X19826,tc_HOL_Obool))
      | hAPP(X19824,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19826,tc_HOL_Obool)),X19823),X19822)) = hAPP(hAPP(X19825,hAPP(X19824,X19823)),hAPP(X19824,X19822)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).

fof(i_0_8742,plain,
    ! [X31374,X31375,X31376,X31377,X31378,X31379,X31380] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X31376,X31375),X31374))
        | ~ hBOOL(hAPP(hAPP(c_member(X31376),X31377),hAPP(c_List_Oset(X31376),X31374)))
        | hBOOL(hAPP(X31375,X31377)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31380),esk422_3(X31378,X31379,X31380)),hAPP(c_List_Oset(X31380),X31378)))
        | hBOOL(hAPP(c_List_Olistsp(X31380,X31379),X31378)) )
      & ( ~ hBOOL(hAPP(X31379,esk422_3(X31378,X31379,X31380)))
        | hBOOL(hAPP(c_List_Olistsp(X31380,X31379),X31378)) ) ),
    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_in__listsp__conv__set])])])])])]) ).

fof(i_0_8743,plain,
    ! [X22528,X22529,X22530,X22531] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22531)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22531),c_Groups_Ozero__class_Ozero(X22531)),X22530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22531),X22529),X22528))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22531),X22529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22531),X22530),X22528))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_8744,plain,
    ! [X22532,X22533,X22534,X22535] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22535)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22535),c_Groups_Ozero__class_Ozero(X22535)),X22534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22535),X22533),X22532))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22535),X22533),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22535),X22534),X22532))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_8745,plain,
    ! [X22306,X22307,X22308,X22309] :
      ( ~ class_Rings_Olinordered__semidom(X22309)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22309),c_Groups_Ozero__class_Ozero(X22309)),X22308))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22309),X22307),X22306))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22309),X22307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22309),X22308),X22306))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_8746,plain,
    ! [X22223,X22224,X22225,X22226] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22226)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22226),c_Groups_Ozero__class_Ozero(X22226)),X22225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22226),X22224),X22223))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22226),X22224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22226),X22225),X22223))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_8747,plain,
    ! [X22219,X22220,X22221,X22222] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22222)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22222),c_Groups_Ozero__class_Ozero(X22222)),X22221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22222),X22220),X22219))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22222),X22220),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22222),X22219),X22221))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_8748,plain,
    ! [X24785,X24786] : X24786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24785),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24786),X24785))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24786,X24785)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).

cnf(i_0_8749,plain,
    c_List_Oconcat(X1,c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1))) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5782]) ).

fof(i_0_8750,plain,
    ! [X20650,X20651,X20652,X20653] :
      ( ~ class_Lattices_Osemilattice__inf(X20653)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20653),X20652),X20651))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20653),X20652),X20650)),X20651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).

fof(i_0_8751,plain,
    ! [X20654,X20655,X20656,X20657] :
      ( ~ class_Lattices_Osemilattice__inf(X20657)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20657),X20656),X20655))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20657),X20654),X20656)),X20655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).

fof(i_0_8752,plain,
    ! [X18950,X18951,X18952,X18953] :
      ( ~ class_Orderings_Olinorder(X18953)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18953),X18952),X18951))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18953),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18953),X18952),X18950)),X18951)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).

fof(i_0_8753,plain,
    ! [X18946,X18947,X18948,X18949] :
      ( ~ class_Orderings_Olinorder(X18949)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18949),X18948),X18947))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18949),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18949),X18946),X18948)),X18947)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).

fof(i_0_8754,plain,
    ! [X20619,X20620,X20621,X20622] :
      ( ~ class_Lattices_Osemilattice__inf(X20622)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20622),X20621),X20620))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20622),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20622),X20621),X20619)),X20620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).

fof(i_0_8755,plain,
    ! [X20623,X20624,X20625,X20626] :
      ( ~ class_Lattices_Osemilattice__inf(X20626)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20626),X20625),X20624))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20626),X20623),X20625)),X20624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).

fof(i_0_8756,plain,
    ! [X18900,X18901,X18902,X18903] :
      ( ~ class_Orderings_Olinorder(X18903)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18903),X18902),X18901))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18903),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18903),X18902),X18900)),X18901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).

fof(i_0_8757,plain,
    ! [X18896,X18897,X18898,X18899] :
      ( ~ class_Orderings_Olinorder(X18899)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18899),X18898),X18897))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18899),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18899),X18896),X18898)),X18897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).

fof(i_0_8758,plain,
    ! [X30303,X30304] : hAPP(c_Relation_OImage(tc_List_Olist(X30304),tc_List_Olist(X30304),c_List_Olistrel(X30304,X30303)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30304)),c_List_Olist_ONil(X30304)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30304),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30304)),c_List_Olist_ONil(X30304)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30304),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).

fof(i_0_8759,plain,
    ! [X19995,X19996,X19997,X19998] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19997,tc_Nat_Onat),X19995),X19996) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X19997),X19998),X19996))
        | hAPP(X19995,X19998) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19997),X19996)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19997),esk79_3(X19995,X19996,X19997)),X19996))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19997,tc_Nat_Onat),X19995),X19996) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19997),X19996)) )
      & ( hAPP(X19995,esk79_3(X19995,X19996,X19997)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19997,tc_Nat_Onat),X19995),X19996) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19997),X19996)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff])])])])]) ).

fof(i_0_8760,plain,
    ! [X22514,X22515,X22516,X22517] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22516,tc_Nat_Onat),X22514),X22515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X22516),X22517),X22515))
        | hAPP(X22514,X22517) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22516),X22515)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22516),esk124_3(X22514,X22515,X22516)),X22515))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22516,tc_Nat_Onat),X22514),X22515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22516),X22515)) )
      & ( hAPP(X22514,esk124_3(X22514,X22515,X22516)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22516,tc_Nat_Onat),X22514),X22515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22516),X22515)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff])])])])]) ).

fof(i_0_8761,plain,
    ! [X33865,X33866,X33867,X33868,X33869] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33869),X33868),X33867))
      | hAPP(c_Quotient_OBabs(X33869,X33866,X33867,X33865),X33868) = hAPP(X33865,X33868) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Babs__def])]) ).

fof(i_0_8762,plain,
    ! [X22636,X22637,X22638,X22639,X22640,X22641,X22642] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22637),X22636))
        | hBOOL(hAPP(X22638,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X22638,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22637),X22636))) )
      & ( X22637 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22636),X22639)
        | hBOOL(hAPP(X22638,X22639))
        | ~ hBOOL(hAPP(X22638,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22637),X22636))) )
      & ( X22641 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22640),esk126_3(X22640,X22641,X22642))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22641),X22640))
        | hBOOL(hAPP(X22642,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22641),X22640))) )
      & ( ~ hBOOL(hAPP(X22642,esk126_3(X22640,X22641,X22642)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22641),X22640))
        | hBOOL(hAPP(X22642,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22641),X22640))) )
      & ( X22641 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22640),esk126_3(X22640,X22641,X22642))
        | ~ hBOOL(hAPP(X22642,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22642,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22641),X22640))) )
      & ( ~ hBOOL(hAPP(X22642,esk126_3(X22640,X22641,X22642)))
        | ~ hBOOL(hAPP(X22642,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22642,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22641),X22640))) ) ),
    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_nat__diff__split])])])])])]) ).

fof(i_0_8763,plain,
    ! [X22628,X22629,X22630,X22631,X22632,X22633,X22634] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22629),X22628))
        | hBOOL(hAPP(X22630,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X22630,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22629),X22628))) )
      & ( X22629 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22628),X22631)
        | hBOOL(hAPP(X22630,X22631))
        | ~ hBOOL(hAPP(X22630,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22629),X22628))) )
      & ( X22633 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22632),esk125_3(X22632,X22633,X22634))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22633),X22632))
        | hBOOL(hAPP(X22634,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22633),X22632))) )
      & ( ~ hBOOL(hAPP(X22634,esk125_3(X22632,X22633,X22634)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22633),X22632))
        | hBOOL(hAPP(X22634,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22633),X22632))) )
      & ( X22633 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22632),esk125_3(X22632,X22633,X22634))
        | ~ hBOOL(hAPP(X22634,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22634,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22633),X22632))) )
      & ( ~ hBOOL(hAPP(X22634,esk125_3(X22632,X22633,X22634)))
        | ~ hBOOL(hAPP(X22634,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22634,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22633),X22632))) ) ),
    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)],[i_0_5783])])])])])]) ).

fof(i_0_8764,plain,
    ! [X34033,X34034,X34035,X34036] :
      ( ~ class_Divides_Osemiring__div(X34036)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34036),X34035),X34034))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34036),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34036),X34034),X34035)),X34033) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34036),X34034),X34033)),X34035) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).

fof(i_0_8765,plain,
    ! [X19742,X19743] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19743,tc_HOL_Obool)),X19742)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),c_Orderings_Otop__class_Otop(tc_fun(X19743,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),X19742)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),c_Orderings_Otop__class_Otop(tc_fun(X19743,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19743,tc_HOL_Obool)),X19742)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19743),X19742)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).

fof(i_0_8766,plain,
    ! [X25943,X25944] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25944),X25943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25943))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25944),X25943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25943))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25944),X25943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25944),X25943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25943))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25944),X25943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25943))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_8767,plain,
    ! [X19596,X19597,X19598,X19599] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19599,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X19599),X19598),X19597)),X19596) = hAPP(hAPP(c_Set_Oinsert(X19599),X19598),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19599,tc_HOL_Obool)),X19597),X19596)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).

fof(i_0_8768,plain,
    ! [X28344,X28345,X28346,X28347] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X28347,X28346,X28345)
      | hAPP(c_Fun_Ocomp(X28346,X28346,X28346,hAPP(X28345,X28344)),hAPP(X28345,X28344)) = hAPP(X28345,X28344) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).

cnf(i_0_8769,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5739]) ).

fof(i_0_8770,plain,
    ! [X23435,X23436] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X23436,X23435)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X23436)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X23435))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I12_J]) ).

fof(i_0_8771,plain,
    ! [X16972,X16973,X16974,X16975] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(X16975,X16974,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16975)),X16973),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16975),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16975,X16974,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16975)),X16973),X16972)) )
      & ( c_Hoare__Mirabelle_Ohoare__derivs(X16975,X16974,X16972)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16975,X16974,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16975)),X16973),X16972)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_derivs__insertD])])]) ).

fof(i_0_8772,plain,
    ! [X26490,X26491,X26492,X26493] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26493,X26492),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26491),X26490)))
      | X26492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X26493,X26492) = X26490 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).

fof(i_0_8773,plain,
    ! [X26896,X26897,X26898] : hAPP(c_Product__Type_Osnd(X26898,X26897),X26896) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26898,X26897,X26897),hAPP(c_COMBK(tc_fun(X26897,X26897),X26898),c_COMBI(X26897))),X26896),
    inference(variable_rename,[status(thm)],[fact_snd__def]) ).

fof(i_0_8774,plain,
    ! [X22965,X22966] :
      ( ~ class_Int_Oring__char__0(X22966)
      | ~ hBOOL(hAPP(hAPP(c_member(X22966),X22965),c_Int_Oring__1__class_OInts(X22966)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22966),c_Groups_Oone__class_Oone(X22966)),X22965)),X22965) != c_Groups_Ozero__class_Ozero(X22966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_8775,plain,
    ! [X20487,X20488,X20489] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20489),X20488))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20489,tc_HOL_Obool)),X20488),X20487))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20489),X20487))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20489,tc_HOL_Obool)),X20488),X20487))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).

fof(i_0_8776,plain,
    ! [X17303,X17304,X17305] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17305),X17304))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17305,tc_HOL_Obool)),X17304),X17303))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).

fof(i_0_8777,plain,
    ! [X32040,X32041,X32042,X32043] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32043),X32042),X32041))
        | ~ c_List_Olinorder__class_Osorted(X32043,hAPP(hAPP(c_List_Olist_OCons(X32043),X32042),hAPP(hAPP(c_List_Olist_OCons(X32043),X32041),X32040)))
        | ~ class_Orderings_Olinorder(X32043) )
      & ( c_List_Olinorder__class_Osorted(X32043,hAPP(hAPP(c_List_Olist_OCons(X32043),X32041),X32040))
        | ~ c_List_Olinorder__class_Osorted(X32043,hAPP(hAPP(c_List_Olist_OCons(X32043),X32042),hAPP(hAPP(c_List_Olist_OCons(X32043),X32041),X32040)))
        | ~ class_Orderings_Olinorder(X32043) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32043),X32042),X32041))
        | ~ c_List_Olinorder__class_Osorted(X32043,hAPP(hAPP(c_List_Olist_OCons(X32043),X32041),X32040))
        | c_List_Olinorder__class_Osorted(X32043,hAPP(hAPP(c_List_Olist_OCons(X32043),X32042),hAPP(hAPP(c_List_Olist_OCons(X32043),X32041),X32040)))
        | ~ class_Orderings_Olinorder(X32043) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).

fof(i_0_8778,plain,
    ! [X32036,X32037,X32038,X32039] :
      ( ~ class_Orderings_Olinorder(X32039)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32039),X32038),X32037))
      | ~ c_List_Olinorder__class_Osorted(X32039,hAPP(hAPP(c_List_Olist_OCons(X32039),X32037),X32036))
      | c_List_Olinorder__class_Osorted(X32039,hAPP(hAPP(c_List_Olist_OCons(X32039),X32038),hAPP(hAPP(c_List_Olist_OCons(X32039),X32037),X32036))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).

fof(i_0_8779,plain,
    ! [X26863,X26864,X26865,X26866] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26866,X26865),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26864),X26863)))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26866,X26865) = X26863 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).

fof(i_0_8780,plain,
    ! [X24777,X24778] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24777,X24778)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24778)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24777,X24778)),X24778))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24778)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).

fof(i_0_8781,plain,
    ! [X24732,X24733] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24733))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24732,X24733)),X24733)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).

fof(i_0_8782,plain,
    ! [X24865,X24866] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24866))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24865,X24866)),X24866)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).

fof(i_0_8783,plain,
    ! [X24728,X24729] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24729))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24729,X24728)),X24729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).

fof(i_0_8784,plain,
    ! [X24889,X24890] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24890))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24889,X24890)),X24890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).

fof(i_0_8785,plain,
    ! [X31606,X31607] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31607)),c_List_Oremdups(X31607,X31606))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31607)),X31606))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__leq]) ).

fof(i_0_8786,plain,
    ! [X29861,X29862] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X29862),hAPP(c_List_Oset(X29862),X29861))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29862)),X29861))),
    inference(variable_rename,[status(thm)],[fact_card__length]) ).

fof(i_0_8787,plain,
    ! [X24501,X24502,X24503,X24504,X24505] :
      ( hAPP(c_Set_Oimage(X24505,X24504,X24503),X24502) != X24501
      | hAPP(c_Set_Oimage(tc_fun(X24505,tc_HOL_Obool),tc_fun(X24504,tc_HOL_Obool),c_Set_Oimage(X24505,X24504,X24503)),hAPP(c_Set_OPow(X24505),X24502)) = hAPP(c_Set_OPow(X24504),X24501) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).

fof(i_0_8788,plain,
    ! [X30138,X30139,X30140] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30140),X30139),hAPP(c_List_Oset(X30140),X30138)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Olist_OCons(X30140),X30139),X30138))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30140),X30138))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Olist_OCons(X30140),X30139),X30138))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30140),X30139),hAPP(c_List_Oset(X30140),X30138)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30140),X30138))
        | hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Olist_OCons(X30140),X30139),X30138))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5784])])]) ).

fof(i_0_8789,plain,
    ! [X20882,X20883,X20884,X20885] :
      ( hAPP(c_Set_Oimage(X20885,X20884,X20883),c_Orderings_Otop__class_Otop(tc_fun(X20885,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20884,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X20885,X20884,X20883),hAPP(c_Set_Ovimage(X20885,X20884,X20883),X20882)) = X20882 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).

cnf(i_0_8790,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = X3
    | c_List_Oupt(X1,X2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5718]) ).

fof(i_0_8791,plain,
    ! [X26494,X26495,X26496,X26497] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26497,X26496),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26495),X26494)))
      | X26496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26497),X26496) = X26495 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).

fof(i_0_8792,plain,
    ! [X18940,X18941,X18942] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18942),hAPP(c_Groups_Ouminus__class_Ouminus(X18942),X18941)),X18940))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18942),hAPP(c_Groups_Ouminus__class_Ouminus(X18942),X18940)),X18941))
        | ~ class_Groups_Oordered__ab__group__add(X18942) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18942),hAPP(c_Groups_Ouminus__class_Ouminus(X18942),X18940)),X18941))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18942),hAPP(c_Groups_Ouminus__class_Ouminus(X18942),X18941)),X18940))
        | ~ class_Groups_Oordered__ab__group__add(X18942) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_8793,plain,
    ! [X25065,X25066,X25067] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25067)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25067),hAPP(c_Groups_Oabs__class_Oabs(X25067),X25066)),X25065))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25067),hAPP(c_Groups_Ouminus__class_Ouminus(X25067),X25066)),X25065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).

fof(i_0_8794,plain,
    ! [X18864,X18865,X18866] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18866),hAPP(c_Groups_Ouminus__class_Ouminus(X18866),X18865)),X18864))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18866),hAPP(c_Groups_Ouminus__class_Ouminus(X18866),X18864)),X18865))
        | ~ class_Groups_Oordered__ab__group__add(X18866) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18866),hAPP(c_Groups_Ouminus__class_Ouminus(X18866),X18864)),X18865))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18866),hAPP(c_Groups_Ouminus__class_Ouminus(X18866),X18865)),X18864))
        | ~ class_Groups_Oordered__ab__group__add(X18866) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_8795,plain,
    ! [X24771,X24772] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24771,X24772)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24772),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24772),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24771,X24772)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24772),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__conj])])]) ).

fof(i_0_8796,plain,
    ! [X24773,X24774] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24774),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24773,X24774)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])]) ).

cnf(i_0_8797,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
    inference(split_conjunct,[status(thm)],[i_0_5785]) ).

fof(i_0_8798,plain,
    ! [X25316,X25317,X25318,X25319] : hAPP(c_Set_Ovimage(X25319,X25318,X25317),hAPP(c_Set_OCollect(X25318),X25316)) = hAPP(c_Set_OCollect(X25319),hAPP(hAPP(c_COMBB(X25318,tc_HOL_Obool,X25319),X25316),X25317)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(i_0_8799,plain,
    ! [X26867,X26868,X26869,X26870] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26870,X26869),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26868),X26867)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26870),X26869) = X26868 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).

fof(i_0_8800,plain,
    ! [X19695,X19696,X19697,X19698] :
      ( ~ c_Fun_Oinj__on(X19698,X19697,X19696,X19695)
      | hAPP(c_Finite__Set_Ocard(X19697),hAPP(c_Set_Oimage(X19698,X19697,X19696),X19695)) = hAPP(c_Finite__Set_Ocard(X19698),X19695) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_8801,plain,
    ! [X30609,X30610,X30611,X30612] : hAPP(hAPP(c_List_Otake(X30612),X30611),hAPP(hAPP(c_List_Odrop(X30612),X30610),X30609)) = hAPP(hAPP(c_List_Odrop(X30612),X30610),hAPP(hAPP(c_List_Otake(X30612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30611),X30610)),X30609)),
    inference(variable_rename,[status(thm)],[fact_take__drop]) ).

fof(i_0_8802,plain,
    ! [X32068,X32069,X32070,X32071,X32072] :
      ( ~ class_Orderings_Olinorder(X32072)
      | ~ c_List_Olinorder__class_Osorted(X32072,hAPP(hAPP(c_List_Omap(X32071,X32072),X32070),X32069))
      | c_List_Olinorder__class_Osorted(X32072,hAPP(hAPP(c_List_Omap(X32071,X32072),X32070),hAPP(c_List_Ofilter(X32071,X32068),X32069))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).

fof(i_0_8803,plain,
    ! [X25560,X25561,X25562] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25562,X25561) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25560,X25561)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25560),X25562))
      | X25562 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25561),esk249_3(X25560,X25561,X25562))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).

fof(i_0_8804,plain,
    ! [X32251,X32252,X32253,X32254,X32255,X32256,X32257] :
      ( ( c_List_OtakeWhile(X32253,X32252,X32251) != X32251
        | ~ hBOOL(hAPP(hAPP(c_member(X32253),X32254),hAPP(c_List_Oset(X32253),X32251)))
        | hBOOL(hAPP(X32252,X32254)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32257),esk441_3(X32255,X32256,X32257)),hAPP(c_List_Oset(X32257),X32255)))
        | c_List_OtakeWhile(X32257,X32256,X32255) = X32255 )
      & ( ~ hBOOL(hAPP(X32256,esk441_3(X32255,X32256,X32257)))
        | c_List_OtakeWhile(X32257,X32256,X32255) = X32255 ) ),
    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_takeWhile__eq__all__conv])])])])])]) ).

fof(i_0_8805,plain,
    ! [X22296,X22297] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22297),c_Groups_Ozero__class_Ozero(X22297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22297),X22296),X22296)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22297),c_Groups_Ozero__class_Ozero(X22297)),X22296))
        | ~ class_Groups_Olinordered__ab__group__add(X22297) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22297),c_Groups_Ozero__class_Ozero(X22297)),X22296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22297),c_Groups_Ozero__class_Ozero(X22297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22297),X22296),X22296)))
        | ~ class_Groups_Olinordered__ab__group__add(X22297) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).

fof(i_0_8806,plain,
    ! [X22235,X22236] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22236),c_Groups_Ozero__class_Ozero(X22236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22236),X22235),X22235)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22236),c_Groups_Ozero__class_Ozero(X22236)),X22235))
        | ~ class_Groups_Olinordered__ab__group__add(X22236) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22236),c_Groups_Ozero__class_Ozero(X22236)),X22235))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22236),c_Groups_Ozero__class_Ozero(X22236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22236),X22235),X22235)))
        | ~ class_Groups_Olinordered__ab__group__add(X22236) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])]) ).

fof(i_0_8807,plain,
    ! [X32683,X32684,X32685,X32687,X32688,X32689,X32690] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32685),esk483_3(X32683,X32684,X32685)),hAPP(c_List_Oset(X32685),X32684)))
        | c_List_Olist__all(X32685,X32683,X32684) )
      & ( ~ hBOOL(hAPP(X32683,esk483_3(X32683,X32684,X32685)))
        | c_List_Olist__all(X32685,X32683,X32684) )
      & ( ~ c_List_Olist__all(X32689,X32687,X32688)
        | ~ hBOOL(hAPP(hAPP(c_member(X32689),X32690),hAPP(c_List_Oset(X32689),X32688)))
        | hBOOL(hAPP(X32687,X32690)) ) ),
    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_Ball__set__list__all])])])])])]) ).

fof(i_0_8808,plain,
    ! [X32691,X32692,X32693,X32694,X32695,X32696,X32697] :
      ( ( ~ c_List_Olist__all(X32693,X32692,X32691)
        | ~ hBOOL(hAPP(hAPP(c_member(X32693),X32694),hAPP(c_List_Oset(X32693),X32691)))
        | hBOOL(hAPP(X32692,X32694)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32697),esk484_3(X32695,X32696,X32697)),hAPP(c_List_Oset(X32697),X32695)))
        | c_List_Olist__all(X32697,X32696,X32695) )
      & ( ~ hBOOL(hAPP(X32696,esk484_3(X32695,X32696,X32697)))
        | c_List_Olist__all(X32697,X32696,X32695) ) ),
    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_list__all__iff__raw])])])])])]) ).

fof(i_0_8809,plain,
    ! [X32662,X32663,X32664,X32665,X32666,X32667,X32668] :
      ( ( ~ c_List_Olist__all(X32664,X32663,X32662)
        | ~ hBOOL(hAPP(hAPP(c_member(X32664),X32665),hAPP(c_List_Oset(X32664),X32662)))
        | hBOOL(hAPP(X32663,X32665)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32668),esk482_3(X32666,X32667,X32668)),hAPP(c_List_Oset(X32668),X32666)))
        | c_List_Olist__all(X32668,X32667,X32666) )
      & ( ~ hBOOL(hAPP(X32667,esk482_3(X32666,X32667,X32668)))
        | c_List_Olist__all(X32668,X32667,X32666) ) ),
    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_list__all__iff])])])])])]) ).

fof(i_0_8810,plain,
    ! [X22467,X22468] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22468),X22467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22468))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22467)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22468))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22468),X22467))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22467))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22468),X22467))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_8811,plain,
    ! [X17852,X17853,X17854] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X17854),tc_HOL_Obool)),X17853),X17852))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17854,X17852,X17853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).

cnf(i_0_8812,plain,
    c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5786]) ).

fof(i_0_8813,plain,
    ! [X24671,X24672,X24673,X24674,X24675,X24676] :
      ( ~ class_Divides_Osemiring__div(X24676)
      | c_Divides_Odiv__class_Omod(X24676,X24675,X24674) != c_Divides_Odiv__class_Omod(X24676,X24673,X24674)
      | c_Divides_Odiv__class_Omod(X24676,X24672,X24674) != c_Divides_Odiv__class_Omod(X24676,X24671,X24674)
      | c_Divides_Odiv__class_Omod(X24676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24676),X24675),X24672),X24674) = c_Divides_Odiv__class_Omod(X24676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24676),X24673),X24671),X24674) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).

fof(i_0_8814,plain,
    ! [X24623,X24624,X24625,X24626,X24627,X24628] :
      ( ~ class_Divides_Osemiring__div(X24628)
      | c_Divides_Odiv__class_Omod(X24628,X24627,X24626) != c_Divides_Odiv__class_Omod(X24628,X24625,X24626)
      | c_Divides_Odiv__class_Omod(X24628,X24624,X24626) != c_Divides_Odiv__class_Omod(X24628,X24623,X24626)
      | c_Divides_Odiv__class_Omod(X24628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24628),X24627),X24624),X24626) = c_Divides_Odiv__class_Omod(X24628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24628),X24625),X24623),X24626) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).

fof(i_0_8815,plain,
    ! [X24597,X24598,X24599,X24600,X24601,X24602] :
      ( ~ class_Divides_Oring__div(X24602)
      | c_Divides_Odiv__class_Omod(X24602,X24601,X24600) != c_Divides_Odiv__class_Omod(X24602,X24599,X24600)
      | c_Divides_Odiv__class_Omod(X24602,X24598,X24600) != c_Divides_Odiv__class_Omod(X24602,X24597,X24600)
      | c_Divides_Odiv__class_Omod(X24602,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24602),X24601),X24598),X24600) = c_Divides_Odiv__class_Omod(X24602,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24602),X24599),X24597),X24600) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).

fof(i_0_8816,plain,
    ! [X34146,X34147,X34148,X34149] :
      ( ~ class_Divides_Osemiring__div(X34149)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34149),X34148),X34147))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34149),X34148),X34146))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34149),X34148),c_Divides_Odiv__class_Omod(X34149,X34147,X34146))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).

fof(i_0_8817,plain,
    ! [X23698,X23699,X23700,X23701] :
      ( ~ class_Fields_Ofield(X23701)
      | X23700 = c_Groups_Ozero__class_Ozero(X23701)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23699),X23698))
      | hAPP(hAPP(c_Power_Opower__class_Opower(X23701),X23700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23698),X23699)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23701),hAPP(hAPP(c_Power_Opower__class_Opower(X23701),X23700),X23698)),hAPP(hAPP(c_Power_Opower__class_Opower(X23701),X23700),X23699)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).

fof(i_0_8818,plain,
    ! [X17385,X17386,X17387] :
      ( hBOOL(hAPP(hAPP(c_member(X17387),X17386),X17385))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17387,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17387),X17386),X17385)),hAPP(hAPP(c_Set_Oinsert(X17387),X17386),c_Orderings_Obot__class_Obot(tc_fun(X17387,tc_HOL_Obool)))) = X17385 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5787])]) ).

fof(i_0_8819,plain,
    ! [X19116,X19117,X19118,X19119,X19120] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19120)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19119),X19118))
      | hBOOL(hAPP(hAPP(c_member(X19119),X19117),X19118))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19119,X19120),X19116),hAPP(hAPP(c_Set_Oinsert(X19119),X19117),X19118)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19120),hAPP(X19116,X19117)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19119,X19120),X19116),X19118)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5788])]) ).

fof(i_0_8820,plain,
    ! [X19111,X19112,X19113,X19114,X19115] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19115)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19114),X19113))
      | hBOOL(hAPP(hAPP(c_member(X19114),X19112),X19113))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19114,X19115),X19111),hAPP(hAPP(c_Set_Oinsert(X19114),X19112),X19113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19115),hAPP(X19111,X19112)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X19114,X19115),X19111),X19113)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5789])]) ).

fof(i_0_8821,plain,
    ! [X18159,X18160,X18161,X18162,X18163] :
      ( ~ class_Groups_Ocomm__monoid__add(X18163)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18162),X18161))
      | hBOOL(hAPP(hAPP(c_member(X18162),X18160),X18161))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18162,X18163),X18159),hAPP(hAPP(c_Set_Oinsert(X18162),X18160),X18161)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18163),hAPP(X18159,X18160)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18162,X18163),X18159),X18161)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5790])]) ).

fof(i_0_8822,plain,
    ! [X18154,X18155,X18156,X18157,X18158] :
      ( ~ class_Groups_Ocomm__monoid__add(X18158)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18157),X18156))
      | hBOOL(hAPP(hAPP(c_member(X18157),X18155),X18156))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18157,X18158),X18154),hAPP(hAPP(c_Set_Oinsert(X18157),X18155),X18156)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18158),hAPP(X18154,X18155)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18157,X18158),X18154),X18156)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5791])]) ).

fof(i_0_8823,plain,
    ! [X26822,X26823,X26824] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26824),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26823)),X26822))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26824,X26823),hAPP(c_Divides_OnegateSnd,X26822))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).

fof(i_0_8824,plain,
    ! [X17345,X17346,X17347,X17348] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17348),X17347),X17346))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17348,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17348),X17347),X17345)),X17346) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17348,tc_HOL_Obool)),X17345),X17346) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).

fof(i_0_8825,plain,
    ! [X20132,X20133,X20134] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20134),X20133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20134),X20132))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20133),X20134)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20132),X20134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20133),X20132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).

fof(i_0_8826,plain,
    ! [X32285,X32286,X32287] : c_List_OtakeWhile(X32287,X32286,X32285) = hAPP(hAPP(c_List_Otake(X32287),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32287)),c_List_OtakeWhile(X32287,X32286,X32285))),X32285),
    inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(i_0_8827,plain,
    ! [X23250,X23251,X23252,X23254,X23255,X23256] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk148_2(X23250,X23251)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23252),X23251))
        | ~ hBOOL(hAPP(X23250,X23252)) )
      & ( hBOOL(hAPP(X23250,esk148_2(X23250,X23251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23252),X23251))
        | ~ hBOOL(hAPP(X23250,X23252)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk149_2(X23254,X23255)),X23255))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23256),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23255)))
        | ~ hBOOL(hAPP(X23254,X23256)) )
      & ( hBOOL(hAPP(X23254,esk149_2(X23254,X23255)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23256),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23255)))
        | ~ hBOOL(hAPP(X23254,X23256)) ) ),
    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_ex__nat__less__eq])])])])])]) ).

fof(i_0_8828,plain,
    ! [X21588,X21589,X21590] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21590)),X21589)),hAPP(c_Nat_OSuc,X21588)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21590),X21589)),X21588),
    inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).

fof(i_0_8829,plain,
    ! [X22611,X22612,X22613,X22614] :
      ( ~ class_Rings_Olinordered__semidom(X22614)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22614),X22613),hAPP(c_Nat_OSuc,X22612)) != hAPP(hAPP(c_Power_Opower__class_Opower(X22614),X22611),hAPP(c_Nat_OSuc,X22612))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22614),c_Groups_Ozero__class_Ozero(X22614)),X22613))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22614),c_Groups_Ozero__class_Ozero(X22614)),X22611))
      | X22613 = X22611 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).

cnf(i_0_8830,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Oupt(X2,X3)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_5792]) ).

fof(i_0_8831,plain,
    ! [X33841,X33842,X33843,X33844,X33846] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33843),X33844),c_Quotient_ORespects(X33843,X33842)))
        | ~ hBOOL(hAPP(X33841,X33844))
        | hBOOL(hAPP(X33841,esk543_3(X33841,X33842,X33843)))
        | ~ c_Equiv__Relations_Oequivp(X33843,X33842) )
      & ( hBOOL(hAPP(hAPP(c_member(X33843),esk544_3(X33841,X33842,X33843)),c_Quotient_ORespects(X33843,X33842)))
        | ~ hBOOL(hAPP(X33841,X33846))
        | ~ c_Equiv__Relations_Oequivp(X33843,X33842) )
      & ( hBOOL(hAPP(X33841,esk544_3(X33841,X33842,X33843)))
        | ~ hBOOL(hAPP(X33841,X33846))
        | ~ c_Equiv__Relations_Oequivp(X33843,X33842) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__reg__eqv])])])])]) ).

fof(i_0_8832,plain,
    ! [X22854,X22855] :
      ( ( X22855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22855)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22854)))) )
      & ( X22854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22855)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22854)))) )
      & ( X22855 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22854 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22855)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22854)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).

fof(i_0_8833,plain,
    ! [X27589] :
      ( ~ class_Orderings_Owellorder(X27589)
      | c_Wellfounded_Owf(X27589,hAPP(c_Set_OCollect(tc_prod(X27589,X27589)),hAPP(c_Product__Type_Oprod_Oprod__case(X27589,X27589,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X27589)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).

fof(i_0_8834,plain,
    ! [X31806,X31807,X31808,X31809,X31810,X31811,X31812] :
      ( ( hAPP(c_List_Ofilter(X31808,X31807),X31806) != c_List_Olist_ONil(X31808)
        | ~ hBOOL(hAPP(hAPP(c_member(X31808),X31809),hAPP(c_List_Oset(X31808),X31806)))
        | ~ hBOOL(hAPP(X31807,X31809)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31812),esk432_3(X31810,X31811,X31812)),hAPP(c_List_Oset(X31812),X31810)))
        | hAPP(c_List_Ofilter(X31812,X31811),X31810) = c_List_Olist_ONil(X31812) )
      & ( hBOOL(hAPP(X31811,esk432_3(X31810,X31811,X31812)))
        | hAPP(c_List_Ofilter(X31812,X31811),X31810) = c_List_Olist_ONil(X31812) ) ),
    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)],[i_0_5793])])])])])]) ).

fof(i_0_8835,plain,
    ! [X18958,X18959,X18960,X18961] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),X18959))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18961),X18959),X18958)))
        | ~ class_Orderings_Olinorder(X18961) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),X18958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18961),X18959),X18958)))
        | ~ class_Orderings_Olinorder(X18961) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),X18959))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),X18958))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18961),X18960),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18961),X18959),X18958)))
        | ~ class_Orderings_Olinorder(X18961) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).

fof(i_0_8836,plain,
    ! [X20637,X20638,X20639,X20640] :
      ( ~ class_Lattices_Osemilattice__inf(X20640)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20640),X20639),X20638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20640),X20639),X20637))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20640),X20639),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20640),X20638),X20637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).

fof(i_0_8837,plain,
    ! [X20633,X20634,X20635,X20636] :
      ( ~ class_Lattices_Osemilattice__inf(X20636)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20636),X20635),X20634))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20636),X20635),X20633))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20636),X20635),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20636),X20634),X20633))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).

fof(i_0_8838,plain,
    ! [X20615,X20616,X20617,X20618] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),X20616))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20618),X20616),X20615)))
        | ~ class_Lattices_Osemilattice__inf(X20618) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),X20615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20618),X20616),X20615)))
        | ~ class_Lattices_Osemilattice__inf(X20618) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),X20616))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),X20615))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20618),X20616),X20615)))
        | ~ class_Lattices_Osemilattice__inf(X20618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).

fof(i_0_8839,plain,
    ! [X18904,X18905,X18906,X18907] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),X18905))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18907),X18905),X18904)))
        | ~ class_Orderings_Olinorder(X18907) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),X18904))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18907),X18905),X18904)))
        | ~ class_Orderings_Olinorder(X18907) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),X18905))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),X18904))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18907),X18906),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18907),X18905),X18904)))
        | ~ class_Orderings_Olinorder(X18907) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).

fof(i_0_8840,plain,
    ! [X18886,X18887,X18888,X18889] :
      ( ~ class_Orderings_Olinorder(X18889)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18889),X18888),X18887))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18889),X18888),X18886))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18889),X18888),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18889),X18887),X18886))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).

fof(i_0_8841,plain,
    ! [X18882,X18883,X18884,X18885] :
      ( ~ class_Orderings_Olinorder(X18885)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18885),X18884),X18883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18885),X18884),X18882))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18885),X18884),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18885),X18883),X18882))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).

fof(i_0_8842,plain,
    ! [X23013,X23014] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23014)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23013)))),
    inference(variable_rename,[status(thm)],[i_0_5794]) ).

fof(i_0_8843,plain,
    ! [X23203,X23204,X23205] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23205))
      | X23205 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23205),X23203))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23204))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23203),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).

fof(i_0_8844,plain,
    ! [X31755,X31756,X31757,X31758,X31759,X31760,X31761] :
      ( ( hAPP(c_List_Ofilter(X31757,X31756),X31755) != X31755
        | ~ hBOOL(hAPP(hAPP(c_member(X31757),X31758),hAPP(c_List_Oset(X31757),X31755)))
        | hBOOL(hAPP(X31756,X31758)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31761),esk431_3(X31759,X31760,X31761)),hAPP(c_List_Oset(X31761),X31759)))
        | hAPP(c_List_Ofilter(X31761,X31760),X31759) = X31759 )
      & ( ~ hBOOL(hAPP(X31760,esk431_3(X31759,X31760,X31761)))
        | hAPP(c_List_Ofilter(X31761,X31760),X31759) = X31759 ) ),
    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_filter__id__conv])])])])])]) ).

fof(i_0_8845,plain,
    ! [X24730,X24731] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24731))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24730))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24731,X24730))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8846,plain,
    ! [X30479,X30480,X30481,X30482] : hAPP(hAPP(c_List_Onth(X30482),hAPP(hAPP(c_List_Oappend(X30482),X30481),X30480)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30482)),X30481)),X30479)) = hAPP(hAPP(c_List_Onth(X30482),X30480),X30479),
    inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).

cnf(i_0_8847,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_List_Oset(X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_5795]) ).

fof(i_0_8848,plain,
    ! [X30321,X30322,X30323,X30324,X30325,X30326] : hAPP(c_List_Olist_Olist__case(X30326,X30325,X30324,X30323),hAPP(hAPP(c_List_Olist_OCons(X30325),X30322),X30321)) = hAPP(hAPP(X30323,X30322),X30321),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(i_0_8849,plain,
    ! [X19421,X19422,X19423,X19424] :
      ( ~ hBOOL(hAPP(X19424,X19423))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19422,tc_HOL_Obool)),X19424),X19421),X19423)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).

fof(i_0_8850,plain,
    ! [X19349,X19350,X19351,X19352] :
      ( ( ~ hBOOL(hAPP(X19352,X19351))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19349,tc_HOL_Obool)),X19350),X19352),X19351)) )
      & ( ~ hBOOL(hAPP(X19350,X19351))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19349,tc_HOL_Obool)),X19350),X19352),X19351)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5796])])]) ).

fof(i_0_8851,plain,
    ! [X19425,X19426,X19427,X19428] :
      ( ~ hBOOL(hAPP(X19428,X19427))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19426,tc_HOL_Obool)),X19425),X19428),X19427)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).

fof(i_0_8852,plain,
    ! [X25147,X25148,X25149] :
      ( ~ class_Rings_Olinordered__idom(X25149)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25149),c_Groups_Ozero__class_Ozero(X25149)),hAPP(hAPP(c_Power_Opower__class_Opower(X25149),hAPP(c_Groups_Oabs__class_Oabs(X25149),X25148)),X25147))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).

fof(i_0_8853,plain,
    ! [X21942,X21943,X21944] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21944),X21943))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21942),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21943),X21944))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21942),X21944)),hAPP(c_Nat_OSuc,X21943)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).

fof(i_0_8854,plain,
    ! [X17796,X17797] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17797,tc_HOL_Obool)),X17796),c_Orderings_Obot__class_Obot(tc_fun(X17797,tc_HOL_Obool))))
        | X17796 = c_Orderings_Obot__class_Obot(tc_fun(X17797,tc_HOL_Obool)) )
      & ( X17796 != c_Orderings_Obot__class_Obot(tc_fun(X17797,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17797,tc_HOL_Obool)),X17796),c_Orderings_Obot__class_Obot(tc_fun(X17797,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).

fof(i_0_8855,plain,
    ! [X28225,X28226] :
      ( ~ c_Wellfounded_OwfP(X28226,X28225)
      | c_Wellfounded_Oacyclic(X28226,hAPP(c_Set_OCollect(tc_prod(X28226,X28226)),hAPP(c_Product__Type_Oprod_Oprod__case(X28226,X28226,tc_HOL_Obool),X28225))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).

fof(i_0_8856,plain,
    ! [X27364,X27365,X27366,X27367] : hAPP(hAPP(c_Relation_Orel__comp(X27367,X27366,X27365),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27367,X27366),tc_HOL_Obool))),X27364) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27367,X27365),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).

fof(i_0_8857,plain,
    ! [X24830,X24831] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24830,X24831) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24830)),X24831) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24830),X24831))
        | X24831 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24830,X24831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24830)),X24831) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24830),X24831))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X24831 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if])])]) ).

fof(i_0_8858,plain,
    ! [X31404,X31405,X31406,X31407,X31408,X31409,X31410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31408),X31409),hAPP(c_List_Oset(X31408),X31405)))
        | hBOOL(hAPP(X31407,X31409))
        | c_List_Opartition(X31408,X31407,X31406) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31408),tc_List_Olist(X31408)),X31405),X31404) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31408),X31410),hAPP(c_List_Oset(X31408),X31404)))
        | ~ hBOOL(hAPP(X31407,X31410))
        | c_List_Opartition(X31408,X31407,X31406) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31408),tc_List_Olist(X31408)),X31405),X31404) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5797])])])]) ).

fof(i_0_8859,plain,
    ! [X18937,X18938,X18939] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),hAPP(c_Groups_Ouminus__class_Ouminus(X18939),X18938)),hAPP(c_Groups_Ouminus__class_Ouminus(X18939),X18937)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),X18937),X18938))
        | ~ class_Groups_Oordered__ab__group__add(X18939) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),X18937),X18938))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),hAPP(c_Groups_Ouminus__class_Ouminus(X18939),X18938)),hAPP(c_Groups_Ouminus__class_Ouminus(X18939),X18937)))
        | ~ class_Groups_Oordered__ab__group__add(X18939) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_8860,plain,
    ! [X18858,X18859,X18860] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18860),hAPP(c_Groups_Ouminus__class_Ouminus(X18860),X18859)),hAPP(c_Groups_Ouminus__class_Ouminus(X18860),X18858)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18860),X18858),X18859))
        | ~ class_Lattices_Oboolean__algebra(X18860) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18860),X18858),X18859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18860),hAPP(c_Groups_Ouminus__class_Ouminus(X18860),X18859)),hAPP(c_Groups_Ouminus__class_Ouminus(X18860),X18858)))
        | ~ class_Lattices_Oboolean__algebra(X18860) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_8861,plain,
    ! [X18867,X18868,X18869] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18869),hAPP(c_Groups_Ouminus__class_Ouminus(X18869),X18868)),hAPP(c_Groups_Ouminus__class_Ouminus(X18869),X18867)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18869),X18867),X18868))
        | ~ class_Groups_Oordered__ab__group__add(X18869) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18869),X18867),X18868))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18869),hAPP(c_Groups_Ouminus__class_Ouminus(X18869),X18868)),hAPP(c_Groups_Ouminus__class_Ouminus(X18869),X18867)))
        | ~ class_Groups_Oordered__ab__group__add(X18869) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_8862,plain,
    ! [X23242,X23243,X23245,X23246,X23247,X23249] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk146_2(X23242,X23243)),X23243))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23245),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23243)))
        | hBOOL(hAPP(X23242,X23245)) )
      & ( ~ hBOOL(hAPP(X23242,esk146_2(X23242,X23243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23245),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23243)))
        | hBOOL(hAPP(X23242,X23245)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk147_2(X23246,X23247)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23249),X23247))
        | hBOOL(hAPP(X23246,X23249)) )
      & ( ~ hBOOL(hAPP(X23246,esk147_2(X23246,X23247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23249),X23247))
        | hBOOL(hAPP(X23246,X23249)) ) ),
    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_all__nat__less__eq])])])])])]) ).

fof(i_0_8863,plain,
    ! [X21924,X21925,X21926] :
      ( ~ class_Rings_Olinordered__semidom(X21926)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21926),c_Groups_Oone__class_Oone(X21926)),X21925))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21926),c_Groups_Oone__class_Oone(X21926)),hAPP(hAPP(c_Power_Opower__class_Opower(X21926),X21925),hAPP(c_Nat_OSuc,X21924)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).

fof(i_0_8864,plain,
    ! [X33956,X33957,X33958,X33959] : hAPP(c_Lazy__Sequence_Obind(X33959,X33958,X33957),X33956) = c_Lazy__Sequence_Oflat(X33958,c_Lazy__Sequence_Omap(X33959,tc_Lazy__Sequence_Olazy__sequence(X33958),X33956,X33957)),
    inference(variable_rename,[status(thm)],[fact__05]) ).

fof(i_0_8865,plain,
    ! [X23206,X23207,X23208] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23208))
      | X23208 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23208),X23206))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23207),X23208))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23206)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).

fof(i_0_8866,plain,
    ! [X32818,X32819,X32820,X32821,X32822] :
      ( ~ hBOOL(hAPP(hAPP(X32822,X32821),X32820))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32819,X32818,X32822),X32820),X32821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])]) ).

cnf(i_0_8867,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)) = hAPP(c_Relation_ODomain(X1,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_5798]) ).

cnf(i_0_8868,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)) = hAPP(c_Relation_ORange(X1,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_5799]) ).

fof(i_0_8869,plain,
    ! [X25945,X25946] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25946)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25945)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25946),X25945))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25946),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25946),X25945))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25946)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25945))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25946),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25946)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25945))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5800])])]) ).

fof(i_0_8870,plain,
    ! [X25733,X25734,X25735] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25735),hAPP(c_Int_Onumber__class_Onumber__of(X25735),X25734)),hAPP(c_Int_Onumber__class_Onumber__of(X25735),X25733)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25734),X25733))
        | ~ class_Int_Onumber__ring(X25735)
        | ~ class_Rings_Olinordered__idom(X25735) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25734),X25733))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25735),hAPP(c_Int_Onumber__class_Onumber__of(X25735),X25734)),hAPP(c_Int_Onumber__class_Onumber__of(X25735),X25733)))
        | ~ class_Int_Onumber__ring(X25735)
        | ~ class_Rings_Olinordered__idom(X25735) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_8871,plain,
    ! [X25730,X25731,X25732] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25732),hAPP(c_Int_Onumber__class_Onumber__of(X25732),X25731)),hAPP(c_Int_Onumber__class_Onumber__of(X25732),X25730)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25731),X25730))
        | ~ class_Int_Onumber__ring(X25732)
        | ~ class_Rings_Olinordered__idom(X25732) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25731),X25730))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25732),hAPP(c_Int_Onumber__class_Onumber__of(X25732),X25731)),hAPP(c_Int_Onumber__class_Onumber__of(X25732),X25730)))
        | ~ class_Int_Onumber__ring(X25732)
        | ~ class_Rings_Olinordered__idom(X25732) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_8872,plain,
    ! [X34166,X34167,X34168] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34168),X34166))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34167),X34166))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34166),X34167))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34168),X34167))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34167),X34168)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34166),X34168))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34167),X34166))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34166),X34167))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34168),X34167))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34167),X34168)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5801])])]) ).

fof(i_0_8873,plain,
    ! [X30012,X30013,X30014,X30015] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30015)),X30014)),X30013))
      | hAPP(hAPP(c_List_Olist__update(X30015,X30014),X30013),X30012) = X30014 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).

fof(i_0_8874,plain,
    ! [X19981] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19981),X19981)))),
    inference(variable_rename,[status(thm)],[fact_le__cube]) ).

fof(i_0_8875,plain,
    ! [X30070,X30071,X30072] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30072),X30071),hAPP(c_List_Oset(X30072),c_List_Obutlast(X30072,X30070))))
      | hBOOL(hAPP(hAPP(c_member(X30072),X30071),hAPP(c_List_Oset(X30072),X30070))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).

fof(i_0_8876,plain,
    ! [X17009,X17010,X17011,X17012,X17013] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17013),X17012),X17011))
      | hAPP(hAPP(c_Set_Oinsert(X17010),hAPP(X17009,X17012)),hAPP(c_Set_Oimage(X17013,X17010,X17009),X17011)) = hAPP(c_Set_Oimage(X17013,X17010,X17009),X17011) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

cnf(i_0_8877,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5802]) ).

cnf(i_0_8878,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5803]) ).

fof(i_0_8879,plain,
    ! [X26487,X26488,X26489] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26489,X26489),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26488),X26487)))
      | X26489 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X26488 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).

fof(i_0_8880,plain,
    ! [X26471,X26472,X26473] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26473,X26473),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26472),X26471)))
      | X26473 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X26471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).

fof(i_0_8881,plain,
    ! [X17523,X17524,X17525,X17526,X17527] :
      ( ~ c_Finite__Set_Ofolding__one(X17527,X17526,X17525)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17527),X17524))
      | hBOOL(hAPP(hAPP(c_member(X17527),X17523),X17524))
      | hAPP(X17525,hAPP(hAPP(c_Set_Oinsert(X17527),X17523),X17524)) = hAPP(hAPP(c_Finite__Set_Ofold(X17527,X17527,X17526),X17523),X17524) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5804])]) ).

fof(i_0_8882,plain,
    ! [X29291,X29292,X29293] :
      ( ~ c_Wellfounded_Owf(X29293,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29293,X29293),tc_HOL_Obool),X29292),X29291))
      | c_Wellfounded_Owf(X29293,X29291) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).

fof(i_0_8883,plain,
    ! [X24047,X24048,X24049] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24049),hAPP(c_Int_Oring__1__class_Oof__int(X24049),X24048)),hAPP(c_Int_Oring__1__class_Oof__int(X24049),X24047)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24048),X24047))
        | ~ class_Rings_Olinordered__idom(X24049) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24048),X24047))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24049),hAPP(c_Int_Oring__1__class_Oof__int(X24049),X24048)),hAPP(c_Int_Oring__1__class_Oof__int(X24049),X24047)))
        | ~ class_Rings_Olinordered__idom(X24049) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).

fof(i_0_8884,plain,
    ! [X22911,X22912,X22913] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22913),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22913),X22912)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22913),X22911)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22912),X22911))
        | ~ class_Rings_Olinordered__semidom(X22913) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22912),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22913),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22913),X22912)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22913),X22911)))
        | ~ class_Rings_Olinordered__semidom(X22913) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).

fof(i_0_8885,plain,
    ! [X22905,X22906,X22907] :
      ( ~ class_Rings_Olinordered__semidom(X22907)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22907),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22907),X22906)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22907),X22905)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22906),X22905)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).

fof(i_0_8886,plain,
    ! [X24044,X24045,X24046] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),hAPP(c_Int_Oring__1__class_Oof__int(X24046),X24045)),hAPP(c_Int_Oring__1__class_Oof__int(X24046),X24044)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24045),X24044))
        | ~ class_Rings_Olinordered__idom(X24046) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24045),X24044))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),hAPP(c_Int_Oring__1__class_Oof__int(X24046),X24045)),hAPP(c_Int_Oring__1__class_Oof__int(X24046),X24044)))
        | ~ class_Rings_Olinordered__idom(X24046) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).

fof(i_0_8887,plain,
    ! [X22914,X22915,X22916] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22916),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22916),X22915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22916),X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22915),X22914))
        | ~ class_Rings_Olinordered__semidom(X22916) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22915),X22914))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22916),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22916),X22915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22916),X22914)))
        | ~ class_Rings_Olinordered__semidom(X22916) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).

fof(i_0_8888,plain,
    ! [X28259] :
      ( X28259 = hAPP(c_Int_OAbs__Integ,esk318_1(X28259))
      & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk318_1(X28259)),c_Int_OInteg)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5805])])]) ).

cnf(i_0_8889,plain,
    ( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5806]) ).

cnf(i_0_8890,plain,
    ( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5807]) ).

fof(i_0_8891,plain,
    ! [X23636,X23637,X23638,X23639] :
      ( ~ class_Fields_Ofield(X23639)
      | X23638 = c_Groups_Ozero__class_Ozero(X23639)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X23639),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23639),X23637),X23638)),X23636) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23639),hAPP(hAPP(c_Power_Opower__class_Opower(X23639),X23637),X23636)),hAPP(hAPP(c_Power_Opower__class_Opower(X23639),X23638),X23636)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).

fof(i_0_8892,plain,
    ! [X23080,X23081] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23081),X23080))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23081),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23080)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

fof(i_0_8893,plain,
    ! [X21984,X21985,X21986] :
      ( ~ class_Lattices_Olattice(X21986)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21986),X21985))
      | X21985 = c_Orderings_Obot__class_Obot(tc_fun(X21986,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21986),X21984))
      | X21984 = c_Orderings_Obot__class_Obot(tc_fun(X21986,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X21986,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21986,tc_HOL_Obool)),X21985),X21984)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21986),c_Big__Operators_Olattice__class_OInf__fin(X21986,X21985)),c_Big__Operators_Olattice__class_OInf__fin(X21986,X21984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).

fof(i_0_8894,plain,
    ! [X20348,X20349,X20350] :
      ( ~ class_Lattices_Olattice(X20350)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20350),X20349))
      | X20349 = c_Orderings_Obot__class_Obot(tc_fun(X20350,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20350),X20348))
      | X20348 = c_Orderings_Obot__class_Obot(tc_fun(X20350,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20350,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20350,tc_HOL_Obool)),X20349),X20348)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20350),c_Big__Operators_Olattice__class_OSup__fin(X20350,X20349)),c_Big__Operators_Olattice__class_OSup__fin(X20350,X20348)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).

fof(i_0_8895,plain,
    ! [X19340,X19341,X19342] :
      ( ~ class_Orderings_Olinorder(X19342)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19342),X19341))
      | X19341 = c_Orderings_Obot__class_Obot(tc_fun(X19342,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19342),X19340))
      | X19340 = c_Orderings_Obot__class_Obot(tc_fun(X19342,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X19342,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19342,tc_HOL_Obool)),X19341),X19340)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19342),c_Big__Operators_Olinorder__class_OMin(X19342,X19341)),c_Big__Operators_Olinorder__class_OMin(X19342,X19340)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).

fof(i_0_8896,plain,
    ! [X19337,X19338,X19339] :
      ( ~ class_Orderings_Olinorder(X19339)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19339),X19338))
      | X19338 = c_Orderings_Obot__class_Obot(tc_fun(X19339,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19339),X19337))
      | X19337 = c_Orderings_Obot__class_Obot(tc_fun(X19339,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X19339,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19339,tc_HOL_Obool)),X19338),X19337)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19339),c_Big__Operators_Olinorder__class_OMax(X19339,X19338)),c_Big__Operators_Olinorder__class_OMax(X19339,X19337)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).

fof(i_0_8897,plain,
    ! [X32793,X32794,X32795,X32796,X32797] : c_List_Osplice(X32797,hAPP(hAPP(c_List_Olist_OCons(X32797),X32796),X32795),hAPP(hAPP(c_List_Olist_OCons(X32797),X32794),X32793)) = hAPP(hAPP(c_List_Olist_OCons(X32797),X32796),hAPP(hAPP(c_List_Olist_OCons(X32797),X32794),c_List_Osplice(X32797,X32795,X32793))),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(i_0_8898,plain,
    ! [X31276,X31277] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X31277) != hAPP(c_Code__Numeral_Oof__nat,X31276)
        | X31277 = X31276
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31276),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31277),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
      & ( X31277 != X31276
        | hAPP(c_Code__Numeral_Oof__nat,X31277) = hAPP(c_Code__Numeral_Oof__nat,X31276)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31276),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31277),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject])])]) ).

fof(i_0_8899,plain,
    ! [X23676,X23677] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23676)),hAPP(c_Int_Onat,X23677)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23676),X23677))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23677)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23676),X23677))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23676)),hAPP(c_Int_Onat,X23677)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23677)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).

fof(i_0_8900,plain,
    ! [X23702,X23703] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23703)),hAPP(c_Int_Onat,X23702)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23703),X23702))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23703)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23703),X23702))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23703)),hAPP(c_Int_Onat,X23702)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23703)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).

fof(i_0_8901,plain,
    ! [X23710,X23711] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23711)),hAPP(c_Int_Onat,X23710)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23711),X23710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23711)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23711),X23710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23711)),hAPP(c_Int_Onat,X23710)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23711)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23711)),hAPP(c_Int_Onat,X23710)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23711),X23710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23710)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23711),X23710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23711)),hAPP(c_Int_Onat,X23710)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23710)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).

fof(i_0_8902,plain,
    ! [X29298,X29299,X29300,X29301] : hAPP(X29301,hAPP(hAPP(hAPP(c_Nat_Ocompow(X29300,X29300),X29299),X29301),X29298)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X29300,X29300),X29299),X29301),hAPP(X29301,X29298)),
    inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).

fof(i_0_8903,plain,
    ! [X31784,X31785,X31786,X31787,X31788,X31789] :
      ( ~ class_Orderings_Olinorder(X31789)
      | hBOOL(hAPP(X31788,X31787))
      | hAPP(c_List_Ofilter(X31786,X31788),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31786,X31789,X31785),X31787),X31784)) = hAPP(c_List_Ofilter(X31786,X31788),X31784) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5808])]) ).

fof(i_0_8904,plain,
    ! [X18639,X18640,X18641,X18642] :
      ( ~ class_Rings_Ocomm__semiring__1(X18642)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18642),X18641),X18640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18642),X18639),X18640)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18642),X18641),X18639)),X18640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_8905,plain,
    ! [X23598,X23599,X23600,X23601] :
      ( ~ class_Rings_Odivision__ring(X23601)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23601),X23600),X23599)),X23598) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23601),X23600),X23598)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23601),X23599),X23598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_8906,plain,
    ! [X23590,X23591,X23592,X23593] :
      ( ~ class_Rings_Odivision__ring(X23593)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23593),X23592),X23591)),X23590) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23593),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23593),X23592),X23590)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23593),X23591),X23590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).

fof(i_0_8907,plain,
    ! [X20676,X20677,X20678,X20679] :
      ( ~ class_Lattices_Odistrib__lattice(X20679)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20679),X20678),X20677)),X20676) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20679),X20678),X20676)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20679),X20677),X20676)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).

fof(i_0_8908,plain,
    ! [X23576,X23577,X23578,X23579] :
      ( ~ class_Fields_Ofield__inverse__zero(X23579)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X23579),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23579),X23578),X23577)),X23576) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23579),hAPP(hAPP(c_Power_Opower__class_Opower(X23579),X23578),X23576)),hAPP(hAPP(c_Power_Opower__class_Opower(X23579),X23577),X23576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).

fof(i_0_8909,plain,
    ! [X20396,X20397,X20398,X20399] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20399)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20399),X20398),X20397)),X20396) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20399),hAPP(hAPP(c_Power_Opower__class_Opower(X20399),X20398),X20396)),hAPP(hAPP(c_Power_Opower__class_Opower(X20399),X20397),X20396)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).

fof(i_0_8910,plain,
    ! [X20317,X20318,X20319,X20320] :
      ( ~ class_Rings_Ocomm__semiring__1(X20320)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20320),X20319),X20318)),X20317) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20320),hAPP(hAPP(c_Power_Opower__class_Opower(X20320),X20319),X20317)),hAPP(hAPP(c_Power_Opower__class_Opower(X20320),X20318),X20317)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).

fof(i_0_8911,plain,
    ! [X20680,X20681,X20682,X20683] :
      ( ~ class_Lattices_Odistrib__lattice(X20683)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20683),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20683),X20682),X20681)),X20680) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20683),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20683),X20682),X20680)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20683),X20681),X20680)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).

fof(i_0_8912,plain,
    ! [X18712,X18713,X18714,X18715] :
      ( ~ class_Orderings_Olinorder(X18715)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18715),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18715),X18714),X18713)),X18712) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18715),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18715),X18714),X18712)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18715),X18713),X18712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).

fof(i_0_8913,plain,
    ! [X18708,X18709,X18710,X18711] :
      ( ~ class_Orderings_Olinorder(X18711)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18711),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18711),X18710),X18709)),X18708) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18711),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18711),X18710),X18708)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18711),X18709),X18708)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).

fof(i_0_8914,plain,
    ! [X18560,X18561,X18562,X18563] :
      ( ~ class_Rings_Ocomm__semiring(X18563)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18563),X18562),X18561)),X18560) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18563),X18562),X18560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18563),X18561),X18560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_8915,plain,
    ! [X18564,X18565,X18566,X18567] :
      ( ~ class_Rings_Ocomm__semiring__1(X18567)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18567),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18567),X18566),X18565)),X18564) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18567),X18566),X18564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18567),X18565),X18564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_8916,plain,
    ! [X18962,X18963,X18964,X18965] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18965)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18965),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18965),X18964),X18963)),X18962) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18965),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18965),X18964),X18962)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18965),X18963),X18962)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).

fof(i_0_8917,plain,
    ! [X18993,X18994,X18995,X18996] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18996)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18996),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18996),X18995),X18994)),X18993) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18996),X18995),X18993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18996),X18994),X18993)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).

fof(i_0_8918,plain,
    ! [X19010,X19011,X19012,X19013] :
      ( ~ class_Groups_Oordered__ab__group__add(X19013)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19013),hAPP(hAPP(c_Orderings_Oord__class_Omax(X19013),X19012),X19011)),X19010) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19013),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19013),X19012),X19010)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19013),X19011),X19010)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).

fof(i_0_8919,plain,
    ! [X19017,X19018,X19019,X19020] :
      ( ~ class_Groups_Oordered__ab__group__add(X19020)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19020),hAPP(hAPP(c_Orderings_Oord__class_Omin(X19020),X19019),X19018)),X19017) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19020),X19019),X19017)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19020),X19018),X19017)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).

fof(i_0_8920,plain,
    ! [X30904,X30905,X30906,X30907,X30908] :
      ( ~ class_Orderings_Olinorder(X30908)
      | hAPP(c_List_Oset(X30907),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30907,X30908,X30906),X30905),X30904)) = hAPP(hAPP(c_Set_Oinsert(X30907),X30905),hAPP(c_List_Oset(X30907),X30904)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).

fof(i_0_8921,plain,
    ! [X22484,X22485] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22485))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22485),X22484))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22484))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22485),X22484))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22485))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22484))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22485),X22484))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).

fof(i_0_8922,plain,
    ! [X23305,X23306] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23306))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23305))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23306),X23305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8923,plain,
    ! [X23171,X23172] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23171))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23172),X23171))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8924,plain,
    ! [X23057,X23058] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23058))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23057))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23058),X23057))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8925,plain,
    ! [X34018,X34019,X34020,X34021,X34022] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34022),X34019),X34021) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34022),X34018),X34020)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34022),X34019),X34020) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34022),X34021),X34018)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34022),X34020),X34018))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34022),X34021),X34019))
        | X34020 = c_Groups_Ozero__class_Ozero(X34022)
        | X34021 = c_Groups_Ozero__class_Ozero(X34022)
        | ~ class_Divides_Osemiring__div(X34022) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34022),X34019),X34020) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34022),X34021),X34018)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34022),X34019),X34021) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34022),X34018),X34020)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34022),X34020),X34018))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34022),X34021),X34019))
        | X34020 = c_Groups_Ozero__class_Ozero(X34022)
        | X34021 = c_Groups_Ozero__class_Ozero(X34022)
        | ~ class_Divides_Osemiring__div(X34022) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).

fof(i_0_8926,plain,
    ! [X19259,X19260,X19261] :
      ( ~ class_Orderings_Olinorder(X19261)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19261),X19260))
      | hBOOL(hAPP(hAPP(c_member(X19261),X19259),X19260))
      | c_Big__Operators_Olattice_OInf__fin(X19261,c_Orderings_Oord__class_Omin(X19261),hAPP(hAPP(c_Set_Oinsert(X19261),X19259),X19260)) = hAPP(hAPP(c_Finite__Set_Ofold(X19261,X19261,c_Orderings_Oord__class_Omin(X19261)),X19259),X19260) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5809])]) ).

fof(i_0_8927,plain,
    ! [X19262,X19263,X19264] :
      ( ~ class_Orderings_Olinorder(X19264)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19264),X19263))
      | hBOOL(hAPP(hAPP(c_member(X19264),X19262),X19263))
      | c_Big__Operators_Olattice_OSup__fin(X19264,c_Orderings_Oord__class_Omax(X19264),hAPP(hAPP(c_Set_Oinsert(X19264),X19262),X19263)) = hAPP(hAPP(c_Finite__Set_Ofold(X19264,X19264,c_Orderings_Oord__class_Omax(X19264)),X19262),X19263) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5810])]) ).

fof(i_0_8928,plain,
    ! [X24381,X24382] :
      ( ~ class_Orderings_Olinorder(X24382)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24382,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24382),X24381),c_Orderings_Obot__class_Obot(tc_fun(X24382,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24382),X24381)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24382),X24381) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).

fof(i_0_8929,plain,
    ! [X29112,X29113,X29114] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29114,X29113)),hAPP(c_Relation_Oconverse(X29113,X29114),X29112)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29113,X29114)),X29112)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29113,X29114)),X29112))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29114,X29113)),hAPP(c_Relation_Oconverse(X29113,X29114),X29112))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).

fof(i_0_8930,plain,
    ! [X22709] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22709),c_Orderings_Otop__class_Otop(tc_fun(X22709,tc_HOL_Obool))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22709),c_Orderings_Otop__class_Otop(tc_fun(X22709,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_8931,plain,
    ! [X30166,X30167,X30168] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30168),X30167))
      | hAPP(c_List_Oset(X30168),c_List_Oremove1(X30168,X30166,X30167)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30168,tc_HOL_Obool)),hAPP(c_List_Oset(X30168),X30167)),hAPP(hAPP(c_Set_Oinsert(X30168),X30166),c_Orderings_Obot__class_Obot(tc_fun(X30168,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).

fof(i_0_8932,plain,
    ! [X25011,X25012,X25013] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25013,tc_HOL_Obool)),X25012),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25013,tc_HOL_Obool),X25011)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25013,tc_HOL_Obool),tc_fun(X25013,tc_HOL_Obool)),X25011),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25013,tc_HOL_Obool)),X25012)),
    inference(variable_rename,[status(thm)],[fact_Int__Union]) ).

fof(i_0_8933,plain,
    ! [X21531,X21532,X21533] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21533,tc_HOL_Obool)),X21532),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21533,tc_HOL_Obool),X21531)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X21533,tc_HOL_Obool),tc_fun(X21533,tc_HOL_Obool)),X21531),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21533,tc_HOL_Obool)),X21532)),
    inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).

fof(i_0_8934,plain,
    ! [X30909,X30910,X30911,X30912,X30913] :
      ( ~ class_Orderings_Olinorder(X30913)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30912)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30912,X30913,X30911),X30910),X30909)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30912)),X30909)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).

fof(i_0_8935,plain,
    ! [X23743,X23744] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23744)),X23743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23743)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23744)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23743)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23744)),X23743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23744)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).

cnf(i_0_8936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5747]) ).

fof(i_0_8937,plain,
    ! [X18438,X18439] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18439,tc_HOL_Obool)),X18438),c_Orderings_Obot__class_Obot(tc_fun(X18439,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5811]) ).

fof(i_0_8938,plain,
    ! [X30925,X30926,X30927] :
      ( ~ class_Orderings_Olinorder(X30927)
      | c_List_Oremove1(X30927,X30926,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30927,X30927,c_COMBI(X30927)),X30926),X30925)) = X30925 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).

fof(i_0_8939,plain,
    ! [X28265,X28266,X28267,X28268,X28269,X28270,X28271] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X28267,X28266),X28265))
        | ~ hBOOL(hAPP(hAPP(c_member(X28267),X28268),X28265))
        | hBOOL(hAPP(X28266,X28268)) )
      & ( hBOOL(hAPP(hAPP(c_member(X28271),esk319_3(X28269,X28270,X28271)),X28269))
        | hBOOL(hAPP(c_Predicate_OPowp(X28271,X28270),X28269)) )
      & ( ~ hBOOL(hAPP(X28270,esk319_3(X28269,X28270,X28271)))
        | hBOOL(hAPP(c_Predicate_OPowp(X28271,X28270),X28269)) ) ),
    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_Powp__def])])])])])]) ).

fof(i_0_8940,plain,
    ! [X33710,X33711,X33712,X33713] : hAPP(c_Product__Type_Oprod_Oprod__case(X33713,X33712,X33711),c_Product__Type_Ocurry(X33713,X33712,X33711,X33710)) = X33710,
    inference(variable_rename,[status(thm)],[fact_split__curry]) ).

fof(i_0_8941,plain,
    ! [X26114,X26115,X26116] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X26116),X26115) != hAPP(c_Int_Onumber__class_Onumber__of(X26116),X26114)
        | c_Int_Oiszero(X26116,hAPP(c_Int_Onumber__class_Onumber__of(X26116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26115),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26114))))
        | ~ class_Int_Onumber__ring(X26116) )
      & ( ~ c_Int_Oiszero(X26116,hAPP(c_Int_Onumber__class_Onumber__of(X26116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26115),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26114))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X26116),X26115) = hAPP(c_Int_Onumber__class_Onumber__of(X26116),X26114)
        | ~ class_Int_Onumber__ring(X26116) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).

fof(i_0_8942,plain,
    ! [X30656,X30657,X30658,X30659] :
      ( ( X30658 = hAPP(hAPP(c_List_Otake(X30659),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30659)),X30658)),X30656)
        | hAPP(hAPP(c_List_Oappend(X30659),X30658),X30657) != X30656 )
      & ( X30657 = hAPP(hAPP(c_List_Odrop(X30659),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30659)),X30658)),X30656)
        | hAPP(hAPP(c_List_Oappend(X30659),X30658),X30657) != X30656 )
      & ( X30658 != hAPP(hAPP(c_List_Otake(X30659),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30659)),X30658)),X30656)
        | X30657 != hAPP(hAPP(c_List_Odrop(X30659),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30659)),X30658)),X30656)
        | hAPP(hAPP(c_List_Oappend(X30659),X30658),X30657) = X30656 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).

fof(i_0_8943,plain,
    ! [X18655,X18656,X18657] :
      ( ~ class_Groups_Oab__semigroup__mult(X18657)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18657),X18656))
      | hBOOL(hAPP(hAPP(c_member(X18657),X18655),X18656))
      | hAPP(c_Finite__Set_Ofold1(X18657,c_Groups_Otimes__class_Otimes(X18657)),hAPP(hAPP(c_Set_Oinsert(X18657),X18655),X18656)) = hAPP(hAPP(c_Finite__Set_Ofold(X18657,X18657,c_Groups_Otimes__class_Otimes(X18657)),X18655),X18656) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5812])]) ).

cnf(i_0_8944,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5813]) ).

fof(i_0_8945,plain,
    ! [X24828,X24829] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24828,X24829) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24829)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24828),X24829))
        | X24829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24828,X24829) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24829)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24828),X24829))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X24829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if])])]) ).

fof(i_0_8946,plain,
    ! [X25338,X25339] : hAPP(c_Set_OCollect(X25339),hAPP(hAPP(c_COMBC(X25339,X25339,tc_HOL_Obool),c_fequal),X25338)) = hAPP(hAPP(c_Set_Oinsert(X25339),X25338),c_Orderings_Obot__class_Obot(tc_fun(X25339,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).

cnf(i_0_8947,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5584]) ).

fof(i_0_8948,plain,
    ! [X19699,X19700,X19701] : hAPP(hAPP(c_Set_Oinsert(X19701),X19700),X19699) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19701,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X19701),X19700),c_Orderings_Obot__class_Obot(tc_fun(X19701,tc_HOL_Obool)))),X19699),
    inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).

fof(i_0_8949,plain,
    ! [X33599,X33600] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33600),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X33599,hAPP(c_Code__Numeral_Onat__of,esk534_2(X33599,X33600))))
      | hBOOL(hAPP(X33599,X33600)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__induct])])]) ).

cnf(i_0_8950,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5814]) ).

fof(i_0_8951,plain,
    ! [X19882,X19883,X19884] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19884),X19883))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19884),X19882)),X19883)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).

fof(i_0_8952,plain,
    ! [X20646,X20647,X20648,X20649] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20649),X20648),X20647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20649),X20648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20649),X20647),X20646)))
        | ~ class_Lattices_Osemilattice__inf(X20649) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20649),X20648),X20646))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20649),X20648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20649),X20647),X20646)))
        | ~ class_Lattices_Osemilattice__inf(X20649) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5815])])]) ).

fof(i_0_8953,plain,
    ! [X18873,X18874,X18875,X18876] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18876),X18875),X18874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18876),X18875),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18876),X18874),X18873)))
        | ~ class_Orderings_Olinorder(X18876) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18876),X18875),X18873))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18876),X18875),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18876),X18874),X18873)))
        | ~ class_Orderings_Olinorder(X18876) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5816])])]) ).

fof(i_0_8954,plain,
    ! [X30307,X30308,X30309] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30309),X30308),hAPP(c_List_Oset(X30309),X30307)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30309)),c_List_Oremove1(X30309,X30308,X30307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30309)),X30307)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30309),X30308),hAPP(c_List_Oset(X30309),X30307)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30309)),c_List_Oremove1(X30309,X30308,X30307)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30309)),X30307) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5817])]) ).

fof(i_0_8955,plain,
    ! [X20141,X20142,X20143] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20143),X20142))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20142),X20143)),X20141) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20142),X20141)),X20143) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).

fof(i_0_8956,plain,
    ! [X20138,X20139,X20140] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20140),X20139))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20139),X20138)),X20140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20139),X20140)),X20138) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).

fof(i_0_8957,plain,
    ! [X20759,X20760,X20761] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20761,tc_HOL_Obool)),X20760),X20759))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20761,tc_HOL_Obool)),X20760),X20759) = X20760 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).

fof(i_0_8958,plain,
    ! [X20762,X20763,X20764] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20764,tc_HOL_Obool)),X20763),X20762))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20764,tc_HOL_Obool)),X20762),X20763) = X20763 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).

fof(i_0_8959,plain,
    ! [X19609,X19610,X19611] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19611,tc_HOL_Obool)),X19610),X19609))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19611,tc_HOL_Obool)),X19610),X19609) = X19609 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).

fof(i_0_8960,plain,
    ! [X19606,X19607,X19608] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19608,tc_HOL_Obool)),X19607),X19606))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19608,tc_HOL_Obool)),X19607),X19606) = X19606 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19608,tc_HOL_Obool)),X19607),X19606) != X19606
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19608,tc_HOL_Obool)),X19607),X19606)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).

fof(i_0_8961,plain,
    ! [X19612,X19613,X19614] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19614,tc_HOL_Obool)),X19613),X19612))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19614,tc_HOL_Obool)),X19612),X19613) = X19612 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).

fof(i_0_8962,plain,
    ! [X20866,X20867,X20868,X20869] :
      ( hBOOL(hAPP(hAPP(c_member(X20869),X20868),X20867))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20869,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20869),X20868),X20866)),X20867) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20869,tc_HOL_Obool)),X20866),X20867) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5818])]) ).

fof(i_0_8963,plain,
    ! [X25314,X25315] : hAPP(c_Set_OCollect(X25315),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25315),c_fNot),X25314)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25315,tc_HOL_Obool)),hAPP(c_Set_OCollect(X25315),X25314)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(i_0_8964,plain,
    ! [X30649,X30650,X30651] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30651)),X30650)),X30649))
      | hAPP(hAPP(c_List_Odrop(X30651),X30649),X30650) = c_List_Olist_ONil(X30651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).

fof(i_0_8965,plain,
    ! [X30646,X30647,X30648] :
      ( ( hAPP(hAPP(c_List_Odrop(X30648),X30647),X30646) != c_List_Olist_ONil(X30648)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30648)),X30646)),X30647)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30648)),X30646)),X30647))
        | hAPP(hAPP(c_List_Odrop(X30648),X30647),X30646) = c_List_Olist_ONil(X30648) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).

fof(i_0_8966,plain,
    ! [X17088,X17089,X17090,X17091] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17091),X17090),hAPP(hAPP(c_Set_Oinsert(X17091),X17089),X17088)))
        | X17090 = X17089
        | hBOOL(hAPP(hAPP(c_member(X17091),X17090),X17088)) )
      & ( X17090 != X17089
        | hBOOL(hAPP(hAPP(c_member(X17091),X17090),hAPP(hAPP(c_Set_Oinsert(X17091),X17089),X17088))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17091),X17090),X17088))
        | hBOOL(hAPP(hAPP(c_member(X17091),X17090),hAPP(hAPP(c_Set_Oinsert(X17091),X17089),X17088))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_8967,plain,
    ! [X16990,X16991,X16992,X16993] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16993),X16992),hAPP(hAPP(c_Set_Oinsert(X16993),X16991),X16990)))
      | X16992 = X16991
      | hBOOL(hAPP(hAPP(c_member(X16993),X16992),X16990)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

cnf(i_0_8968,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5751]) ).

cnf(i_0_8969,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5750]) ).

cnf(i_0_8970,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5752]) ).

cnf(i_0_8971,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5753]) ).

cnf(i_0_8972,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5754]) ).

fof(i_0_8973,plain,
    ! [X29811,X29812,X29813] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29813)),X29812)),X29811))
      | hAPP(hAPP(c_List_Otake(X29813),X29811),X29812) = X29812 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).

cnf(i_0_8974,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | c_Code__Numeral_Onat__of__aux(X1,X2) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5819]) ).

cnf(i_0_8975,plain,
    c_Code__Numeral_Onat__of__aux(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_5820]) ).

cnf(i_0_8976,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5821]) ).

cnf(i_0_8977,plain,
    ( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5822]) ).

fof(i_0_8978,plain,
    ! [X23136,X23137,X23138,X23139] :
      ( ~ class_Orderings_Olinorder(X23139)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23139),X23138),X23137))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23139,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23139,X23138),X23136)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23139,X23138),X23137)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23139,X23137),X23136) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).

fof(i_0_8979,plain,
    ! [X26955,X26956,X26957,X26958,X26959,X26960,X26961] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26957,X26956),X26955))
        | ~ hBOOL(hAPP(hAPP(X26956,X26958),X26955))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26957,X26956),X26958)) )
      & ( hBOOL(hAPP(hAPP(X26960,esk275_3(X26959,X26960,X26961)),X26959))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26961,X26960),X26959)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26961,X26960),esk275_3(X26959,X26960,X26961)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26961,X26960),X26959)) ) ),
    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_accp_Oequations])])])])])]) ).

fof(i_0_8980,plain,
    ! [X26947,X26948,X26949,X26950,X26951,X26952,X26953] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26949,X26948),X26947))
        | ~ hBOOL(hAPP(hAPP(X26948,X26950),X26947))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26949,X26948),X26950)) )
      & ( hBOOL(hAPP(hAPP(X26952,esk274_3(X26951,X26952,X26953)),X26951))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26953,X26952),X26951)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26953,X26952),esk274_3(X26951,X26952,X26953)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26953,X26952),X26951)) ) ),
    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_accp_Osimps])])])])])]) ).

cnf(i_0_8981,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5823]) ).

fof(i_0_8982,plain,
    ! [X27814,X27815,X27816,X27817] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27817,X27816),X27815),hAPP(c_COMBK(tc_fun(X27816,tc_HOL_Obool),X27817),X27814)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27817,X27816),tc_HOL_Obool))
        | X27815 = c_Orderings_Obot__class_Obot(tc_fun(X27817,tc_HOL_Obool))
        | X27814 = c_Orderings_Obot__class_Obot(tc_fun(X27816,tc_HOL_Obool)) )
      & ( X27815 != c_Orderings_Obot__class_Obot(tc_fun(X27817,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27817,X27816),X27815),hAPP(c_COMBK(tc_fun(X27816,tc_HOL_Obool),X27817),X27814)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27817,X27816),tc_HOL_Obool)) )
      & ( X27814 != c_Orderings_Obot__class_Obot(tc_fun(X27816,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27817,X27816),X27815),hAPP(c_COMBK(tc_fun(X27816,tc_HOL_Obool),X27817),X27814)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27817,X27816),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).

cnf(i_0_8983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5757]) ).

fof(i_0_8984,plain,
    ! [X24383,X24384,X24385] :
      ( ~ class_Orderings_Olinorder(X24385)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24385),X24384),X24383))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24385,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24385,X24384,X24383)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24385),X24383)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24385),X24384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).

fof(i_0_8985,plain,
    ! [X24096,X24097,X24098] :
      ( ~ class_Orderings_Olinorder(X24098)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24098),X24097),X24096))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24098,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24098,X24097,X24096)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24098),X24096)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24098),X24097) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).

fof(i_0_8986,plain,
    ! [X24268,X24269,X24270] :
      ( ~ class_Orderings_Olinorder(X24270)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24270),X24269),X24268))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24270,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24270,X24269,X24268)),hAPP(c_SetInterval_Oord__class_OatLeast(X24270),X24268)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24270),X24269) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).

fof(i_0_8987,plain,
    ! [X30849,X30850] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30850)
      | c_Complete__Lattice_OSup__class_OSup(X30850,hAPP(c_List_Oset(X30850),X30849)) = hAPP(c_List_Ofoldl(X30850,X30850,c_Lattices_Osemilattice__sup__class_Osup(X30850),c_Orderings_Obot__class_Obot(X30850)),X30849) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).

fof(i_0_8988,plain,
    ! [X30851,X30852] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30852)
      | c_Complete__Lattice_OInf__class_OInf(X30852,hAPP(c_List_Oset(X30852),X30851)) = hAPP(c_List_Ofoldl(X30852,X30852,c_Lattices_Osemilattice__inf__class_Oinf(X30852),c_Orderings_Otop__class_Otop(X30852)),X30851) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).

fof(i_0_8989,plain,
    ! [X24372,X24373] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24373,X24372)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24372),X24373)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(i_0_8990,plain,
    ! [X16976,X16977,X16978,X16979] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16979),X16978))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16977),hAPP(c_Set_Oimage(X16979,X16977,X16976),X16978))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

cnf(i_0_8991,plain,
    ( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
    | esk427_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5664]) ).

cnf(i_0_8992,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
    | esk428_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5665]) ).

fof(i_0_8993,plain,
    ! [X25190,X25191,X25192] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25192)
      | c_Complete__Lattice_OSup__class_OSup(X25192,hAPP(hAPP(c_Set_Oinsert(X25192),X25191),hAPP(hAPP(c_Set_Oinsert(X25192),X25190),c_Orderings_Obot__class_Obot(tc_fun(X25192,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25192),X25191),X25190) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).

fof(i_0_8994,plain,
    ! [X21972,X21973,X21974] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21974)
      | c_Complete__Lattice_OInf__class_OInf(X21974,hAPP(hAPP(c_Set_Oinsert(X21974),X21973),hAPP(hAPP(c_Set_Oinsert(X21974),X21972),c_Orderings_Obot__class_Obot(tc_fun(X21974,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21974),X21973),X21972) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).

fof(i_0_8995,plain,
    ! [X34026,X34027,X34028,X34029] :
      ( ~ class_Divides_Osemiring__div(X34029)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34029),X34028),X34027))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34029),X34026),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34029),X34027),X34028)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34029),X34026),X34027)),X34028) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).

fof(i_0_8996,plain,
    ! [X20262,X20263,X20264,X20265] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20265),X20264),c_SetInterval_Oord_OlessThan(X20265,X20263,X20262)))
        | hBOOL(hAPP(hAPP(X20263,X20264),X20262)) )
      & ( ~ hBOOL(hAPP(hAPP(X20263,X20264),X20262))
        | hBOOL(hAPP(hAPP(c_member(X20265),X20264),c_SetInterval_Oord_OlessThan(X20265,X20263,X20262))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).

fof(i_0_8997,plain,
    ! [X20254,X20255,X20256,X20257] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20257),X20256),c_SetInterval_Oord_OatMost(X20257,X20255,X20254)))
        | hBOOL(hAPP(hAPP(X20255,X20256),X20254)) )
      & ( ~ hBOOL(hAPP(hAPP(X20255,X20256),X20254))
        | hBOOL(hAPP(hAPP(c_member(X20257),X20256),c_SetInterval_Oord_OatMost(X20257,X20255,X20254))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).

fof(i_0_8998,plain,
    ! [X20266,X20267,X20268,X20269] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20269),X20268),c_SetInterval_Oord_OgreaterThan(X20269,X20267,X20266)))
        | hBOOL(hAPP(hAPP(X20267,X20266),X20268)) )
      & ( ~ hBOOL(hAPP(hAPP(X20267,X20266),X20268))
        | hBOOL(hAPP(hAPP(c_member(X20269),X20268),c_SetInterval_Oord_OgreaterThan(X20269,X20267,X20266))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).

fof(i_0_8999,plain,
    ! [X20258,X20259,X20260,X20261] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20261),X20260),c_SetInterval_Oord_OatLeast(X20261,X20259,X20258)))
        | hBOOL(hAPP(hAPP(X20259,X20258),X20260)) )
      & ( ~ hBOOL(hAPP(hAPP(X20259,X20258),X20260))
        | hBOOL(hAPP(hAPP(c_member(X20261),X20260),c_SetInterval_Oord_OatLeast(X20261,X20259,X20258))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).

fof(i_0_9000,plain,
    ! [X31361,X31362,X31363,X31364,X31365] :
      ( c_List_Opartition(X31365,X31364,X31363) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31365),tc_List_Olist(X31365)),X31362),X31361)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31365,tc_HOL_Obool)),hAPP(c_List_Oset(X31365),X31362)),hAPP(c_List_Oset(X31365),X31361)) = hAPP(c_List_Oset(X31365),X31363) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).

fof(i_0_9001,plain,
    ! [X29789,X29790,X29791,X29792] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29792) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29791),hAPP(hAPP(c_List_Olist_OCons(X29791),X29790),X29789)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29792)) = X29790 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29792) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29791),hAPP(hAPP(c_List_Olist_OCons(X29791),X29790),X29789)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29792)) = hAPP(hAPP(c_List_Onth(X29791),X29789),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29792)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])]) ).

fof(i_0_9002,plain,
    ! [X28969,X28970] : hAPP(hAPP(c_Relation_Orel__comp(X28970,X28970,X28970),X28969),c_Transitive__Closure_Ortrancl(X28970,X28969)) = hAPP(hAPP(c_Relation_Orel__comp(X28970,X28970,X28970),c_Transitive__Closure_Ortrancl(X28970,X28969)),X28969),
    inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

cnf(i_0_9003,plain,
    c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_5824]) ).

fof(i_0_9004,plain,
    ! [X34246,X34247,X34248,X34249,X34250,X34251] : hAPP(hAPP(hAPP(c_COMBS(X34251,X34250,X34249),X34248),X34247),X34246) = hAPP(hAPP(X34248,X34246),hAPP(X34247,X34246)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

cnf(i_0_9005,plain,
    c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5825]) ).

fof(i_0_9006,plain,
    ! [X25141,X25142] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25142)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25142),hAPP(c_Groups_Ouminus__class_Ouminus(X25142),hAPP(c_Groups_Oabs__class_Oabs(X25142),X25141))),c_Groups_Ozero__class_Ozero(X25142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_9007,plain,
    ! [X19592,X19593,X19594,X19595] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19595,tc_HOL_Obool)),X19594),hAPP(hAPP(c_Set_Oinsert(X19595),X19593),X19592)) = hAPP(hAPP(c_Set_Oinsert(X19595),X19593),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19595,tc_HOL_Obool)),X19594),X19592)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).

fof(i_0_9008,plain,
    ! [X22182,X22183,X22184] :
      ( ( X22183 = c_Groups_Ozero__class_Ozero(X22184)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22183),X22183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22182),X22182)) != c_Groups_Ozero__class_Ozero(X22184)
        | ~ class_Rings_Olinordered__ring__strict(X22184) )
      & ( X22182 = c_Groups_Ozero__class_Ozero(X22184)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22183),X22183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22182),X22182)) != c_Groups_Ozero__class_Ozero(X22184)
        | ~ class_Rings_Olinordered__ring__strict(X22184) )
      & ( X22183 != c_Groups_Ozero__class_Ozero(X22184)
        | X22182 != c_Groups_Ozero__class_Ozero(X22184)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22183),X22183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22184),X22182),X22182)) = c_Groups_Ozero__class_Ozero(X22184)
        | ~ class_Rings_Olinordered__ring__strict(X22184) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_9009,plain,
    ! [X19855,X19856,X19857] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19857),X19856))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19857,tc_HOL_Obool)),X19856),X19855) = hAPP(hAPP(c_Finite__Set_Ofold(X19857,tc_fun(X19857,tc_HOL_Obool),c_Set_Oinsert(X19857)),X19855),X19856) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).

fof(i_0_9010,plain,
    ! [X26032,X26033] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X26033),X26032) != c_Groups_Ozero__class_Ozero(X26033)
        | c_Int_Oiszero(X26033,hAPP(c_Int_Onumber__class_Onumber__of(X26033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26032),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ class_Int_Onumber__ring(X26033) )
      & ( ~ c_Int_Oiszero(X26033,hAPP(c_Int_Onumber__class_Onumber__of(X26033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26032),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X26033),X26032) = c_Groups_Ozero__class_Ozero(X26033)
        | ~ class_Int_Onumber__ring(X26033) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).

fof(i_0_9011,plain,
    ! [X26034,X26035] :
      ( ( c_Groups_Ozero__class_Ozero(X26035) != hAPP(c_Int_Onumber__class_Onumber__of(X26035),X26034)
        | c_Int_Oiszero(X26035,hAPP(c_Int_Onumber__class_Onumber__of(X26035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26034))))
        | ~ class_Int_Onumber__ring(X26035) )
      & ( ~ c_Int_Oiszero(X26035,hAPP(c_Int_Onumber__class_Onumber__of(X26035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26034))))
        | c_Groups_Ozero__class_Ozero(X26035) = hAPP(c_Int_Onumber__class_Onumber__of(X26035),X26034)
        | ~ class_Int_Onumber__ring(X26035) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).

fof(i_0_9012,plain,
    ! [X33205,X33206,X33207,X33208] :
      ( ~ c_Relation_Otrans(X33208,X33207)
      | ~ c_Relation_Otrans(X33206,X33205)
      | c_Relation_Otrans(tc_prod(X33208,X33206),c_Wellfounded_Olex__prod(X33208,X33206,X33207,X33205)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).

fof(i_0_9013,plain,
    ! [X27504,X27505,X27506,X27507] :
      ( ~ c_Wellfounded_Owf(X27507,X27506)
      | ~ c_Wellfounded_Owf(X27505,X27504)
      | c_Wellfounded_Owf(tc_prod(X27507,X27505),c_Wellfounded_Olex__prod(X27507,X27505,X27506,X27504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).

cnf(i_0_9014,plain,
    c_List_Oconcat(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5826]) ).

fof(i_0_9015,plain,
    ! [X34113,X34114] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34114,X34113) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34114),X34113)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34114),X34113))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34114,X34113) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5827])]) ).

fof(i_0_9016,plain,
    ! [X34111,X34112] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34112,X34111)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34112),X34111)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34112),X34111))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34112,X34111) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5828])]) ).

fof(i_0_9017,plain,
    ! [X30130,X30131,X30132,X30133] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30133),X30132))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30133,X30131)),hAPP(hAPP(c_List_Ozip(X30133,X30131),X30132),X30130))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).

fof(i_0_9018,plain,
    ! [X30134,X30135,X30136,X30137] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30137),X30136))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30135,X30137)),hAPP(hAPP(c_List_Ozip(X30135,X30137),X30134),X30136))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).

fof(i_0_9019,plain,
    ! [X22012,X22013,X22014] :
      ( ~ class_Lattices_Olattice(X22014)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22014),X22013))
      | hBOOL(hAPP(hAPP(c_member(X22014),X22012),X22013))
      | c_Big__Operators_Olattice__class_OInf__fin(X22014,hAPP(hAPP(c_Set_Oinsert(X22014),X22012),X22013)) = hAPP(hAPP(c_Finite__Set_Ofold(X22014,X22014,c_Lattices_Osemilattice__inf__class_Oinf(X22014)),X22012),X22013) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5829])]) ).

fof(i_0_9020,plain,
    ! [X20360,X20361,X20362] :
      ( ~ class_Lattices_Olattice(X20362)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20362),X20361))
      | hBOOL(hAPP(hAPP(c_member(X20362),X20360),X20361))
      | c_Big__Operators_Olattice__class_OSup__fin(X20362,hAPP(hAPP(c_Set_Oinsert(X20362),X20360),X20361)) = hAPP(hAPP(c_Finite__Set_Ofold(X20362,X20362,c_Lattices_Osemilattice__sup__class_Osup(X20362)),X20360),X20361) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5830])]) ).

fof(i_0_9021,plain,
    ! [X19173,X19174,X19175] :
      ( ~ class_Orderings_Olinorder(X19175)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19175),X19174))
      | hBOOL(hAPP(hAPP(c_member(X19175),X19173),X19174))
      | c_Big__Operators_Olinorder__class_OMin(X19175,hAPP(hAPP(c_Set_Oinsert(X19175),X19173),X19174)) = hAPP(hAPP(c_Finite__Set_Ofold(X19175,X19175,c_Orderings_Oord__class_Omin(X19175)),X19173),X19174) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5831])]) ).

fof(i_0_9022,plain,
    ! [X19170,X19171,X19172] :
      ( ~ class_Orderings_Olinorder(X19172)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19172),X19171))
      | hBOOL(hAPP(hAPP(c_member(X19172),X19170),X19171))
      | c_Big__Operators_Olinorder__class_OMax(X19172,hAPP(hAPP(c_Set_Oinsert(X19172),X19170),X19171)) = hAPP(hAPP(c_Finite__Set_Ofold(X19172,X19172,c_Orderings_Oord__class_Omax(X19172)),X19170),X19171) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5832])]) ).

fof(i_0_9023,plain,
    ! [X25032,X25033,X25034,X25035] : hAPP(c_Set_Ovimage(X25035,X25034,X25033),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25034,tc_HOL_Obool),X25032)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25034,tc_HOL_Obool),tc_fun(X25035,tc_HOL_Obool)),X25032),c_Set_Ovimage(X25035,X25034,X25033)),
    inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).

fof(i_0_9024,plain,
    ! [X25004,X25005,X25006,X25007] : hAPP(c_Set_Oimage(X25007,X25006,X25005),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25007,tc_HOL_Obool),X25004)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25007,tc_HOL_Obool),tc_fun(X25006,tc_HOL_Obool)),X25004),c_Set_Oimage(X25007,X25006,X25005)),
    inference(variable_rename,[status(thm)],[fact_image__Union]) ).

fof(i_0_9025,plain,
    ! [X24517,X24518] : hBOOL(hAPP(hAPP(c_member(tc_fun(X24518,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24518,tc_HOL_Obool))),hAPP(c_Set_OPow(X24518),X24517))),
    inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).

fof(i_0_9026,plain,
    ! [X31123,X31124,X31125] :
      ( ~ class_Groups_Omonoid__add(X31125)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31125),hAPP(hAPP(c_List_Omap(X31124,X31125),hAPP(c_COMBK(X31125,X31124),c_Groups_Ozero__class_Ozero(X31125))),X31123)) = c_Groups_Ozero__class_Ozero(X31125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).

fof(i_0_9027,plain,
    ! [X20503,X20504,X20505] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20505,tc_HOL_Obool)),X20504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20505,tc_HOL_Obool)),X20504),X20503)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20505,tc_HOL_Obool)),X20504),X20503),
    inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).

fof(i_0_9028,plain,
    ! [X19379,X19380,X19381] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19381,tc_HOL_Obool)),X19380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19381,tc_HOL_Obool)),X19380),X19379)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19381,tc_HOL_Obool)),X19380),X19379),
    inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).

fof(i_0_9029,plain,
    ! [X19629,X19630,X19631] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19631,tc_HOL_Obool)),X19630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19631,tc_HOL_Obool)),X19629),X19630)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19631,tc_HOL_Obool)),X19630),X19629),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(i_0_9030,plain,
    ! [X30692,X30693] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30693)),X30692)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate1(X30693),X30692) = X30692 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).

fof(i_0_9031,plain,
    ! [X19653,X19654,X19655,X19656,X19657] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19657,X19656,X19655),X19654),X19653),c_Orderings_Obot__class_Obot(tc_fun(X19656,tc_HOL_Obool))) = X19653,
    inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).

cnf(i_0_9032,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5833]) ).

fof(i_0_9033,plain,
    ! [X22594,X22595] :
      ( ( X22595 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22595),X22594) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22595),X22594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22595),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22594)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).

fof(i_0_9034,plain,
    ! [X31390,X31391,X31392] : c_List_Olistsp(X31392,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31392,tc_HOL_Obool)),X31391),X31390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X31392),tc_HOL_Obool)),c_List_Olistsp(X31392,X31391)),c_List_Olistsp(X31392,X31390)),
    inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).

fof(i_0_9035,plain,
    ! [X17165,X17166,X17167,X17168,X17169,X17170] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X17170,X17169,X17168,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17170),X17167),X17166),X17165)) = hAPP(hAPP(hAPP(X17168,X17167),X17166),X17165),
    inference(variable_rename,[status(thm)],[fact_triple_Orecs]) ).

fof(i_0_9036,plain,
    ! [X17159,X17160,X17161,X17162,X17163,X17164] : c_Hoare__Mirabelle_Otriple_Otriple__case(X17164,X17163,X17162,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17164),X17161),X17160),X17159)) = hAPP(hAPP(hAPP(X17162,X17161),X17160),X17159),
    inference(variable_rename,[status(thm)],[fact_triple_Osimps_I2_J]) ).

fof(i_0_9037,plain,
    ! [X27687,X27688,X27689,X27690,X27692,X27693,X27694,X27695,X27696] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X27690,X27689,X27688),X27687))
        | hBOOL(hAPP(hAPP(X27688,esk295_2(X27687,X27688)),X27687)) )
      & ( ~ hBOOL(hAPP(hAPP(X27693,X27694),X27692))
        | hBOOL(hAPP(c_Predicate_ORangeP(X27696,X27695,X27693),X27692)) ) ),
    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_RangeP_Oequations])])])])]) ).

fof(i_0_9038,plain,
    ! [X25889,X25890] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | X25890 = X25889
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( X25890 != X25889
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( X25890 != X25889
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( X25890 != X25889
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) )
      & ( X25890 != X25889
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25890) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25889)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25890) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25889) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5834])])]) ).

fof(i_0_9039,plain,
    ! [X23746,X23747] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23747),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23747),X23746)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23747))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23746))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).

fof(i_0_9040,plain,
    ! [X33076,X33077,X33078,X33079] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X33079,X33078)),c_Nitpick_Opair__box_OPairBox(X33079,X33078,X33077,X33076)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(i_0_9041,plain,
    ! [X30028,X30029,X30030,X30031] :
      ( ( X30031 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30030)),X30029)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X30030,hAPP(hAPP(c_List_Olist__update(X30030,X30029),X30031),X30028)) = c_List_Obutlast(X30030,X30029) )
      & ( X30031 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30030)),X30029)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X30030,hAPP(hAPP(c_List_Olist__update(X30030,X30029),X30031),X30028)) = hAPP(hAPP(c_List_Olist__update(X30030,c_List_Obutlast(X30030,X30029)),X30031),X30028) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).

fof(i_0_9042,plain,
    ! [X17147,X17148,X17149,X17150,X17151] : hAPP(c_Set_Oimage(X17151,X17150,X17149),hAPP(hAPP(c_Set_Oinsert(X17151),X17148),X17147)) = hAPP(hAPP(c_Set_Oinsert(X17150),hAPP(X17149,X17148)),hAPP(c_Set_Oimage(X17151,X17150,X17149),X17147)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

cnf(i_0_9043,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
    | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5605]) ).

fof(i_0_9044,plain,
    ! [X17798,X17799,X17800] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17800,tc_HOL_Obool)),X17799),X17798))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17800),X17798))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17800),X17799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_9045,plain,
    ! [X17801,X17802,X17803] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17803),X17802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17803,tc_HOL_Obool)),X17801),X17802))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17803),X17801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_9046,plain,
    ! [X22397,X22398] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22398),hAPP(c_Groups_Ouminus__class_Ouminus(X22398),X22397)),c_Groups_Ozero__class_Ozero(X22398)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22398),c_Groups_Ozero__class_Ozero(X22398)),X22397))
        | ~ class_Groups_Oordered__ab__group__add(X22398) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22398),c_Groups_Ozero__class_Ozero(X22398)),X22397))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22398),hAPP(c_Groups_Ouminus__class_Ouminus(X22398),X22397)),c_Groups_Ozero__class_Ozero(X22398)))
        | ~ class_Groups_Oordered__ab__group__add(X22398) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_9047,plain,
    ! [X22389,X22390] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22390),hAPP(c_Groups_Ouminus__class_Ouminus(X22390),X22389)),c_Groups_Ozero__class_Ozero(X22390)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22390),c_Groups_Ozero__class_Ozero(X22390)),X22389))
        | ~ class_Groups_Oordered__ab__group__add(X22390) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22390),c_Groups_Ozero__class_Ozero(X22390)),X22389))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22390),hAPP(c_Groups_Ouminus__class_Ouminus(X22390),X22389)),c_Groups_Ozero__class_Ozero(X22390)))
        | ~ class_Groups_Oordered__ab__group__add(X22390) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_9048,plain,
    ! [X31674,X31675,X31676,X31677] :
      ( ~ class_Orderings_Olinorder(X31677)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31676)),c_List_Olinorder__class_Osort__key(X31676,X31677,X31675,X31674)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31676)),X31674) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__sort])]) ).

fof(i_0_9049,plain,
    ! [X32158,X32159,X32160,X32161] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32161)),X32160) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32159)),X32158)
      | hAPP(hAPP(c_List_Ozip(X32161,X32159),hAPP(c_List_Orev(X32161),X32160)),hAPP(c_List_Orev(X32159),X32158)) = hAPP(c_List_Orev(tc_prod(X32161,X32159)),hAPP(hAPP(c_List_Ozip(X32161,X32159),X32160),X32158)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).

fof(i_0_9050,plain,
    ! [X22145,X22146] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22146),X22145)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22146))
        | X22145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22146))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22146),X22145))) )
      & ( X22145 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22146),X22145))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).

fof(i_0_9051,plain,
    ! [X24352,X24353,X24354,X24355] :
      ( ~ class_Orderings_Olinorder(X24355)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24355,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24355,X24354,X24353)),hAPP(c_SetInterval_Oord__class_OatLeast(X24355),X24352)) = c_SetInterval_Oord__class_OatLeastAtMost(X24355,hAPP(hAPP(c_Orderings_Oord__class_Omax(X24355),X24354),X24352),X24353) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).

fof(i_0_9052,plain,
    ! [X24344,X24345,X24346,X24347] :
      ( ~ class_Orderings_Olinorder(X24347)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24347,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24347,X24346,X24345)),hAPP(c_SetInterval_Oord__class_OatMost(X24347),X24344)) = c_SetInterval_Oord__class_OatLeastAtMost(X24347,X24346,hAPP(hAPP(c_Orderings_Oord__class_Omin(X24347),X24345),X24344)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).

fof(i_0_9053,plain,
    ! [X30061,X30062,X30063,X30064] : hAPP(hAPP(c_List_Olist__update(X30064,hAPP(hAPP(c_List_Olist_OCons(X30064),X30063),X30062)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30061) = hAPP(hAPP(c_List_Olist_OCons(X30064),X30061),X30062),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(i_0_9054,plain,
    ! [X34240,X34241,X34242,X34243,X34244,X34245] : hAPP(hAPP(hAPP(c_COMBC(X34245,X34244,X34243),X34242),X34241),X34240) = hAPP(hAPP(X34242,X34240),X34241),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_9055,plain,
    ! [X34234,X34235,X34236,X34237,X34238,X34239] : hAPP(hAPP(hAPP(c_COMBB(X34239,X34238,X34237),X34236),X34235),X34234) = hAPP(X34236,hAPP(X34235,X34234)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_9056,plain,
    ! [X25816,X25817] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816)),c_Groups_Ozero__class_Ozero(X25817)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25817),hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25817),hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816))
        | ~ class_Int_Onumber__ring(X25817)
        | ~ class_Rings_Olinordered__idom(X25817) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816)),c_Groups_Ozero__class_Ozero(X25817)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25817),hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816)) = hAPP(c_Int_Onumber__class_Onumber__of(X25817),X25816)
        | ~ class_Int_Onumber__ring(X25817)
        | ~ class_Rings_Olinordered__idom(X25817) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5835])])]) ).

fof(i_0_9057,plain,
    ! [X20824,X20825,X20826,X20827] : hAPP(c_Set_Ovimage(X20827,X20826,X20825),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20826,tc_HOL_Obool)),X20824)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20827,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20827,X20826,X20825),X20824)),
    inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).

fof(i_0_9058,plain,
    ! [X24877,X24878,X24879] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24879),X24878)),X24877),X24878) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24877,X24878),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).

fof(i_0_9059,plain,
    ! [X23686,X23687] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23686))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X23687)),hAPP(c_Int_Onat,X23686)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23687),X23686)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9060,plain,
    ! [X23724,X23725] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23725))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23724))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X23725)),hAPP(c_Int_Onat,X23724)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23725),X23724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9061,plain,
    ! [X23720,X23721] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23720))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X23721)),hAPP(c_Int_Onat,X23720)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23721),X23720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9062,plain,
    ! [X23718,X23719] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23718))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23719),X23718)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X23719)),hAPP(c_Int_Onat,X23718)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).

fof(i_0_9063,plain,
    ! [X18247,X18248,X18249] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18249),X18248))
      | X18248 = c_Orderings_Obot__class_Obot(tc_fun(X18249,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18249,X18247,X18248),esk36_3(X18247,X18248,X18249))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nonempty__imp__fold1Set])])]) ).

fof(i_0_9064,plain,
    ! [X29934,X29935,X29936,X29937] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X29937,X29936))),hAPP(hAPP(c_List_Ozip(X29937,X29936),X29935),X29934)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29937)),X29935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29936)),X29934)),
    inference(variable_rename,[status(thm)],[fact_length__zip]) ).

fof(i_0_9065,plain,
    ! [X25127,X25128,X25129,X25130] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25130,tc_HOL_Obool),hAPP(c_Set_Oimage(X25129,tc_fun(X25130,tc_HOL_Obool),X25128),X25127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25129,tc_fun(X25130,tc_HOL_Obool)),X25127),X25128),
    inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).

fof(i_0_9066,plain,
    ! [X22039,X22040,X22041,X22042] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X22042,tc_HOL_Obool),hAPP(c_Set_Oimage(X22041,tc_fun(X22042,tc_HOL_Obool),X22040),X22039)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22041,tc_fun(X22042,tc_HOL_Obool)),X22039),X22040),
    inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).

fof(i_0_9067,plain,
    ! [X22035,X22036,X22037,X22038] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X22038,tc_fun(X22037,tc_HOL_Obool)),X22036),X22035) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X22037,tc_HOL_Obool),hAPP(c_Set_Oimage(X22038,tc_fun(X22037,tc_HOL_Obool),X22035),X22036)),
    inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(i_0_9068,plain,
    ! [X25123,X25124,X25125,X25126] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25126,tc_fun(X25125,tc_HOL_Obool)),X25124),X25123) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X25125,tc_HOL_Obool),hAPP(c_Set_Oimage(X25126,tc_fun(X25125,tc_HOL_Obool),X25123),X25124)),
    inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(i_0_9069,plain,
    ! [X23160,X23161,X23162,X23163] :
      ( ~ class_Rings_Osemiring__1(X23163)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X23163,X23162,hAPP(c_Nat_OSuc,X23161),X23160) = c_Nat_Osemiring__1__class_Oof__nat__aux(X23163,X23162,X23161,hAPP(X23162,X23160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).

fof(i_0_9070,plain,
    ! [X24926,X24927] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24927))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24926))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X24927),hAPP(c_Int_Onat,X24926)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24927,X24926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9071,plain,
    ! [X24928,X24929] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24929))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24928))
      | hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24929,X24928)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X24929),hAPP(c_Int_Onat,X24928)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).

fof(i_0_9072,plain,
    ! [X24798,X24799] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X24799,X24798) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24799),X24798)),X24798)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(i_0_9073,plain,
    ! [X24908,X24909] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24909,X24908) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24909),X24908)),X24908)),
    inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(i_0_9074,plain,
    ! [X22420,X22421,X22422] :
      ( ~ class_Rings_Olinordered__semidom(X22422)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22422),c_Groups_Ozero__class_Ozero(X22422)),X22421))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22422),c_Groups_Ozero__class_Ozero(X22422)),hAPP(hAPP(c_Power_Opower__class_Opower(X22422),X22421),X22420))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(i_0_9075,plain,
    ! [X22417,X22418,X22419] :
      ( ~ class_Rings_Olinordered__semidom(X22419)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22419),c_Groups_Ozero__class_Ozero(X22419)),X22418))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22419),c_Groups_Ozero__class_Ozero(X22419)),hAPP(hAPP(c_Power_Opower__class_Opower(X22419),X22418),X22417))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).

fof(i_0_9076,plain,
    ! [X20408,X20409,X20410] :
      ( ~ class_Rings_Olinordered__semidom(X20410)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20410),c_Groups_Oone__class_Oone(X20410)),X20409))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20410),c_Groups_Oone__class_Oone(X20410)),hAPP(hAPP(c_Power_Opower__class_Opower(X20410),X20409),X20408))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).

fof(i_0_9077,plain,
    ! [X17000,X17001,X17002,X17003,X17004] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17004),X17003),X17002))
      | hAPP(c_Set_Oimage(X17004,X17001,hAPP(c_COMBK(X17001,X17004),X17000)),X17002) = hAPP(hAPP(c_Set_Oinsert(X17001),X17000),c_Orderings_Obot__class_Obot(tc_fun(X17001,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).

fof(i_0_9078,plain,
    ! [X23674,X23675] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23674))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23675)),hAPP(c_Int_Onat,X23674))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23675),X23674))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23675)),hAPP(c_Int_Onat,X23674))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23674))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23675),X23674))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23675)),hAPP(c_Int_Onat,X23674))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).

fof(i_0_9079,plain,
    ! [X27909,X27910] : hAPP(hAPP(c_Product__Type_OSigma(X27910,X27909),c_Orderings_Otop__class_Otop(tc_fun(X27910,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27909,tc_HOL_Obool),X27910),c_Orderings_Otop__class_Otop(tc_fun(X27909,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27910,X27909),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(i_0_9080,plain,
    ! [X23025,X23026] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23025),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23026),X23025))
        | X23026 = X23025 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23026),X23025))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23025),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
      & ( X23026 != X23025
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23025),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).

cnf(i_0_9081,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5836]) ).

fof(i_0_9082,plain,
    ! [X22399,X22400] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22400),hAPP(c_Groups_Ouminus__class_Ouminus(X22400),X22399)),X22399))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22400),c_Groups_Ozero__class_Ozero(X22400)),X22399))
        | ~ class_Groups_Olinordered__ab__group__add(X22400) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22400),c_Groups_Ozero__class_Ozero(X22400)),X22399))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22400),hAPP(c_Groups_Ouminus__class_Ouminus(X22400),X22399)),X22399))
        | ~ class_Groups_Olinordered__ab__group__add(X22400) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).

fof(i_0_9083,plain,
    ! [X22391,X22392] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22392),hAPP(c_Groups_Ouminus__class_Ouminus(X22392),X22391)),X22391))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22392),c_Groups_Ozero__class_Ozero(X22392)),X22391))
        | ~ class_Groups_Olinordered__ab__group__add(X22392) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22392),c_Groups_Ozero__class_Ozero(X22392)),X22391))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22392),hAPP(c_Groups_Ouminus__class_Ouminus(X22392),X22391)),X22391))
        | ~ class_Groups_Olinordered__ab__group__add(X22392) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_9084,plain,
    ! [X31397,X31398,X31399,X31400] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X31400,X31399),X31398))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31400,X31399),hAPP(hAPP(c_List_Oappend(X31400),X31398),X31397))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31400,X31399),X31397))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31400,X31399),hAPP(hAPP(c_List_Oappend(X31400),X31398),X31397))) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X31400,X31399),X31398))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31400,X31399),X31397))
        | hBOOL(hAPP(c_List_Olistsp(X31400,X31399),hAPP(hAPP(c_List_Oappend(X31400),X31398),X31397))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).

fof(i_0_9085,plain,
    ! [X29294,X29295,X29296,X29297] : hAPP(hAPP(c_Nat_Ocompow(X29297,X29297),X29296),hAPP(hAPP(c_Nat_Ocompow(X29297,X29297),X29295),X29294)) = hAPP(hAPP(c_Nat_Ocompow(X29297,X29297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29295),X29296)),X29294),
    inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).

fof(i_0_9086,plain,
    ! [X25871,X25872] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25872)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25871)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25872),X25871)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25872),X25871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25872)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25871))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_9087,plain,
    ! [X23165,X23166] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23166)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23165)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23166),X23165)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23166),X23165))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23166)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23165))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).

fof(i_0_9088,plain,
    ! [X22869,X22870] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22870)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22869)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22870),X22869)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22870),X22869))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22870)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22869))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).

fof(i_0_9089,plain,
    ! [X25863,X25864] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25864)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25863)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25864),X25863)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25864),X25863))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25864)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25863))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_9090,plain,
    ! [X23169,X23170] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23170)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23169)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23170),X23169)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23170),X23169))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23170)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23169))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).

fof(i_0_9091,plain,
    ! [X22876,X22877] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22877)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22876)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22877),X22876)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22877),X22876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22877)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22876))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).

fof(i_0_9092,plain,
    ! [X22480,X22481] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22481),X22480)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22480),X22481)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22480),X22481))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22481),X22480))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).

fof(i_0_9093,plain,
    ! [X23072,X23073] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23072),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23073),X23072)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23073),X23072))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23072),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).

fof(i_0_9094,plain,
    ! [X23075,X23076] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23076),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23075),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23076),X23075)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23076),X23075))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23076),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23075),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).

fof(i_0_9095,plain,
    ! [X25794,X25795,X25796] :
      ( ~ class_Int_Onumber__ring(X25796)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25796),hAPP(c_Groups_Ouminus__class_Ouminus(X25796),hAPP(c_Int_Onumber__class_Onumber__of(X25796),X25795))),X25794) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25796),hAPP(c_Int_Onumber__class_Onumber__of(X25796),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25795))),X25794) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).

fof(i_0_9096,plain,
    ! [X20008,X20009,X20010] :
      ( ~ class_Rings_Ocomm__semiring__1(X20010)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20010),X20009),X20008)),X20008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20010),X20009),c_Groups_Oone__class_Oone(X20010))),X20008) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_9097,plain,
    ! [X30087,X30088,X30089,X30090] :
      ( ( hAPP(hAPP(c_List_Olist__update(X30089,X30088),X30090),X30087) != X30088
        | hAPP(hAPP(c_List_Onth(X30089),X30088),X30090) = X30087
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30090),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30089)),X30088))) )
      & ( hAPP(hAPP(c_List_Onth(X30089),X30088),X30090) != X30087
        | hAPP(hAPP(c_List_Olist__update(X30089,X30088),X30090),X30087) = X30088
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30090),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30089)),X30088))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).

fof(i_0_9098,plain,
    ! [X25895,X25896] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25896)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25895)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25895)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25895)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25896)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25896))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25895)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25895)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25895)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25896))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5837])])]) ).

fof(i_0_9099,plain,
    ! [X19247,X19248,X19249] :
      ( ~ class_Orderings_Olinorder(X19249)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19249),X19248))
      | hBOOL(hAPP(hAPP(c_member(X19249),X19247),X19248))
      | X19248 = c_Orderings_Obot__class_Obot(tc_fun(X19249,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X19249,c_Orderings_Oord__class_Omin(X19249),hAPP(hAPP(c_Set_Oinsert(X19249),X19247),X19248)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19249),X19247),c_Big__Operators_Olattice_OInf__fin(X19249,c_Orderings_Oord__class_Omin(X19249),X19248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5838])]) ).

fof(i_0_9100,plain,
    ! [X19250,X19251,X19252] :
      ( ~ class_Orderings_Olinorder(X19252)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19252),X19251))
      | hBOOL(hAPP(hAPP(c_member(X19252),X19250),X19251))
      | X19251 = c_Orderings_Obot__class_Obot(tc_fun(X19252,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X19252,c_Orderings_Oord__class_Omax(X19252),hAPP(hAPP(c_Set_Oinsert(X19252),X19250),X19251)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19252),X19250),c_Big__Operators_Olattice_OSup__fin(X19252,c_Orderings_Oord__class_Omax(X19252),X19251)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5839])]) ).

fof(i_0_9101,plain,
    ! [X22987,X22988] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22988))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22987))),
    inference(variable_rename,[status(thm)],[fact_negative__zle]) ).

fof(i_0_9102,plain,
    ! [X25167,X25168] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25168)),X25167))),
    inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(i_0_9103,plain,
    ! [X20104,X20105,X20106] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20106),X20105)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20104),X20105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X20106),X20104)),X20105),
    inference(variable_rename,[status(thm)],[fact_min__diff]) ).

cnf(i_0_9104,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X1)),X2) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5840]) ).

fof(i_0_9105,plain,
    ! [X22843,X22844,X22845] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22845),X22844)),X22843) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22845),X22843)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22844),X22843)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(i_0_9106,plain,
    ! [X22840,X22841,X22842] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22842),X22841)),X22840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22842),X22840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22841),X22840)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(i_0_9107,plain,
    ! [X19968,X19969,X19970] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19970),X19969)),X19968) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19970),X19968)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19969),X19968)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

fof(i_0_9108,plain,
    ! [X20110,X20111,X20112] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20112),X20111)),X20110) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20112),X20110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20111),X20110)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).

fof(i_0_9109,plain,
    ! [X29781,X29782,X29783,X29784] : hAPP(hAPP(c_List_Onth(X29784),hAPP(hAPP(c_List_Olist_OCons(X29784),X29783),X29782)),X29781) = c_Nat_Onat_Onat__case(X29784,X29783,hAPP(c_List_Onth(X29784),X29782),X29781),
    inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).

fof(i_0_9110,plain,
    ! [X32862,X32863,X32864] : c_List_Oreplicate(X32864,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32864)),hAPP(c_List_Ofilter(X32864,hAPP(c_fequal,X32863)),X32862)),X32863) = hAPP(c_List_Ofilter(X32864,hAPP(c_fequal,X32863)),X32862),
    inference(variable_rename,[status(thm)],[fact_replicate__length__filter]) ).

fof(i_0_9111,plain,
    ! [X23560,X23561,X23562,X23563] :
      ( ( X23561 = c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X23563,X23562,X23561,X23560) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X23563,X23562),tc_HOL_Obool)) )
      & ( X23560 = c_Orderings_Obot__class_Obot(tc_fun(X23562,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X23563,X23562,X23561,X23560) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X23563,X23562),tc_HOL_Obool)) )
      & ( X23561 != c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))
        | X23560 != c_Orderings_Obot__class_Obot(tc_fun(X23562,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X23563,X23562,X23561,X23560) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X23563,X23562),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])]) ).

fof(i_0_9112,plain,
    ! [X31678,X31679,X31680,X31681] :
      ( ~ class_Orderings_Olinorder(X31681)
      | hAPP(c_List_Oset(X31680),c_List_Olinorder__class_Osort__key(X31680,X31681,X31679,X31678)) = hAPP(c_List_Oset(X31680),X31678) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__sort])]) ).

fof(i_0_9113,plain,
    ! [X32962,X32963,X32964] : hAPP(hAPP(c_List_Oappend(X32964),c_List_Oreplicate(X32964,X32963,X32962)),hAPP(hAPP(c_List_Olist_OCons(X32964),X32962),c_List_Olist_ONil(X32964))) = hAPP(hAPP(c_List_Olist_OCons(X32964),X32962),c_List_Oreplicate(X32964,X32963,X32962)),
    inference(variable_rename,[status(thm)],[fact_replicate__append__same]) ).

fof(i_0_9114,plain,
    ! [X34094,X34095,X34096] :
      ( ( X34096 = X34095
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34096,X34095) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34094),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
      & ( X34095 = X34094
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34096,X34095) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34094),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
      & ( X34096 != X34095
        | X34095 != X34094
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34096,X34095) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34094),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff])])]) ).

fof(i_0_9115,plain,
    ! [X25106,X25107,X25108] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25108,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X25108,tc_HOL_Obool)),X25107),X25106)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25108,tc_HOL_Obool)),X25107),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25108,tc_HOL_Obool),X25106)),
    inference(variable_rename,[status(thm)],[fact_Union__insert]) ).

fof(i_0_9116,plain,
    ! [X21609,X21610,X21611] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X21611,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X21611,tc_HOL_Obool)),X21610),X21609)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21611,tc_HOL_Obool)),X21610),c_Complete__Lattice_OInf__class_OInf(tc_fun(X21611,tc_HOL_Obool),X21609)),
    inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).

fof(i_0_9117,plain,
    ! [X27570,X27571] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27571,X27571,X27571),X27570),X27570) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27571,X27571),tc_HOL_Obool))
      | c_Wellfounded_Owf(X27571,X27570) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).

fof(i_0_9118,plain,
    ! [X22520,X22521] :
      ( ( X22521 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22521),X22520) = X22520 )
      & ( X22521 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22521),X22520) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22521),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22520)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).

fof(i_0_9119,plain,
    ! [X22957,X22958,X22959,X22960] :
      ( ~ class_Rings_Osemiring__1(X22960)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22959,X22960),hAPP(c_COMBK(X22960,X22959),X22958)),X22957) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22960),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22960),hAPP(c_Finite__Set_Ocard(X22959),X22957))),X22958) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).

fof(i_0_9120,plain,
    ! [X24092,X24093] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24093),hAPP(c_Int_Oring__1__class_Oof__int(X24093),X24092)),c_Groups_Ozero__class_Ozero(X24093)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24092),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X24093) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24092),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24093),hAPP(c_Int_Oring__1__class_Oof__int(X24093),X24092)),c_Groups_Ozero__class_Ozero(X24093)))
        | ~ class_Rings_Olinordered__idom(X24093) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).

fof(i_0_9121,plain,
    ! [X24088,X24089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24089),hAPP(c_Int_Oring__1__class_Oof__int(X24089),X24088)),c_Groups_Ozero__class_Ozero(X24089)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X24089) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24088),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24089),hAPP(c_Int_Oring__1__class_Oof__int(X24089),X24088)),c_Groups_Ozero__class_Ozero(X24089)))
        | ~ class_Rings_Olinordered__idom(X24089) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).

fof(i_0_9122,plain,
    ! [X24633,X24634,X24635,X24636] :
      ( ~ class_Divides_Osemiring__div(X24636)
      | c_Divides_Odiv__class_Omod(X24636,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24636),X24635),c_Divides_Odiv__class_Omod(X24636,X24634,X24633)),X24633) = c_Divides_Odiv__class_Omod(X24636,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24636),X24635),X24634),X24633) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).

fof(i_0_9123,plain,
    ! [X24697,X24698,X24699,X24700] :
      ( ~ class_Divides_Osemiring__div(X24700)
      | c_Divides_Odiv__class_Omod(X24700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24700),X24699),X24698),X24697) = c_Divides_Odiv__class_Omod(X24700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24700),X24699),c_Divides_Odiv__class_Omod(X24700,X24698,X24697)),X24697) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).

fof(i_0_9124,plain,
    ! [X24645,X24646,X24647,X24648] :
      ( ~ class_Divides_Osemiring__div(X24648)
      | c_Divides_Odiv__class_Omod(X24648,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24648),X24647),X24646),X24645) = c_Divides_Odiv__class_Omod(X24648,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24648),X24647),c_Divides_Odiv__class_Omod(X24648,X24646,X24645)),X24645) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).

fof(i_0_9125,plain,
    ! [X24611,X24612,X24613,X24614] :
      ( ~ class_Divides_Oring__div(X24614)
      | c_Divides_Odiv__class_Omod(X24614,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24614),X24613),X24612),X24611) = c_Divides_Odiv__class_Omod(X24614,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24614),X24613),c_Divides_Odiv__class_Omod(X24614,X24612,X24611)),X24611) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).

fof(i_0_9126,plain,
    ! [X17612,X17613,X17614,X17615] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17615,tc_HOL_Obool)),X17614),X17613))
      | ~ hBOOL(hAPP(X17614,X17612))
      | hBOOL(hAPP(X17613,X17612)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_9127,plain,
    ! [X17627,X17628,X17629,X17630] :
      ( ~ hBOOL(hAPP(X17630,X17629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17628,tc_HOL_Obool)),X17630),X17627))
      | hBOOL(hAPP(X17627,X17629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_9128,plain,
    ! [X23728,X23729] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23729),X23728))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23728),X23729)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X23728)),hAPP(c_Int_Onat,X23729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).

fof(i_0_9129,plain,
    ! [X31393,X31394,X31395,X31396] :
      ( ( hBOOL(hAPP(X31395,X31394))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31396,X31395),hAPP(hAPP(c_List_Olist_OCons(X31396),X31394),X31393))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31396,X31395),X31393))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31396,X31395),hAPP(hAPP(c_List_Olist_OCons(X31396),X31394),X31393))) )
      & ( ~ hBOOL(hAPP(X31395,X31394))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31396,X31395),X31393))
        | hBOOL(hAPP(c_List_Olistsp(X31396,X31395),hAPP(hAPP(c_List_Olist_OCons(X31396),X31394),X31393))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).

fof(i_0_9130,plain,
    ! [X24332,X24333,X24334] :
      ( ~ class_Orderings_Olinorder(X24334)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24334),X24333),X24332))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24334,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24334,X24333),X24332)),hAPP(c_SetInterval_Oord__class_OatLeast(X24334),X24332)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24334),X24333) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).

fof(i_0_9131,plain,
    ! [X25952,X25953] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25953),hAPP(c_Int_Onumber__class_Onumber__of(X25953),X25952)),c_Groups_Ozero__class_Ozero(X25953)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25952),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X25953)
        | ~ class_Rings_Olinordered__idom(X25953) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25952),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25953),hAPP(c_Int_Onumber__class_Onumber__of(X25953),X25952)),c_Groups_Ozero__class_Ozero(X25953)))
        | ~ class_Int_Onumber__ring(X25953)
        | ~ class_Rings_Olinordered__idom(X25953) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_9132,plain,
    ! [X25950,X25951] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25951),hAPP(c_Int_Onumber__class_Onumber__of(X25951),X25950)),c_Groups_Ozero__class_Ozero(X25951)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25950),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X25951)
        | ~ class_Rings_Olinordered__idom(X25951) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25950),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25951),hAPP(c_Int_Onumber__class_Onumber__of(X25951),X25950)),c_Groups_Ozero__class_Ozero(X25951)))
        | ~ class_Int_Onumber__ring(X25951)
        | ~ class_Rings_Olinordered__idom(X25951) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

fof(i_0_9133,plain,
    ! [X31278,X31279,X31280,X31281] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31281)),X31280) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31279)),X31278)
      | hAPP(hAPP(c_List_Omap(tc_prod(X31281,X31279),X31281),c_Product__Type_Ofst(X31281,X31279)),hAPP(hAPP(c_List_Ozip(X31281,X31279),X31280),X31278)) = X31280 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).

fof(i_0_9134,plain,
    ! [X31282,X31283,X31284,X31285] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31285)),X31284) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31283)),X31282)
      | hAPP(hAPP(c_List_Omap(tc_prod(X31285,X31283),X31283),c_Product__Type_Osnd(X31285,X31283)),hAPP(hAPP(c_List_Ozip(X31285,X31283),X31284),X31282)) = X31282 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).

fof(i_0_9135,plain,
    ! [X23388,X23389,X23390] :
      ( ~ class_Divides_Osemiring__div(X23390)
      | X23389 = c_Groups_Ozero__class_Ozero(X23390)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23390),X23389),X23388)),X23389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23390),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23390),X23388),X23389)),c_Groups_Oone__class_Oone(X23390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).

fof(i_0_9136,plain,
    ! [X23385,X23386,X23387] :
      ( ~ class_Divides_Osemiring__div(X23387)
      | X23386 = c_Groups_Ozero__class_Ozero(X23387)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23387),X23385),X23386)),X23386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23387),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23387),X23385),X23386)),c_Groups_Oone__class_Oone(X23387)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).

fof(i_0_9137,plain,
    ! [X24681,X24682,X24683,X24684] :
      ( ~ class_Divides_Osemiring__div(X24684)
      | c_Divides_Odiv__class_Omod(X24684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24684),X24683),X24682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24684),X24681),X24682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24684),c_Divides_Odiv__class_Omod(X24684,X24683,X24681)),X24682) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).

fof(i_0_9138,plain,
    ! [X25165,X25166] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25166),X25165))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25166))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25165))),
    inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(i_0_9139,plain,
    ! [X23479,X23480,X23481] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23481))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23481),X23480)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23481),X23479)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23480),X23479) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).

fof(i_0_9140,plain,
    ! [X23374,X23375,X23376] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23376))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23374),X23376)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23375),X23374)),X23376) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).

fof(i_0_9141,plain,
    ! [X32292,X32293,X32294,X32295,X32296] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32296),X32295),hAPP(c_List_Oset(X32296),X32294)))
      | hBOOL(hAPP(X32293,X32295))
      | c_List_OtakeWhile(X32296,X32293,hAPP(hAPP(c_List_Oappend(X32296),X32294),X32292)) = c_List_OtakeWhile(X32296,X32293,X32294) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5841])]) ).

fof(i_0_9142,plain,
    ! [X25906,X25907] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25907)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25906)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25907)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25906)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25906))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5842])]) ).

fof(i_0_9143,plain,
    ! [X25910,X25911] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25911)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25911)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25910)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25910)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25911)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25911)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25910)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25911)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25910))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5843])]) ).

fof(i_0_9144,plain,
    ! [X27032,X27033,X27034,X27035,X27036] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X27036,X27035,X27034),X27033),X27032) = hAPP(hAPP(X27033,hAPP(c_Product__Type_Ofst(X27036,X27035),X27032)),hAPP(c_Product__Type_Osnd(X27036,X27035),X27032)),
    inference(variable_rename,[status(thm)],[fact_split__def]) ).

fof(i_0_9145,plain,
    ! [X27027,X27028,X27029,X27030,X27031] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X27031,X27030,X27029),X27028),X27027) = hAPP(hAPP(X27028,hAPP(c_Product__Type_Ofst(X27031,X27030),X27027)),hAPP(c_Product__Type_Osnd(X27031,X27030),X27027)),
    inference(variable_rename,[status(thm)],[fact_split__beta]) ).

fof(i_0_9146,plain,
    ! [X27014,X27015,X27016,X27017,X27018] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X27018,X27017,X27016),X27015),X27014) = hAPP(hAPP(X27015,hAPP(c_Product__Type_Ofst(X27018,X27017),X27014)),hAPP(c_Product__Type_Osnd(X27018,X27017),X27014)),
    inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).

fof(i_0_9147,plain,
    ! [X32012,X32013] :
      ( ~ class_Orderings_Olinorder(X32013)
      | c_List_Olinorder__class_Osorted(X32013,c_List_Olinorder__class_Osort__key(X32013,X32013,c_COMBI(X32013),X32012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])]) ).

fof(i_0_9148,plain,
    ! [X30381,X30382,X30383,X30384,X30385] :
      ( ( X30384 = X30382
        | hAPP(hAPP(c_List_Oappend(X30385),X30384),hAPP(hAPP(c_List_Olist_OCons(X30385),X30383),c_List_Olist_ONil(X30385))) != hAPP(hAPP(c_List_Oappend(X30385),X30382),hAPP(hAPP(c_List_Olist_OCons(X30385),X30381),c_List_Olist_ONil(X30385))) )
      & ( X30383 = X30381
        | hAPP(hAPP(c_List_Oappend(X30385),X30384),hAPP(hAPP(c_List_Olist_OCons(X30385),X30383),c_List_Olist_ONil(X30385))) != hAPP(hAPP(c_List_Oappend(X30385),X30382),hAPP(hAPP(c_List_Olist_OCons(X30385),X30381),c_List_Olist_ONil(X30385))) )
      & ( X30384 != X30382
        | X30383 != X30381
        | hAPP(hAPP(c_List_Oappend(X30385),X30384),hAPP(hAPP(c_List_Olist_OCons(X30385),X30383),c_List_Olist_ONil(X30385))) = hAPP(hAPP(c_List_Oappend(X30385),X30382),hAPP(hAPP(c_List_Olist_OCons(X30385),X30381),c_List_Olist_ONil(X30385))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).

fof(i_0_9149,plain,
    ! [X30710,X30711,X30712] :
      ( X30712 = c_List_Olist_ONil(X30711)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30710),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30711)),X30712)))
      | hAPP(c_List_Ohd(X30711),hAPP(hAPP(c_List_Odrop(X30711),X30710),X30712)) = hAPP(hAPP(c_List_Onth(X30711),X30712),X30710) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).

fof(i_0_9150,plain,
    ! [X24986,X24987,X24988] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24988)
      | hAPP(c_Groups_Oabs__class_Oabs(X24988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24988),hAPP(c_Groups_Oabs__class_Oabs(X24988),X24987)),hAPP(c_Groups_Oabs__class_Oabs(X24988),X24986))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24988),hAPP(c_Groups_Oabs__class_Oabs(X24988),X24987)),hAPP(c_Groups_Oabs__class_Oabs(X24988),X24986)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).

fof(i_0_9151,plain,
    ! [X17955,X17956,X17957,X17958,X17959] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17959,X17958,X17957)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17959),X17956))
      | hAPP(X17957,hAPP(hAPP(c_Set_Oinsert(X17959),X17955),X17956)) = hAPP(hAPP(c_Finite__Set_Ofold(X17959,X17959,X17958),X17955),X17956) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).

fof(i_0_9152,plain,
    ! [X20603,X20604,X20605] :
      ( ~ class_Lattices_Osemilattice__inf(X20605)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20605),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20605),X20604),X20603)),X20604)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).

fof(i_0_9153,plain,
    ! [X20600,X20601,X20602] :
      ( ~ class_Lattices_Olattice(X20602)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20602),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20602),X20601),X20600)),X20601)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).

fof(i_0_9154,plain,
    ! [X20609,X20610,X20611] :
      ( ~ class_Lattices_Osemilattice__inf(X20611)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20611),X20610),X20609)),X20609)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).

fof(i_0_9155,plain,
    ! [X20606,X20607,X20608] :
      ( ~ class_Lattices_Olattice(X20608)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20608),X20607),X20606)),X20606)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).

fof(i_0_9156,plain,
    ! [X18914,X18915,X18916] :
      ( ~ class_Orderings_Olinorder(X18916)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18916),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18916),X18915),X18914)),X18915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).

fof(i_0_9157,plain,
    ! [X18911,X18912,X18913] :
      ( ~ class_Orderings_Olinorder(X18913)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18913),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18913),X18912),X18911)),X18911)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).

fof(i_0_9158,plain,
    ! [X25644] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25644)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25644) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25644)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).

fof(i_0_9159,plain,
    ! [X24356,X24357,X24358] :
      ( ~ class_Orderings_Olinorder(X24358)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24358),X24357),X24356))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24358,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24358),X24357)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24358,X24357,X24356)) = hAPP(c_SetInterval_Oord__class_OatMost(X24358),X24356) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).

fof(i_0_9160,plain,
    ! [X24386,X24387,X24388] :
      ( ~ class_Orderings_Olinorder(X24388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24388),X24387),X24386))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24388,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24388),X24387)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24388,X24387,X24386)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24388),X24386) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).

fof(i_0_9161,plain,
    ! [X24378,X24379,X24380] :
      ( ~ class_Orderings_Olinorder(X24380)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24380),X24379),X24378))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24380,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24380),X24379)),c_SetInterval_Oord__class_OatLeastAtMost(X24380,X24379,X24378)) = hAPP(c_SetInterval_Oord__class_OatMost(X24380),X24378) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).

fof(i_0_9162,plain,
    ! [X34123,X34124,X34125] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34125),hAPP(c_Groups_Ouminus__class_Ouminus(X34125),X34124)),X34123))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34125),X34124),X34123))
        | ~ class_Rings_Ocomm__ring__1(X34125) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34125),X34124),X34123))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34125),hAPP(c_Groups_Ouminus__class_Ouminus(X34125),X34124)),X34123))
        | ~ class_Rings_Ocomm__ring__1(X34125) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).

fof(i_0_9163,plain,
    ! [X24966,X24967,X24968] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24968)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24968),hAPP(c_Groups_Oabs__class_Oabs(X24968),X24967)),X24966))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24968),X24967),X24966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).

fof(i_0_9164,plain,
    ! [X20668,X20669,X20670,X20671] :
      ( ~ class_Lattices_Odistrib__lattice(X20671)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20671),X20670),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20671),X20669),X20668)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20671),X20670),X20669)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20671),X20670),X20668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).

fof(i_0_9165,plain,
    ! [X20672,X20673,X20674,X20675] :
      ( ~ class_Lattices_Odistrib__lattice(X20675)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20675),X20674),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20675),X20673),X20672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20675),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20675),X20674),X20673)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20675),X20674),X20672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).

fof(i_0_9166,plain,
    ! [X18739,X18740,X18741,X18742] :
      ( ~ class_Orderings_Olinorder(X18742)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18742),X18741),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18742),X18740),X18739)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18742),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18742),X18741),X18740)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18742),X18741),X18739)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).

fof(i_0_9167,plain,
    ! [X18735,X18736,X18737,X18738] :
      ( ~ class_Orderings_Olinorder(X18738)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18738),X18737),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18738),X18736),X18735)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18738),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18738),X18737),X18736)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18738),X18737),X18735)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).

fof(i_0_9168,plain,
    ! [X18551,X18552,X18553,X18554] :
      ( ~ class_Rings_Ocomm__semiring__1(X18554)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18554),X18553),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18554),X18552),X18551)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18554),X18553),X18552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18554),X18553),X18551)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

fof(i_0_9169,plain,
    ! [X18610,X18611,X18612,X18613] :
      ( ~ class_Rings_Ocomm__semiring__1(X18613)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18613),X18612),X18611)),X18610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18613),X18612),X18610)),X18611) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).

fof(i_0_9170,plain,
    ! [X18576,X18577,X18578,X18579] :
      ( ~ class_Rings_Ocomm__semiring__1(X18579)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18579),X18578),X18577)),X18576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18579),X18578),X18576)),X18577) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_9171,plain,
    ! [X28331,X28332,X28333] : hAPP(c_Fun_Ocomp(X28333,X28333,X28332,c_Fun_Oid(X28333)),X28331) = X28331,
    inference(variable_rename,[status(thm)],[fact_id__o]) ).

fof(i_0_9172,plain,
    ! [X29891,X29892,X29893] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29893),X29892),hAPP(c_List_Oset(X29893),X29891)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29893)),X29891))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).

cnf(i_0_9173,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_5739]) ).

fof(i_0_9174,plain,
    ! [X18658,X18659,X18660] :
      ( ~ class_Groups_Oab__semigroup__mult(X18660)
      | X18659 = c_Orderings_Obot__class_Obot(tc_fun(X18660,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18660),X18659))
      | hBOOL(hAPP(hAPP(c_member(X18660),X18658),X18659))
      | hAPP(c_Finite__Set_Ofold1(X18660,c_Groups_Otimes__class_Otimes(X18660)),hAPP(hAPP(c_Set_Oinsert(X18660),X18658),X18659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18660),X18658),hAPP(c_Finite__Set_Ofold1(X18660,c_Groups_Otimes__class_Otimes(X18660)),X18659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5844])]) ).

fof(i_0_9175,plain,
    ! [X29284,X29285,X29286] :
      ( ~ c_Relation_Osingle__valued(X29286,X29286,X29285)
      | c_Relation_Osingle__valued(X29286,X29286,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29286,X29286),tc_HOL_Obool),X29284),X29285)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).

fof(i_0_9176,plain,
    ! [X33179,X33180,X33181,X33182] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X33182),X33181),X33180),X33179) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33182)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X33182),X33181)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(i_0_9177,plain,
    ! [X27899,X27900,X27901,X27902,X27904,X27905,X27906,X27907,X27908] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X27902,X27901,X27900),X27899))
        | hBOOL(hAPP(hAPP(X27900,X27899),esk299_2(X27899,X27900))) )
      & ( ~ hBOOL(hAPP(hAPP(X27905,X27904),X27906))
        | hBOOL(hAPP(c_Predicate_ODomainP(X27908,X27907,X27905),X27904)) ) ),
    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_DomainP_Oequations])])])])]) ).

fof(i_0_9178,plain,
    ! [X19643,X19644,X19645,X19646,X19647] :
      ( ( hAPP(X19645,X19644) != hAPP(X19645,X19643)
        | X19644 = X19643
        | ~ c_Fun_Oinj__on(X19647,X19646,X19645,c_Orderings_Otop__class_Otop(tc_fun(X19647,tc_HOL_Obool))) )
      & ( X19644 != X19643
        | hAPP(X19645,X19644) = hAPP(X19645,X19643)
        | ~ c_Fun_Oinj__on(X19647,X19646,X19645,c_Orderings_Otop__class_Otop(tc_fun(X19647,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_9179,plain,
    ! [X19648,X19649,X19650,X19651,X19652] :
      ( ~ c_Fun_Oinj__on(X19652,X19651,X19650,c_Orderings_Otop__class_Otop(tc_fun(X19652,tc_HOL_Obool)))
      | hAPP(X19650,X19649) != hAPP(X19650,X19648)
      | X19649 = X19648 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_9180,plain,
    ! [X32935,X32936,X32937,X32938] : c_List_Oreplicate(X32938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32937),X32936),X32935) = hAPP(hAPP(c_List_Oappend(X32938),c_List_Oreplicate(X32938,X32937,X32935)),c_List_Oreplicate(X32938,X32936,X32935)),
    inference(variable_rename,[status(thm)],[fact_replicate__add]) ).

fof(i_0_9181,plain,
    ! [X34115,X34116] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34116),X34115))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34115),X34116))
      | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34115,X34116) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5845])]) ).

fof(i_0_9182,plain,
    ! [X19241,X19242,X19243] :
      ( ~ class_Orderings_Olinorder(X19243)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19243),X19242))
      | c_Big__Operators_Olattice_OInf__fin(X19243,c_Orderings_Oord__class_Omin(X19243),hAPP(hAPP(c_Set_Oinsert(X19243),X19241),X19242)) = hAPP(hAPP(c_Finite__Set_Ofold(X19243,X19243,c_Orderings_Oord__class_Omin(X19243)),X19241),X19242) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9183,plain,
    ! [X19244,X19245,X19246] :
      ( ~ class_Orderings_Olinorder(X19246)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19246),X19245))
      | c_Big__Operators_Olattice_OSup__fin(X19246,c_Orderings_Oord__class_Omax(X19246),hAPP(hAPP(c_Set_Oinsert(X19246),X19244),X19245)) = hAPP(hAPP(c_Finite__Set_Ofold(X19246,X19246,c_Orderings_Oord__class_Omax(X19246)),X19244),X19245) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).

cnf(i_0_9184,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5846]) ).

fof(i_0_9185,plain,
    ! [X24472,X24473,X24475] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk204_2(X24472,X24473)),X24472))
        | ~ hBOOL(hAPP(X24473,X24472))
        | hBOOL(hAPP(X24473,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24475),esk204_2(X24472,X24473)))
        | ~ hBOOL(hAPP(X24473,X24475))
        | ~ hBOOL(hAPP(X24473,X24472))
        | hBOOL(hAPP(X24473,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X24473,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk204_2(X24472,X24473)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X24473,X24472))
        | hBOOL(hAPP(X24473,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    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_5847])])])])]) ).

fof(i_0_9186,plain,
    ! [X30811,X30812,X30813,X30814] : hAPP(c_List_Ofoldl(X30814,X30813,X30812,X30811),c_List_Olist_ONil(X30813)) = X30811,
    inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).

fof(i_0_9187,plain,
    ! [X30327,X30328,X30329,X30330] : hAPP(c_List_Olist_Olist__case(X30330,X30329,X30328,X30327),c_List_Olist_ONil(X30329)) = X30328,
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(i_0_9188,plain,
    ! [X28334,X28335,X28336] : hAPP(c_Fun_Ocomp(X28336,X28335,X28336,X28334),c_Fun_Oid(X28336)) = X28334,
    inference(variable_rename,[status(thm)],[fact_o__id]) ).

fof(i_0_9189,plain,
    ! [X22227,X22228,X22229] :
      ( ( X22228 = c_Groups_Ozero__class_Ozero(X22229)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22229),X22228),X22227) != c_Groups_Ozero__class_Ozero(X22229)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22227))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22228))
        | ~ class_Groups_Oordered__comm__monoid__add(X22229) )
      & ( X22227 = c_Groups_Ozero__class_Ozero(X22229)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22229),X22228),X22227) != c_Groups_Ozero__class_Ozero(X22229)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22227))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22228))
        | ~ class_Groups_Oordered__comm__monoid__add(X22229) )
      & ( X22228 != c_Groups_Ozero__class_Ozero(X22229)
        | X22227 != c_Groups_Ozero__class_Ozero(X22229)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22229),X22228),X22227) = c_Groups_Ozero__class_Ozero(X22229)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22227))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22229),c_Groups_Ozero__class_Ozero(X22229)),X22228))
        | ~ class_Groups_Oordered__comm__monoid__add(X22229) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_9190,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5848]) ).

fof(i_0_9191,plain,
    ! [X20144,X20145,X20146] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20146),X20145))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20144),X20145)),X20146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20145),X20146)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).

fof(i_0_9192,plain,
    ! [X20155,X20156,X20157] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20157),X20156))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20156),X20157)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20155),X20156)),X20157) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).

fof(i_0_9193,plain,
    ! [X20174,X20175,X20176] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20176),X20175))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20175),X20176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20174),X20176)),X20175) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).

fof(i_0_9194,plain,
    ! [X18855,X18856,X18857] :
      ( ~ class_Lattices_Oboolean__algebra(X18857)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18857),X18856),X18855))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18857),hAPP(c_Groups_Ouminus__class_Ouminus(X18857),X18855)),hAPP(c_Groups_Ouminus__class_Ouminus(X18857),X18856))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_9195,plain,
    ! [X18870,X18871,X18872] :
      ( ~ class_Groups_Oordered__ab__group__add(X18872)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18872),X18871),X18870))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18872),hAPP(c_Groups_Ouminus__class_Ouminus(X18872),X18870)),hAPP(c_Groups_Ouminus__class_Ouminus(X18872),X18871))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

cnf(i_0_9196,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5849]) ).

cnf(i_0_9197,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5850]) ).

cnf(i_0_9198,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5851]) ).

cnf(i_0_9199,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5852]) ).

fof(i_0_9200,plain,
    ! [X23742] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X23742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23742)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X23742))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).

fof(i_0_9201,plain,
    ! [X24852,X24853] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24853,X24852)),X24853)),
    inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(i_0_9202,plain,
    ! [X24106] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24106)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X24106)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24106)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).

fof(i_0_9203,plain,
    ! [X20327,X20328,X20329,X20330] :
      ( ~ class_Rings_Ocomm__semiring__1(X20330)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20330),hAPP(hAPP(c_Power_Opower__class_Opower(X20330),X20329),X20328)),hAPP(hAPP(c_Power_Opower__class_Opower(X20330),X20329),X20327)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20330),X20329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20328),X20327)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).

fof(i_0_9204,plain,
    ! [X20415,X20416,X20417,X20418] :
      ( ~ class_Groups_Omonoid__mult(X20418)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20418),X20417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20416),X20415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20418),hAPP(hAPP(c_Power_Opower__class_Opower(X20418),X20417),X20416)),hAPP(hAPP(c_Power_Opower__class_Opower(X20418),X20417),X20415)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).

fof(i_0_9205,plain,
    ! [X19155,X19156,X19157] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19157)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19157),X19156))
      | hAPP(c_Finite__Set_Ofold1(X19157,c_Groups_Otimes__class_Otimes(X19157)),hAPP(hAPP(c_Set_Oinsert(X19157),X19155),X19156)) = hAPP(hAPP(c_Finite__Set_Ofold(X19157,X19157,c_Groups_Otimes__class_Otimes(X19157)),X19155),X19156) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).

fof(i_0_9206,plain,
    ! [X22375,X22376,X22377,X22378,X22379,X22380] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22380)
      | X22379 = c_Groups_Ozero__class_Ozero(X22380)
      | X22378 != X22377
      | X22376 = X22375
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22380),X22378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22380),X22379),X22376)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22380),X22377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22380),X22379),X22375)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_9207,plain,
    ! [X28430,X28431] : c_Hilbert__Choice_OEps(X28431,hAPP(hAPP(c_COMBC(X28431,X28431,tc_HOL_Obool),c_fequal),X28430)) = X28430,
    inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).

fof(i_0_9208,plain,
    ! [X17502,X17503] : c_HOL_OThe(X17503,hAPP(hAPP(c_COMBC(X17503,X17503,tc_HOL_Obool),c_fequal),X17502)) = X17502,
    inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).

fof(i_0_9209,plain,
    ! [X21815,X21816] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21816),X21815)),hAPP(c_Nat_OSuc,X21816))),
    inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).

fof(i_0_9210,plain,
    ! [X21771,X21772] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21772),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21772),X21771)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_9211,plain,
    ! [X21773,X21774] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21774),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21773),X21774)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_9212,plain,
    ! [X24218,X24219,X24220,X24221] :
      ( ~ class_Orderings_Oorder(X24221)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24221,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24221,X24220,X24219)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24221,X24219,X24218)) = c_Orderings_Obot__class_Obot(tc_fun(X24221,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).

fof(i_0_9213,plain,
    ! [X24226,X24227,X24228,X24229] :
      ( ~ class_Orderings_Oorder(X24229)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24229,X24228,X24227)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24229,X24227,X24226)) = c_Orderings_Obot__class_Obot(tc_fun(X24229,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).

fof(i_0_9214,plain,
    ! [X23472,X23473,X23474,X23475] :
      ( ~ class_Orderings_Oorder(X23475)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23475,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23475,X23474,X23473)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23475,X23473,X23472)) = c_Orderings_Obot__class_Obot(tc_fun(X23475,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).

fof(i_0_9215,plain,
    ! [X23515,X23516,X23517,X23518] :
      ( ~ class_Orderings_Oorder(X23518)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23518,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23518,X23517,X23516)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23518,X23516,X23515)) = c_Orderings_Obot__class_Obot(tc_fun(X23518,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).

fof(i_0_9216,plain,
    ! [X24222,X24223,X24224,X24225] :
      ( ~ class_Orderings_Oorder(X24225)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24225,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24225,X24224,X24223)),c_SetInterval_Oord__class_OatLeastAtMost(X24225,X24223,X24222)) = c_Orderings_Obot__class_Obot(tc_fun(X24225,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).

fof(i_0_9217,plain,
    ! [X17569,X17570] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17570,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17570,tc_HOL_Obool))),X17569)),
    inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).

fof(i_0_9218,plain,
    ! [X29146,X29147,X29148] :
      ( ~ c_Equiv__Relations_Oequiv(X29148,X29147,X29146)
      | hAPP(hAPP(c_Relation_Orel__comp(X29148,X29148,X29148),hAPP(c_Relation_Oconverse(X29148,X29148),X29146)),X29146) = X29146 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).

fof(i_0_9219,plain,
    ! [X20862,X20863,X20864,X20865] :
      ( hBOOL(hAPP(hAPP(c_member(X20865),X20864),X20863))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20865,tc_HOL_Obool)),X20863),hAPP(hAPP(c_Set_Oinsert(X20865),X20864),X20862)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20865,tc_HOL_Obool)),X20863),X20862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5853])]) ).

fof(i_0_9220,plain,
    ! [X23411,X23412] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23411))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X23412,X23411))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).

fof(i_0_9221,plain,
    ! [X17812,X17813,X17814] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17814,tc_HOL_Obool)),X17813),hAPP(hAPP(c_Set_Oinsert(X17814),X17812),X17813))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_9222,plain,
    ! [X24615,X24616,X24617] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24617),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24616,X24615)),X24615) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24617),X24616),X24615),
    inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(i_0_9223,plain,
    ! [X24594,X24595,X24596] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24596),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24595,X24594)),X24594) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24596),X24595),X24594),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(i_0_9224,plain,
    ! [X24618,X24619,X24620] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24620),X24619),X24618) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24620),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24619,X24618)),X24618),
    inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(i_0_9225,plain,
    ! [X23180,X23181,X23182] :
      ( ~ class_Orderings_Olinorder(X23182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23182),X23181),X23180))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23182),X23181)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23182,X23181),X23180)) = hAPP(c_SetInterval_Oord__class_OlessThan(X23182),X23180) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).

cnf(i_0_9226,plain,
    ( hAPP(c_List_Orotate(X2,X1),X3) = X3
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5854]) ).

fof(i_0_9227,plain,
    ! [X24189,X24190] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24190),hAPP(c_Nat_OSuc,X24189)))
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24190,hAPP(c_Nat_OSuc,X24189)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24189)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24190,X24189)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).

cnf(i_0_9228,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(c_List_Orotate(X1,X2),X3) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5855]) ).

fof(i_0_9229,plain,
    ! [X19363] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X19363)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X19363),tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X19363),c_Orderings_Otop__class_Otop(tc_fun(X19363,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19363),c_Orderings_Otop__class_Otop(tc_fun(X19363,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X19363)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X19363),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_9230,plain,
    ! [X22908,X22909,X22910] :
      ( ~ class_Rings_Olinordered__semidom(X22910)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22909),X22908))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22910),X22909)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22910),X22908))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).

fof(i_0_9231,plain,
    ! [X24348,X24349,X24350,X24351] :
      ( ~ class_Orderings_Olinorder(X24351)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24351,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24351),X24350)),c_SetInterval_Oord__class_OatLeastAtMost(X24351,X24349,X24348)) = c_SetInterval_Oord__class_OatLeastAtMost(X24351,hAPP(hAPP(c_Orderings_Oord__class_Omax(X24351),X24350),X24349),X24348) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).

fof(i_0_9232,plain,
    ! [X24340,X24341,X24342,X24343] :
      ( ~ class_Orderings_Olinorder(X24343)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24343,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24343),X24342)),c_SetInterval_Oord__class_OatLeastAtMost(X24343,X24341,X24340)) = c_SetInterval_Oord__class_OatLeastAtMost(X24343,X24341,hAPP(hAPP(c_Orderings_Oord__class_Omin(X24343),X24342),X24340)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).

fof(i_0_9233,plain,
    ! [X23684,X23685] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23685),hAPP(c_Int_Onat,X23684)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23685)),X23684)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23685)),X23684))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23685),hAPP(c_Int_Onat,X23684))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).

fof(i_0_9234,plain,
    ! [X24335,X24336] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24336),X24335))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24335,X24336) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24336),X24335))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24335,X24336) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X24335),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24335),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24336)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])]) ).

fof(i_0_9235,plain,
    ! [X23740,X23741] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23740))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X23741)),hAPP(c_Int_Onat,X23740)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X23741,X23740)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).

fof(i_0_9236,plain,
    ! [X30605,X30606,X30607,X30608] : hAPP(hAPP(c_List_Odrop(X30608),X30607),hAPP(hAPP(c_List_Otake(X30608),X30606),X30605)) = hAPP(hAPP(c_List_Otake(X30608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30606),X30607)),hAPP(hAPP(c_List_Odrop(X30608),X30607),X30605)),
    inference(variable_rename,[status(thm)],[fact_drop__take]) ).

fof(i_0_9237,plain,
    ! [X27368,X27369,X27370,X27371] : hAPP(hAPP(c_Relation_Orel__comp(X27371,X27370,X27369),X27368),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27370,X27369),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27371,X27369),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).

fof(i_0_9238,plain,
    ! [X33714,X33715,X33716,X33717] : c_Product__Type_Ocurry(X33717,X33716,X33715,hAPP(c_Product__Type_Oprod_Oprod__case(X33717,X33716,X33715),X33714)) = X33714,
    inference(variable_rename,[status(thm)],[fact_curry__split]) ).

fof(i_0_9239,plain,
    ! [X26914] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26914)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26914)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X26914))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).

fof(i_0_9240,plain,
    ! [X24846,X24847,X24848] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24848,X24847)),X24846) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24848),X24846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24847),X24846)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).

fof(i_0_9241,plain,
    ! [X34048,X34049,X34050,X34051] :
      ( ~ class_Rings_Ocomm__semiring__1(X34051)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34051),X34050),X34049))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34051),X34050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34051),X34049),X34048))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).

fof(i_0_9242,plain,
    ! [X34052,X34053,X34054,X34055] :
      ( ~ class_Rings_Ocomm__semiring__1(X34055)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34055),X34054),X34053))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34055),X34054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34055),X34052),X34053))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).

fof(i_0_9243,plain,
    ! [X19551,X19552,X19553,X19554] :
      ( ~ class_Lattices_Osemilattice__sup(X19554)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19554),X19553),X19552))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19554),X19553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19554),X19552),X19551))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).

fof(i_0_9244,plain,
    ! [X19555,X19556,X19557,X19558] :
      ( ~ class_Lattices_Osemilattice__sup(X19558)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19558),X19557),X19556))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19558),X19557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19558),X19555),X19556))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).

fof(i_0_9245,plain,
    ! [X18925,X18926,X18927,X18928] :
      ( ~ class_Orderings_Olinorder(X18928)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18928),X18927),X18926))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18928),X18927),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18928),X18926),X18925))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).

fof(i_0_9246,plain,
    ! [X18921,X18922,X18923,X18924] :
      ( ~ class_Orderings_Olinorder(X18924)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18924),X18923),X18922))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18924),X18923),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18924),X18921),X18922))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).

fof(i_0_9247,plain,
    ! [X19520,X19521,X19522,X19523] :
      ( ~ class_Lattices_Osemilattice__sup(X19523)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19523),X19522),X19521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19523),X19522),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19523),X19521),X19520))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).

fof(i_0_9248,plain,
    ! [X19524,X19525,X19526,X19527] :
      ( ~ class_Lattices_Osemilattice__sup(X19527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19527),X19526),X19525))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19527),X19526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19527),X19524),X19525))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).

fof(i_0_9249,plain,
    ! [X18834,X18835,X18836,X18837] :
      ( ~ class_Orderings_Olinorder(X18837)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),X18836),X18835))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),X18836),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18837),X18835),X18834))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).

fof(i_0_9250,plain,
    ! [X18830,X18831,X18832,X18833] :
      ( ~ class_Orderings_Olinorder(X18833)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18833),X18832),X18831))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18833),X18832),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18833),X18830),X18831))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).

cnf(i_0_9251,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5857]) ).

fof(i_0_9252,plain,
    ! [X23010] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23010))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).

fof(i_0_9253,plain,
    ! [X31856,X31857,X31858,X31859,X31860] :
      ( ( c_List_Otranspose(X31857,X31856) != c_List_Olist_ONil(tc_List_Olist(X31857))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31857)),X31858),hAPP(c_List_Oset(tc_List_Olist(X31857)),X31856)))
        | X31858 = c_List_Olist_ONil(X31857) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31860)),esk433_2(X31859,X31860)),hAPP(c_List_Oset(tc_List_Olist(X31860)),X31859)))
        | c_List_Otranspose(X31860,X31859) = c_List_Olist_ONil(tc_List_Olist(X31860)) )
      & ( esk433_2(X31859,X31860) != c_List_Olist_ONil(X31860)
        | c_List_Otranspose(X31860,X31859) = c_List_Olist_ONil(tc_List_Olist(X31860)) ) ),
    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_transpose__empty])])])])])]) ).

fof(i_0_9254,plain,
    ! [X23186,X23187,X23188] :
      ( ~ class_Groups_Ocomm__monoid__add(X23188)
      | hAPP(X23187,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X23188)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23188),X23187),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X23186)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23188),X23187),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).

fof(i_0_9255,plain,
    ! [X21261,X21262,X21263] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21263,tc_fun(X21262,tc_HOL_Obool)),X21261),hAPP(c_COMBK(tc_fun(X21262,tc_HOL_Obool),X21263),c_Orderings_Obot__class_Obot(tc_fun(X21262,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21262,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).

fof(i_0_9256,plain,
    ! [X21552,X21553,X21554] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21554),X21553))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21553),X21552))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21554)),X21552)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_9257,plain,
    ! [X27044] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X27044)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X27044)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X27044))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).

fof(i_0_9258,plain,
    ! [X24779,X24780] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24780))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24779,X24780))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).

fof(i_0_9259,plain,
    ! [X29979,X29980] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X29980,X29979) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29980),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29979),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(i_0_9260,plain,
    ! [X31161,X31162,X31163,X31164,X31165] : hAPP(hAPP(c_List_Omap(X31165,X31164),X31163),hAPP(hAPP(c_List_Olist_OCons(X31165),X31162),X31161)) = hAPP(hAPP(c_List_Olist_OCons(X31164),hAPP(X31163,X31162)),hAPP(hAPP(c_List_Omap(X31165,X31164),X31163),X31161)),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(i_0_9261,plain,
    ! [X23656,X23657,X23658] :
      ( ~ class_Fields_Ofield__inverse__zero(X23658)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23658),c_Groups_Oone__class_Oone(X23658)),hAPP(hAPP(c_Power_Opower__class_Opower(X23658),X23657),X23656)) = hAPP(hAPP(c_Power_Opower__class_Opower(X23658),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23658),c_Groups_Oone__class_Oone(X23658)),X23657)),X23656) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).

fof(i_0_9262,plain,
    ! [X23079] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23079))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23079))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

fof(i_0_9263,plain,
    ! [X17080,X17081,X17082,X17083] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17083),X17082),X17081))
      | hBOOL(hAPP(hAPP(c_member(X17083),X17082),hAPP(hAPP(c_Set_Oinsert(X17083),X17080),X17081))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_9264,plain,
    ! [X16994,X16995,X16996,X16997] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16997),X16996),X16995))
        | hBOOL(hAPP(hAPP(c_member(X16997),X16996),hAPP(hAPP(c_Set_Oinsert(X16997),X16994),X16995))) )
      & ( X16996 != X16994
        | hBOOL(hAPP(hAPP(c_member(X16997),X16996),hAPP(hAPP(c_Set_Oinsert(X16997),X16994),X16995))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5858])])]) ).

fof(i_0_9265,plain,
    ! [X18943,X18944,X18945] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18945),X18944),hAPP(c_Groups_Ouminus__class_Ouminus(X18945),X18943)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18945),X18943),hAPP(c_Groups_Ouminus__class_Ouminus(X18945),X18944)))
        | ~ class_Groups_Oordered__ab__group__add(X18945) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18945),X18943),hAPP(c_Groups_Ouminus__class_Ouminus(X18945),X18944)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18945),X18944),hAPP(c_Groups_Ouminus__class_Ouminus(X18945),X18943)))
        | ~ class_Groups_Oordered__ab__group__add(X18945) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_9266,plain,
    ! [X18861,X18862,X18863] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18863),X18862),hAPP(c_Groups_Ouminus__class_Ouminus(X18863),X18861)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18863),X18861),hAPP(c_Groups_Ouminus__class_Ouminus(X18863),X18862)))
        | ~ class_Groups_Oordered__ab__group__add(X18863) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18863),X18861),hAPP(c_Groups_Ouminus__class_Ouminus(X18863),X18862)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18863),X18862),hAPP(c_Groups_Ouminus__class_Ouminus(X18863),X18861)))
        | ~ class_Groups_Oordered__ab__group__add(X18863) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_9267,plain,
    ! [X30962,X30963,X30964,X30965] :
      ( ( X30963 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30964)),X30965)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X30964,hAPP(hAPP(c_List_Olist__update(X30964,X30965),X30963),X30962)) = X30962
        | X30965 = c_List_Olist_ONil(X30964) )
      & ( X30963 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30964)),X30965)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X30964,hAPP(hAPP(c_List_Olist__update(X30964,X30965),X30963),X30962)) = c_List_Olast(X30964,X30965)
        | X30965 = c_List_Olist_ONil(X30964) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).

fof(i_0_9268,plain,
    ! [X24896,X24897] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),c_Groups_Osgn__class_Osgn(X24897,X24896)),c_Groups_Ozero__class_Ozero(X24897)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),X24896),c_Groups_Ozero__class_Ozero(X24897)))
        | ~ class_Rings_Olinordered__idom(X24897) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),X24896),c_Groups_Ozero__class_Ozero(X24897)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),c_Groups_Osgn__class_Osgn(X24897,X24896)),c_Groups_Ozero__class_Ozero(X24897)))
        | ~ class_Rings_Olinordered__idom(X24897) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_9269,plain,
    ! [X30095,X30096,X30097] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30097),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30096)),X30095)))
      | hAPP(hAPP(c_List_Otake(X30096),X30097),c_List_Obutlast(X30096,X30095)) = hAPP(hAPP(c_List_Otake(X30096),X30097),X30095) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).

fof(i_0_9270,plain,
    ! [X30991,X30992,X30993] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30993),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30992)),X30991)))
      | c_List_Olast(X30992,hAPP(hAPP(c_List_Odrop(X30992),X30993),X30991)) = c_List_Olast(X30992,X30991) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).

cnf(i_0_9271,plain,
    c_Int_OBit1(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
    inference(split_conjunct,[status(thm)],[i_0_5859]) ).

cnf(i_0_9272,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_5860]) ).

cnf(i_0_9273,plain,
    c_Product__Type_Ointernal__split(X1,X2,X3) = c_Product__Type_Oprod_Oprod__case(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_5861]) ).

fof(i_0_9274,plain,
    ! [X26743,X26744,X26745,X26746,X26747,X26748] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26748,X26747,X26746),X26745),hAPP(hAPP(c_Product__Type_OPair(X26748,X26747),X26744),X26743)) = hAPP(hAPP(X26745,X26744),X26743),
    inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).

fof(i_0_9275,plain,
    ! [X26737,X26738,X26739,X26740,X26741,X26742] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26742,X26741,X26740),X26739),hAPP(hAPP(c_Product__Type_OPair(X26742,X26741),X26738),X26737)) = hAPP(hAPP(X26739,X26738),X26737),
    inference(variable_rename,[status(thm)],[fact_split__conv]) ).

cnf(i_0_9276,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)) = c_List_Oreplicate(X1,X3,X2),
    inference(split_conjunct,[status(thm)],[i_0_5862]) ).

fof(i_0_9277,plain,
    ! [X19212,X19213,X19214] :
      ( ~ class_Orderings_Olinorder(X19214)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19214),X19213))
      | ~ hBOOL(hAPP(hAPP(c_member(X19214),X19212),X19213))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X19214),X19212),c_Big__Operators_Olattice_OSup__fin(X19214,c_Orderings_Oord__class_Omax(X19214),X19213)) = c_Big__Operators_Olattice_OSup__fin(X19214,c_Orderings_Oord__class_Omax(X19214),X19213) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).

fof(i_0_9278,plain,
    ! [X19209,X19210,X19211] :
      ( ~ class_Orderings_Olinorder(X19211)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19211),X19210))
      | ~ hBOOL(hAPP(hAPP(c_member(X19211),X19209),X19210))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X19211),X19209),c_Big__Operators_Olattice_OInf__fin(X19211,c_Orderings_Oord__class_Omin(X19211),X19210)) = c_Big__Operators_Olattice_OInf__fin(X19211,c_Orderings_Oord__class_Omin(X19211),X19210) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).

fof(i_0_9279,plain,
    ! [X18678,X18679,X18680] :
      ( hBOOL(hAPP(hAPP(c_member(X18680),X18679),X18678))
      | hBOOL(hAPP(hAPP(c_member(X18680),X18679),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X18680,tc_HOL_Obool)),X18678))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5863])]) ).

fof(i_0_9280,plain,
    ! [X20980,X20981,X20982,X20983] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20983),X20982),X20981))
        | hAPP(c_Set_Ovimage(X20980,X20983,hAPP(c_COMBK(X20983,X20980),X20982)),X20981) = c_Orderings_Otop__class_Otop(tc_fun(X20980,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20983),X20982),X20981))
        | hAPP(c_Set_Ovimage(X20980,X20983,hAPP(c_COMBK(X20983,X20980),X20982)),X20981) = c_Orderings_Obot__class_Obot(tc_fun(X20980,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5864])]) ).

fof(i_0_9281,plain,
    ! [X23093,X23094,X23095,X23096,X23097] :
      ( ( X23096 = X23094
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23096),X23095) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23094),X23093)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23094),X23093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23096),X23095))
        | ~ class_Orderings_Olinorder(X23097) )
      & ( X23095 = X23093
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23096),X23095) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23094),X23093)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23094),X23093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23096),X23095))
        | ~ class_Orderings_Olinorder(X23097) )
      & ( X23096 != X23094
        | X23095 != X23093
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23096),X23095) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23097,X23094),X23093)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23094),X23093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23097),X23096),X23095))
        | ~ class_Orderings_Olinorder(X23097) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_9282,plain,
    ! [X23088,X23089,X23090,X23091,X23092] :
      ( ~ class_Orderings_Olinorder(X23092)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23092,X23091),X23090) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23092,X23089),X23088)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23092),X23091),X23090))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23092),X23089),X23088))
      | X23091 = X23089 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_9283,plain,
    ! [X23083,X23084,X23085,X23086,X23087] :
      ( ~ class_Orderings_Olinorder(X23087)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23087,X23086),X23085) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23087,X23084),X23083)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23087),X23086),X23085))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23087),X23084),X23083))
      | X23085 = X23083 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_9284,plain,
    ! [X17171,X17172,X17173,X17174,X17175] :
      ( ~ c_Finite__Set_Ofolding__one(X17175,X17174,X17173)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17175),X17172))
      | hBOOL(hAPP(hAPP(c_member(X17175),X17171),X17172))
      | X17172 = c_Orderings_Obot__class_Obot(tc_fun(X17175,tc_HOL_Obool))
      | hAPP(X17173,hAPP(hAPP(c_Set_Oinsert(X17175),X17171),X17172)) = hAPP(hAPP(X17174,X17171),hAPP(X17173,X17172)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5865])]) ).

cnf(i_0_9285,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5779]) ).

fof(i_0_9286,plain,
    ! [X26795,X26796] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26795))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26796,X26795),c_Divides_OposDivAlg(X26796,X26795))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).

fof(i_0_9287,plain,
    ! [X30016,X30017,X30018,X30019,X30020] :
      ( X30020 = X30019
      | hAPP(hAPP(c_List_Onth(X30018),hAPP(hAPP(c_List_Olist__update(X30018,X30017),X30020),X30016)),X30019) = hAPP(hAPP(c_List_Onth(X30018),X30017),X30019) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).

fof(i_0_9288,plain,
    ! [X23391,X23392,X23393,X23394] :
      ( ~ class_Orderings_Oorder(X23394)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23394,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23394,X23393,X23392)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23394,X23392),X23391)) = c_Orderings_Obot__class_Obot(tc_fun(X23394,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).

fof(i_0_9289,plain,
    ! [X29101,X29102,X29103,X29104] : hAPP(c_Relation_Oconverse(X29104,X29104),hAPP(hAPP(c_Relation_Oinv__image(X29103,X29104),X29102),X29101)) = hAPP(hAPP(c_Relation_Oinv__image(X29103,X29104),hAPP(c_Relation_Oconverse(X29103,X29103),X29102)),X29101),
    inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).

fof(i_0_9290,plain,
    ! [X21989,X21990,X21991] :
      ( ~ class_Lattices_Olattice(X21991)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21991),X21990))
      | c_Big__Operators_Olattice__class_OInf__fin(X21991,hAPP(hAPP(c_Set_Oinsert(X21991),X21989),X21990)) = hAPP(hAPP(c_Finite__Set_Ofold(X21991,X21991,c_Lattices_Osemilattice__inf__class_Oinf(X21991)),X21989),X21990) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9291,plain,
    ! [X20351,X20352,X20353] :
      ( ~ class_Lattices_Olattice(X20353)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20353),X20352))
      | c_Big__Operators_Olattice__class_OSup__fin(X20353,hAPP(hAPP(c_Set_Oinsert(X20353),X20351),X20352)) = hAPP(hAPP(c_Finite__Set_Ofold(X20353,X20353,c_Lattices_Osemilattice__sup__class_Osup(X20353)),X20351),X20352) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9292,plain,
    ! [X19144,X19145,X19146] :
      ( ~ class_Orderings_Olinorder(X19146)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19146),X19145))
      | c_Big__Operators_Olinorder__class_OMin(X19146,hAPP(hAPP(c_Set_Oinsert(X19146),X19144),X19145)) = hAPP(hAPP(c_Finite__Set_Ofold(X19146,X19146,c_Orderings_Oord__class_Omin(X19146)),X19144),X19145) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).

fof(i_0_9293,plain,
    ! [X19141,X19142,X19143] :
      ( ~ class_Orderings_Olinorder(X19143)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19143),X19142))
      | c_Big__Operators_Olinorder__class_OMax(X19143,hAPP(hAPP(c_Set_Oinsert(X19143),X19141),X19142)) = hAPP(hAPP(c_Finite__Set_Ofold(X19143,X19143,c_Orderings_Oord__class_Omax(X19143)),X19141),X19142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).

fof(i_0_9294,plain,
    ! [X29065,X29066] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X29066),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | c_Random_Olog(X29066,X29065) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29065),X29066))
        | c_Random_Olog(X29066,X29065) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X29066),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29065),X29066))
        | c_Random_Olog(X29066,X29065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X29066,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X29065),X29066))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).

fof(i_0_9295,plain,
    ! [X22943,X22944] :
      ( ~ class_Rings_Oring__1(X22944)
      | ~ hBOOL(hAPP(hAPP(c_member(X22944),X22943),c_Int_Oring__1__class_OInts(X22944)))
      | hBOOL(hAPP(hAPP(c_member(X22944),hAPP(c_Groups_Ouminus__class_Ouminus(X22944),X22943)),c_Int_Oring__1__class_OInts(X22944))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).

fof(i_0_9296,plain,
    ! [X17157,X17158] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17158,tc_HOL_Obool)),X17157))
        | hBOOL(hAPP(hAPP(c_member(X17158),X17157),c_Orderings_Obot__class_Obot(tc_fun(X17158,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17158),X17157),c_Orderings_Obot__class_Obot(tc_fun(X17158,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17158,tc_HOL_Obool)),X17157)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).

cnf(i_0_9297,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X1,X2)) = c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5866]) ).

fof(i_0_9298,plain,
    ! [X25150,X25151,X25152] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X25152)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25152),c_Groups_Ozero__class_Ozero(X25152)),X25151))
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25152),hAPP(c_Groups_Oabs__class_Oabs(X25152),X25150)),X25151) = hAPP(c_Groups_Oabs__class_Oabs(X25152),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25152),X25150),X25151)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

fof(i_0_9299,plain,
    ! [X25120,X25121,X25122] :
      ( ~ class_Rings_Olinordered__idom(X25122)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25122),c_Groups_Ozero__class_Ozero(X25122)),X25121))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25122),hAPP(c_Groups_Oabs__class_Oabs(X25122),X25120)),X25121) = hAPP(c_Groups_Oabs__class_Oabs(X25122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25122),X25120),X25121)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).

fof(i_0_9300,plain,
    ! [X24551] : hAPP(c_Set_OPow(X24551),c_Orderings_Obot__class_Obot(tc_fun(X24551,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X24551,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24551,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24551,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).

fof(i_0_9301,plain,
    ! [X24191,X24192] :
      ( hAPP(X24192,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X24192),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24191)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X24192),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).

fof(i_0_9302,plain,
    ! [X20583,X20584,X20585,X20586,X20587] :
      ( ~ class_Lattices_Olattice(X20587)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20586,X20587)),X20585),X20584),X20583) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20587),hAPP(X20585,X20583)),hAPP(X20584,X20583)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).

fof(i_0_9303,plain,
    ! [X20536,X20537,X20538,X20539,X20540] :
      ( ~ class_Lattices_Olattice(X20540)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20539,X20540)),X20538),X20537),X20536) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20540),hAPP(X20538,X20536)),hAPP(X20537,X20536)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).

fof(i_0_9304,plain,
    ! [X19484,X19485,X19486,X19487,X19488] :
      ( ~ class_Lattices_Olattice(X19488)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19487,X19488)),X19486),X19485),X19484) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19488),hAPP(X19486,X19484)),hAPP(X19485,X19484)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).

fof(i_0_9305,plain,
    ! [X19437,X19438,X19439,X19440,X19441] :
      ( ~ class_Lattices_Olattice(X19441)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19440,X19441)),X19439),X19438),X19437) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19441),hAPP(X19439,X19437)),hAPP(X19438,X19437)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).

fof(i_0_9306,plain,
    ! [X17414,X17415,X17416,X17417,X17418] :
      ( ~ class_Groups_Ominus(X17418)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17417,X17418)),X17416),X17415),X17414) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17418),hAPP(X17416,X17414)),hAPP(X17415,X17414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).

fof(i_0_9307,plain,
    ! [X17393,X17394,X17395,X17396,X17397] :
      ( ~ class_Groups_Ominus(X17397)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17396,X17397)),X17395),X17394),X17393) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17397),hAPP(X17395,X17393)),hAPP(X17394,X17393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).

fof(i_0_9308,plain,
    ! [X26774,X26775] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26775),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26774))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26775,X26774),c_Divides_OnegDivAlg(X26775,X26774))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).

fof(i_0_9309,plain,
    ! [X24734,X24735] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24735),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24735),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24734,X24735))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).

fof(i_0_9310,plain,
    ! [X28692,X28693,X28694,X28695] :
      ( ~ c_Finite__Set_Ofolding(X28695,X28694,X28693,X28692)
      | hAPP(X28692,c_Orderings_Obot__class_Obot(tc_fun(X28695,tc_HOL_Obool))) = c_Fun_Oid(X28694) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).

fof(i_0_9311,plain,
    ! [X26803,X26804] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26803))
        | c_Divides_Odivmod__int(X26804,X26803) = c_Divides_OposDivAlg(X26804,X26803)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26804)) )
      & ( X26804 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26804,X26803) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26803))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26804)) )
      & ( X26804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X26804,X26803) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26804),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26803))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26804)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26803))
        | c_Divides_Odivmod__int(X26804,X26803) = c_Divides_OnegDivAlg(X26804,X26803)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26804)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26803))
        | c_Divides_Odivmod__int(X26804,X26803) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26804),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26804)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5867])])]) ).

fof(i_0_9312,plain,
    ! [X31331,X31332] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X31332),X31331))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31332)),hAPP(c_Code__Numeral_Onat__of,X31331))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31332)),hAPP(c_Code__Numeral_Onat__of,X31331)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X31332),X31331)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).

fof(i_0_9313,plain,
    ! [X31274,X31275] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31275)),hAPP(c_Code__Numeral_Oof__nat,X31274)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31275),X31274)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31275),X31274))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31275)),hAPP(c_Code__Numeral_Oof__nat,X31274))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).

fof(i_0_9314,plain,
    ! [X21563,X21564] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21564)),hAPP(c_Nat_OSuc,X21563)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21564),X21563)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21564),X21563))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21564)),hAPP(c_Nat_OSuc,X21563))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_9315,plain,
    ! [X21546,X21547] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21547)),hAPP(c_Nat_OSuc,X21546)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21547),X21546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_9316,plain,
    ! [X31335,X31336] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X31336),X31335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31336)),hAPP(c_Code__Numeral_Onat__of,X31335))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31336)),hAPP(c_Code__Numeral_Onat__of,X31335)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X31336),X31335)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).

fof(i_0_9317,plain,
    ! [X31291,X31292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31292)),hAPP(c_Code__Numeral_Oof__nat,X31291)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31292),X31291)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31292),X31291))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31292)),hAPP(c_Code__Numeral_Oof__nat,X31291))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).

fof(i_0_9318,plain,
    ! [X21581,X21582] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21582)),hAPP(c_Nat_OSuc,X21581)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21582),X21581)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21582),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21582)),hAPP(c_Nat_OSuc,X21581))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_9319,plain,
    ! [X29824,X29825,X29826,X29827] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29827),X29826))
      | hAPP(hAPP(c_List_Onth(X29825),hAPP(hAPP(c_List_Otake(X29825),X29826),X29824)),X29827) = hAPP(hAPP(c_List_Onth(X29825),X29824),X29827) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).

fof(i_0_9320,plain,
    ! [X20894,X20895,X20896] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20896,tc_HOL_Obool)),X20895),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20896,tc_HOL_Obool)),X20894),X20895)) = c_Orderings_Obot__class_Obot(tc_fun(X20896,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).

fof(i_0_9321,plain,
    ! [X32196,X32197,X32198,X32199] :
      ( ( hAPP(c_List_Orev(X32199),X32198) != hAPP(hAPP(c_List_Olist_OCons(X32199),X32197),X32196)
        | X32198 = hAPP(hAPP(c_List_Oappend(X32199),hAPP(c_List_Orev(X32199),X32196)),hAPP(hAPP(c_List_Olist_OCons(X32199),X32197),c_List_Olist_ONil(X32199))) )
      & ( X32198 != hAPP(hAPP(c_List_Oappend(X32199),hAPP(c_List_Orev(X32199),X32196)),hAPP(hAPP(c_List_Olist_OCons(X32199),X32197),c_List_Olist_ONil(X32199)))
        | hAPP(c_List_Orev(X32199),X32198) = hAPP(hAPP(c_List_Olist_OCons(X32199),X32197),X32196) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).

fof(i_0_9322,plain,
    ! [X23193,X23194] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23194))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23194),X23193))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).

fof(i_0_9323,plain,
    ! [X23444,X23445] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23445),X23444)),X23445)),
    inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).

fof(i_0_9324,plain,
    ! [X20177,X20178] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20178),X20177)),X20178)),
    inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).

fof(i_0_9325,plain,
    ! [X24376,X24377] :
      ( ~ class_Orderings_Olinorder(X24377)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24377,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24377),X24376)),hAPP(hAPP(c_Set_Oinsert(X24377),X24376),c_Orderings_Obot__class_Obot(tc_fun(X24377,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X24377),X24376) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).

fof(i_0_9326,plain,
    ! [X18505,X18506,X18507] :
      ( ~ class_Orderings_Olinorder(X18507)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18507),X18506))
      | ~ hBOOL(hAPP(hAPP(c_member(X18507),X18505),X18506))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18507),c_Big__Operators_Olinorder__class_OMin(X18507,X18506)),X18505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).

fof(i_0_9327,plain,
    ! [X22777,X22778,X22779] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22778),X22777)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22779),X22778)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22779),X22777)),
    inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(i_0_9328,plain,
    ! [X22846,X22847,X22848] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22847),X22846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22848),X22847)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22848),X22846)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(i_0_9329,plain,
    ! [X22837,X22838,X22839] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22839),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22838),X22837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22839),X22838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22839),X22837)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(i_0_9330,plain,
    ! [X19965,X19966,X19967] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19966),X19965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19967),X19966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19967),X19965)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).

fof(i_0_9331,plain,
    ! [X20107,X20108,X20109] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20109),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20108),X20107)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20109),X20108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20109),X20107)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(i_0_9332,plain,
    ! [X20120,X20121,X20122] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20122),X20121)),X20120) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20122),X20120)),X20121),
    inference(variable_rename,[status(thm)],[fact_diff__commute]) ).

fof(i_0_9333,plain,
    ! [X22395,X22396] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),c_Groups_Ozero__class_Ozero(X22396)),hAPP(c_Groups_Ouminus__class_Ouminus(X22396),X22395)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),X22395),c_Groups_Ozero__class_Ozero(X22396)))
        | ~ class_Groups_Oordered__ab__group__add(X22396) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),X22395),c_Groups_Ozero__class_Ozero(X22396)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),c_Groups_Ozero__class_Ozero(X22396)),hAPP(c_Groups_Ouminus__class_Ouminus(X22396),X22395)))
        | ~ class_Groups_Oordered__ab__group__add(X22396) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_9334,plain,
    ! [X22385,X22386] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22386),c_Groups_Ozero__class_Ozero(X22386)),hAPP(c_Groups_Ouminus__class_Ouminus(X22386),X22385)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22386),X22385),c_Groups_Ozero__class_Ozero(X22386)))
        | ~ class_Groups_Oordered__ab__group__add(X22386) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22386),X22385),c_Groups_Ozero__class_Ozero(X22386)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22386),c_Groups_Ozero__class_Ozero(X22386)),hAPP(c_Groups_Ouminus__class_Ouminus(X22386),X22385)))
        | ~ class_Groups_Oordered__ab__group__add(X22386) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_9335,plain,
    ! [X34158,X34159,X34160,X34161] :
      ( ~ class_Rings_Ocomm__semiring__1(X34161)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34161),X34160),X34159))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34161),X34159),X34158))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34161),X34160),X34158)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).

fof(i_0_9336,plain,
    ! [X18272,X18273,X18274,X18275] :
      ( ~ class_Orderings_Opreorder(X18275)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18275),X18274),X18273))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18275),X18273),X18272))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18275),X18274),X18272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_9337,plain,
    ! [X18342,X18343,X18344,X18345] :
      ( ~ class_Orderings_Opreorder(X18345)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18345),X18344),X18343))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18345),X18343),X18342))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18345),X18344),X18342)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_9338,plain,
    ! [X18350,X18351,X18352,X18353] :
      ( ~ class_Orderings_Opreorder(X18353)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18353),X18352),X18351))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18353),X18351),X18350))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18353),X18352),X18350)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_9339,plain,
    ! [X18268,X18269,X18270,X18271] :
      ( ~ class_Orderings_Oorder(X18271)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18271),X18270),X18269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18271),X18268),X18270))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18271),X18268),X18269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_9340,plain,
    ! [X18338,X18339,X18340,X18341] :
      ( ~ class_Orderings_Oorder(X18341)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18341),X18340),X18339))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),X18338),X18340))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),X18338),X18339)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_9341,plain,
    ! [X18346,X18347,X18348,X18349] :
      ( ~ class_Orderings_Oorder(X18349)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18349),X18348),X18347))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18349),X18346),X18348))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18349),X18346),X18347)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_9342,plain,
    ! [X17589,X17590,X17591,X17592] :
      ( ~ class_Orderings_Opreorder(X17592)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17592),X17591),X17590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17592),X17590),X17589))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17592),X17591),X17589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_9343,plain,
    ! [X17582,X17583,X17584,X17585] :
      ( ~ class_Orderings_Oorder(X17585)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17585),X17584),X17583))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17585),X17582),X17584))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17585),X17582),X17583)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_9344,plain,
    ! [X26474] :
      ( X26474 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26474),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0])]) ).

fof(i_0_9345,plain,
    ! [X26912,X26913] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26913))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26912))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X26913,X26912) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X26913,X26912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).

fof(i_0_9346,plain,
    ! [X32274,X32275,X32276,X32277,X32278] :
      ( hBOOL(hAPP(X32278,X32277))
      | c_List_OtakeWhile(X32276,X32278,hAPP(hAPP(c_List_Oappend(X32276),X32275),hAPP(hAPP(c_List_Olist_OCons(X32276),X32277),X32274))) = c_List_OtakeWhile(X32276,X32278,X32275) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5868])]) ).

fof(i_0_9347,plain,
    ! [X18440,X18441,X18442,X18443,X18444] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18443),X18442))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18441),X18440))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18444),X18443),X18442) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18444),X18441),X18440)
        | ~ class_Groups_Oordered__ab__group__add(X18444) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18441),X18440))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18443),X18442))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18444),X18443),X18442) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18444),X18441),X18440)
        | ~ class_Groups_Oordered__ab__group__add(X18444) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).

fof(i_0_9348,plain,
    ! [X18011,X18012,X18013,X18014,X18015] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18015),X18014),X18013))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18015),X18012),X18011))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18015),X18014),X18013) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18015),X18012),X18011)
        | ~ class_Groups_Oordered__ab__group__add(X18015) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18015),X18012),X18011))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18015),X18014),X18013))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18015),X18014),X18013) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18015),X18012),X18011)
        | ~ class_Groups_Oordered__ab__group__add(X18015) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).

fof(i_0_9349,plain,
    ! [X20135,X20136,X20137] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20136),X20137) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20135),X20137)
        | X20136 = X20135
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20137),X20135))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20137),X20136)) )
      & ( X20136 != X20135
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20136),X20137) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20135),X20137)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20137),X20135))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20137),X20136)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).

fof(i_0_9350,plain,
    ! [X27818,X27819,X27820] : hAPP(hAPP(c_Product__Type_OSigma(X27820,X27819),X27818),hAPP(c_COMBK(tc_fun(X27819,tc_HOL_Obool),X27820),c_Orderings_Obot__class_Obot(tc_fun(X27819,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27820,X27819),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).

cnf(i_0_9351,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5869]) ).

cnf(i_0_9352,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).

fof(i_0_9353,plain,
    ! [X31636,X31637,X31638,X31639] : c_List_Oremdups(X31639,hAPP(hAPP(c_List_Omap(X31638,X31639),X31637),c_List_Oremdups(X31638,X31636))) = c_List_Oremdups(X31639,hAPP(hAPP(c_List_Omap(X31638,X31639),X31637),X31636)),
    inference(variable_rename,[status(thm)],[fact_remdups__map__remdups]) ).

fof(i_0_9354,plain,
    ! [X20011,X20012,X20013] :
      ( ~ class_Rings_Ocomm__semiring__1(X20013)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20013),X20012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20013),X20011),X20012)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20013),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20013),X20011),c_Groups_Oone__class_Oone(X20013))),X20012) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

cnf(i_0_9355,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5870]) ).

cnf(i_0_9356,plain,
    ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5871]) ).

fof(i_0_9357,plain,
    ! [X27042,X27043] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27042))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X27043),X27042) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X27043,X27042)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).

fof(i_0_9358,plain,
    ! [X21585,X21586] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21586),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21585)),X21586)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21585)),X21586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21586),X21585)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5872])]) ).

fof(i_0_9359,plain,
    ! [X24197,X24198,X24199,X24200] :
      ( ~ class_Orderings_Oorder(X24200)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24200,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24200,X24199),X24198)),c_SetInterval_Oord__class_OatLeastAtMost(X24200,X24198,X24197)) = c_Orderings_Obot__class_Obot(tc_fun(X24200,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).

fof(i_0_9360,plain,
    ! [X24090,X24091] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24091),c_Groups_Ozero__class_Ozero(X24091)),hAPP(c_Int_Oring__1__class_Oof__int(X24091),X24090)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24090))
        | ~ class_Rings_Olinordered__idom(X24091) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24090))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24091),c_Groups_Ozero__class_Ozero(X24091)),hAPP(c_Int_Oring__1__class_Oof__int(X24091),X24090)))
        | ~ class_Rings_Olinordered__idom(X24091) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).

fof(i_0_9361,plain,
    ! [X22961,X22962] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22962),X22961)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22961))
        | ~ class_Rings_Olinordered__semidom(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22961))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22962),X22961)))
        | ~ class_Rings_Olinordered__semidom(X22962) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).

fof(i_0_9362,plain,
    ! [X24086,X24087] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24087),c_Groups_Ozero__class_Ozero(X24087)),hAPP(c_Int_Oring__1__class_Oof__int(X24087),X24086)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24086))
        | ~ class_Rings_Olinordered__idom(X24087) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24086))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24087),c_Groups_Ozero__class_Ozero(X24087)),hAPP(c_Int_Oring__1__class_Oof__int(X24087),X24086)))
        | ~ class_Rings_Olinordered__idom(X24087) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).

fof(i_0_9363,plain,
    ! [X25573,X25574,X25575] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X25575,X25574,X25573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X25574)),c_Com_Ocom_Ocom__size(X25573))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I5_J]) ).

fof(i_0_9364,plain,
    ! [X25038,X25039] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25039),hAPP(c_Groups_Oabs__class_Oabs(X25039),X25038)),c_Groups_Ozero__class_Ozero(X25039)))
        | X25038 = c_Groups_Ozero__class_Ozero(X25039)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25039) )
      & ( X25038 != c_Groups_Ozero__class_Ozero(X25039)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25039),hAPP(c_Groups_Oabs__class_Oabs(X25039),X25038)),c_Groups_Ozero__class_Ozero(X25039)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25039) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).

fof(i_0_9365,plain,
    ! [X26910,X26911] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26911),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26910))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X26911,X26910) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X26911,X26910)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).

fof(i_0_9366,plain,
    ! [X19223,X19224,X19225] :
      ( ~ class_Orderings_Olinorder(X19225)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19225),X19224))
      | X19224 = c_Orderings_Obot__class_Obot(tc_fun(X19225,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X19225,c_Orderings_Oord__class_Omin(X19225),hAPP(hAPP(c_Set_Oinsert(X19225),X19223),X19224)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19225),X19223),c_Big__Operators_Olattice_OInf__fin(X19225,c_Orderings_Oord__class_Omin(X19225),X19224)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).

fof(i_0_9367,plain,
    ! [X19226,X19227,X19228] :
      ( ~ class_Orderings_Olinorder(X19228)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19228),X19227))
      | X19227 = c_Orderings_Obot__class_Obot(tc_fun(X19228,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X19228,c_Orderings_Oord__class_Omax(X19228),hAPP(hAPP(c_Set_Oinsert(X19228),X19226),X19227)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19228),X19226),c_Big__Operators_Olattice_OSup__fin(X19228,c_Orderings_Oord__class_Omax(X19228),X19227)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).

fof(i_0_9368,plain,
    ! [X25046,X25047] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25047)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25047),hAPP(c_Groups_Oabs__class_Oabs(X25047),X25046)),c_Groups_Ozero__class_Ozero(X25047))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).

fof(i_0_9369,plain,
    ! [X22902,X22903] :
      ( ~ class_Rings_Olinordered__semidom(X22903)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22903),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22903),X22902)),c_Groups_Ozero__class_Ozero(X22903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).

fof(i_0_9370,plain,
    ! [X34030,X34031,X34032] :
      ( ~ class_Divides_Osemiring__div(X34032)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34032),X34031),X34030))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34032),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34032),X34030),X34031)),X34031) = X34030 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).

fof(i_0_9371,plain,
    ! [X22954,X22955,X22956] :
      ( ~ class_Rings_Oring__1(X22956)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22955),X22954))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22956),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22954),X22955)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22956),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22956),X22954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22956),X22955)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).

cnf(i_0_9372,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5875]) ).

fof(i_0_9373,plain,
    ! [X25957,X25958] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25958),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25957)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25957) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25957),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25957)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25958)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25958),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25957),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25957)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25958),X25957))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25958),c_Int_OPls)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5876])])]) ).

fof(i_0_9374,plain,
    ! [X25908,X25909] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25909)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25909)),X25908) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25908) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25909)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25909)),X25908) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25909)),X25908)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5877])]) ).

fof(i_0_9375,plain,
    ! [X27040,X27041] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27041),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27040))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X27041),X27040) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X27041,X27040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).

fof(i_0_9376,plain,
    ! [X17133,X17134,X17135] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17135),hAPP(hAPP(c_Set_Oinsert(X17135),X17134),X17133)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17135),X17133)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17135),X17133))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17135),hAPP(hAPP(c_Set_Oinsert(X17135),X17134),X17133))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

cnf(i_0_9377,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5878]) ).

fof(i_0_9378,plain,
    ! [X21975,X21976,X21977] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21977)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21977),X21976))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21977),X21975),c_Complete__Lattice_OInf__class_OInf(X21977,X21976)) = hAPP(hAPP(c_Finite__Set_Ofold(X21977,X21977,c_Lattices_Osemilattice__inf__class_Oinf(X21977)),X21975),X21976) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).

fof(i_0_9379,plain,
    ! [X25193,X25194,X25195] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25195)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25195),X25194))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25195),X25193),c_Complete__Lattice_OSup__class_OSup(X25195,X25194)) = hAPP(hAPP(c_Finite__Set_Ofold(X25195,X25195,c_Lattices_Osemilattice__sup__class_Osup(X25195)),X25193),X25194) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).

cnf(i_0_9380,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat__numeral__1__eq__1]) ).

cnf(i_0_9381,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_one__code__numeral__code]) ).

cnf(i_0_9382,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).

cnf(i_0_9383,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_Numeral1__eq1__nat]) ).

fof(i_0_9384,plain,
    ! [X20918,X20919] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20919,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20919,tc_HOL_Obool)),X20918)),X20918) = c_Orderings_Obot__class_Obot(tc_fun(X20919,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).

fof(i_0_9385,plain,
    ! [X19495,X19496] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19496,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19496,tc_HOL_Obool)),X19495)),X19495) = c_Orderings_Otop__class_Otop(tc_fun(X19496,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).

fof(i_0_9386,plain,
    ! [X23558,X23559] : c_Sum__Type_OPlus(X23559,X23558,c_Orderings_Otop__class_Otop(tc_fun(X23559,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X23558,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X23559,X23558),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_9387,plain,
    ! [X24230,X24231,X24232] :
      ( ~ class_Orderings_Oorder(X24232)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24232,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24232,X24231,X24230)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24232),X24230)) = c_Orderings_Obot__class_Obot(tc_fun(X24232,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).

fof(i_0_9388,plain,
    ! [X24103,X24104,X24105] :
      ( ~ class_Orderings_Oorder(X24105)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24105,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24105,X24104,X24103)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24105),X24103)) = c_Orderings_Obot__class_Obot(tc_fun(X24105,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).

fof(i_0_9389,plain,
    ! [X24369,X24370,X24371] :
      ( ~ class_Orderings_Oorder(X24371)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24371,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24371,X24370,X24369)),hAPP(c_SetInterval_Oord__class_OatLeast(X24371),X24369)) = c_Orderings_Obot__class_Obot(tc_fun(X24371,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).

fof(i_0_9390,plain,
    ! [X29067,X29068,X29069] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29069),X29068))
        | c_Random_Ominus__shift(X29067,X29069,X29068) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X29067),X29069)),X29068) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29069),X29068))
        | c_Random_Ominus__shift(X29067,X29069,X29068) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X29069),X29068) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5879])]) ).

fof(i_0_9391,plain,
    ! [X25954,X25955] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25955),c_Groups_Ozero__class_Ozero(X25955)),hAPP(c_Int_Onumber__class_Onumber__of(X25955),X25954)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25954))
        | ~ class_Int_Onumber__ring(X25955)
        | ~ class_Rings_Olinordered__idom(X25955) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25955),c_Groups_Ozero__class_Ozero(X25955)),hAPP(c_Int_Onumber__class_Onumber__of(X25955),X25954)))
        | ~ class_Int_Onumber__ring(X25955)
        | ~ class_Rings_Olinordered__idom(X25955) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_9392,plain,
    ! [X25948,X25949] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25949),c_Groups_Ozero__class_Ozero(X25949)),hAPP(c_Int_Onumber__class_Onumber__of(X25949),X25948)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X25948))
        | ~ class_Int_Onumber__ring(X25949)
        | ~ class_Rings_Olinordered__idom(X25949) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X25948))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25949),c_Groups_Ozero__class_Ozero(X25949)),hAPP(c_Int_Onumber__class_Onumber__of(X25949),X25948)))
        | ~ class_Int_Onumber__ring(X25949)
        | ~ class_Rings_Olinordered__idom(X25949) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_9393,plain,
    ! [X24822,X24823,X24824] :
      ( ( ~ hBOOL(hAPP(X24824,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24823,X24822)))
        | epred2_3(X24824,X24823,X24822) )
      & ( ~ epred2_3(X24824,X24823,X24822)
        | hBOOL(hAPP(X24824,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24823,X24822))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5880])]) ).

fof(i_0_9394,plain,
    ! [X27728,X27729,X27730] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27730,X27729)),X27728))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27730),hAPP(c_Relation_ODomain(X27730,X27729),X27728))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).

fof(i_0_9395,plain,
    ! [X27650,X27651,X27652] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27652,X27651)),X27650))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27651),hAPP(c_Relation_ORange(X27652,X27651),X27650))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).

fof(i_0_9396,plain,
    ! [X18124,X18125,X18126,X18127] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18127,X18126,X18125),X18124))
      | X18125 != c_Orderings_Obot__class_Obot(tc_fun(X18127,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).

fof(i_0_9397,plain,
    ! [X25234,X25235] : hAPP(hAPP(c_Nitpick_Oint__gcd,X25235),X25234) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25235)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25234)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(i_0_9398,plain,
    ! [X31175,X31176,X31177,X31178,X31179] : hAPP(hAPP(c_List_Odrop(X31179),X31178),hAPP(hAPP(c_List_Omap(X31177,X31179),X31176),X31175)) = hAPP(hAPP(c_List_Omap(X31177,X31179),X31176),hAPP(hAPP(c_List_Odrop(X31177),X31178),X31175)),
    inference(variable_rename,[status(thm)],[fact_drop__map]) ).

fof(i_0_9399,plain,
    ! [X31148,X31149,X31150,X31151,X31152] : hAPP(hAPP(c_List_Otake(X31152),X31151),hAPP(hAPP(c_List_Omap(X31150,X31152),X31149),X31148)) = hAPP(hAPP(c_List_Omap(X31150,X31152),X31149),hAPP(hAPP(c_List_Otake(X31150),X31151),X31148)),
    inference(variable_rename,[status(thm)],[fact_take__map]) ).

fof(i_0_9400,plain,
    ! [X31802,X31803,X31804,X31805] : hAPP(c_List_Ofilter(X31805,X31804),hAPP(hAPP(c_List_Oappend(X31805),X31803),X31802)) = hAPP(hAPP(c_List_Oappend(X31805),hAPP(c_List_Ofilter(X31805,X31804),X31803)),hAPP(c_List_Ofilter(X31805,X31804),X31802)),
    inference(variable_rename,[status(thm)],[fact_filter__append]) ).

fof(i_0_9401,plain,
    ! [X30291,X30292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30292),X30291))
        | c_List_Oupto(X30292,X30291) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X30292),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30292),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30291)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30292),X30291))
        | c_List_Oupto(X30292,X30291) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5881])]) ).

fof(i_0_9402,plain,
    ! [X27561,X27562,X27563,X27564,X27565] :
      ( ( ~ c_Wellfounded_Owf(X27562,X27561)
        | hBOOL(hAPP(hAPP(c_member(X27562),X27563),c_Wellfounded_Oacc(X27562,X27561))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27565),esk288_2(X27564,X27565)),c_Wellfounded_Oacc(X27565,X27564)))
        | c_Wellfounded_Owf(X27565,X27564) ) ),
    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_wf__acc__iff])])])])]) ).

fof(i_0_9403,plain,
    ! [X18676,X18677] :
      ( ~ class_Groups_Olinordered__ab__group__add(X18677)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18677),X18676))
      | X18676 = c_Orderings_Obot__class_Obot(tc_fun(X18677,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18677),c_Big__Operators_Olinorder__class_OMin(X18677,X18676)) = c_Big__Operators_Olinorder__class_OMax(X18677,hAPP(c_Set_Oimage(X18677,X18677,c_Groups_Ouminus__class_Ouminus(X18677)),X18676)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).

fof(i_0_9404,plain,
    ! [X18674,X18675] :
      ( ~ class_Groups_Olinordered__ab__group__add(X18675)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18675),X18674))
      | X18674 = c_Orderings_Obot__class_Obot(tc_fun(X18675,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18675),c_Big__Operators_Olinorder__class_OMax(X18675,X18674)) = c_Big__Operators_Olinorder__class_OMin(X18675,hAPP(c_Set_Oimage(X18675,X18675,c_Groups_Ouminus__class_Ouminus(X18675)),X18674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).

fof(i_0_9405,plain,
    ! [X25109,X25110] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25110),c_Complete__Lattice_OSup__class_OSup(tc_fun(X25110,tc_HOL_Obool),X25109)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25110,tc_HOL_Obool)),X25109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).

fof(i_0_9406,plain,
    ! [X24924,X24925] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X24925))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24925),X24924)),X24925) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq])]) ).

fof(i_0_9407,plain,
    ! [X24894,X24895] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24895),c_Groups_Ozero__class_Ozero(X24895)),c_Groups_Osgn__class_Osgn(X24895,X24894)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24895),c_Groups_Ozero__class_Ozero(X24895)),X24894))
        | ~ class_Rings_Olinordered__idom(X24895) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24895),c_Groups_Ozero__class_Ozero(X24895)),X24894))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24895),c_Groups_Ozero__class_Ozero(X24895)),c_Groups_Osgn__class_Osgn(X24895,X24894)))
        | ~ class_Rings_Olinordered__idom(X24895) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

fof(i_0_9408,plain,
    ! [X34120,X34121,X34122] :
      ( ~ class_Divides_Oring__div(X34122)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34122),X34121),X34120))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34122),hAPP(c_Groups_Ouminus__class_Ouminus(X34122),X34120)),X34121) = hAPP(c_Groups_Ouminus__class_Ouminus(X34122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34122),X34120),X34121)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).

cnf(i_0_9409,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_5882]) ).

cnf(i_0_9410,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_5883]) ).

fof(i_0_9411,plain,
    ! [X24685,X24686,X24687,X24688] :
      ( ~ class_Divides_Osemiring__div(X24688)
      | c_Divides_Odiv__class_Omod(X24688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24688),X24687),X24686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24688),X24687),X24685)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24688),X24687),c_Divides_Odiv__class_Omod(X24688,X24686,X24685)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).

fof(i_0_9412,plain,
    ! [X21847,X21848,X21849,X21850] :
      ( ( X21850 != c_Orderings_Obot__class_Obot(tc_fun(X21849,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21849,tc_fun(X21848,tc_HOL_Obool)),X21850),hAPP(c_COMBK(tc_fun(X21848,tc_HOL_Obool),X21849),X21847)) = c_Orderings_Otop__class_Otop(tc_fun(X21848,tc_HOL_Obool)) )
      & ( X21850 = c_Orderings_Obot__class_Obot(tc_fun(X21849,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21849,tc_fun(X21848,tc_HOL_Obool)),X21850),hAPP(c_COMBK(tc_fun(X21848,tc_HOL_Obool),X21849),X21847)) = X21847 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).

fof(i_0_9413,plain,
    ! [X21257,X21258,X21259,X21260] :
      ( ( X21260 != c_Orderings_Obot__class_Obot(tc_fun(X21259,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21259,tc_fun(X21258,tc_HOL_Obool)),X21260),hAPP(c_COMBK(tc_fun(X21258,tc_HOL_Obool),X21259),X21257)) = c_Orderings_Obot__class_Obot(tc_fun(X21258,tc_HOL_Obool)) )
      & ( X21260 = c_Orderings_Obot__class_Obot(tc_fun(X21259,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21259,tc_fun(X21258,tc_HOL_Obool)),X21260),hAPP(c_COMBK(tc_fun(X21258,tc_HOL_Obool),X21259),X21257)) = X21257 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).

fof(i_0_9414,plain,
    ! [X33176,X33177,X33178] : c_Random__Sequence_Oempty(X33178,X33177,X33176) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33178)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X33178)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(i_0_9415,plain,
    ! [X23314,X23315,X23316,X23317] :
      ( ( X23316 != c_Groups_Ozero__class_Ozero(X23317)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23314)) = c_Groups_Ozero__class_Ozero(X23317)
        | ~ class_Divides_Osemiring__div(X23317) )
      & ( X23316 = c_Groups_Ozero__class_Ozero(X23317)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23314)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23317),X23315),X23314)
        | ~ class_Divides_Osemiring__div(X23317) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).

fof(i_0_9416,plain,
    ! [X23829,X23830,X23831,X23832] :
      ( ~ class_Fields_Ofield__inverse__zero(X23832)
      | X23831 = c_Groups_Ozero__class_Ozero(X23832)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23832),X23831),X23830)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23832),X23831),X23829)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23832),X23830),X23829) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_9417,plain,
    ! [X23833,X23834,X23835,X23836] :
      ( ~ class_Fields_Ofield__inverse__zero(X23836)
      | X23835 = c_Groups_Ozero__class_Ozero(X23836)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23836),X23834),X23835)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23836),X23833),X23835)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23836),X23834),X23833) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_9418,plain,
    ! [X23328,X23329,X23330,X23331] :
      ( ~ class_Divides_Osemiring__div(X23331)
      | X23330 = c_Groups_Ozero__class_Ozero(X23331)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23331),X23330),X23329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23331),X23330),X23328)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23331),X23329),X23328) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).

fof(i_0_9419,plain,
    ! [X23324,X23325,X23326,X23327] :
      ( ~ class_Divides_Osemiring__div(X23327)
      | X23326 = c_Groups_Ozero__class_Ozero(X23327)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23327),X23325),X23326)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23327),X23324),X23326)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23327),X23325),X23324) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).

cnf(i_0_9420,plain,
    c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5884]) ).

fof(i_0_9421,plain,
    ! [X26028,X26029,X26030,X26031] : hAPP(c_Nat_Onat_Onat__rec(X26031,X26030,X26029),hAPP(c_Nat_OSuc,X26028)) = hAPP(hAPP(X26029,X26028),hAPP(c_Nat_Onat_Onat__rec(X26031,X26030,X26029),X26028)),
    inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).

fof(i_0_9422,plain,
    ! [X20309,X20310,X20311] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20311),X20310))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20310),X20309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_9423,plain,
    ! [X20063,X20064,X20065] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20065),X20064))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20064),X20063))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_9424,plain,
    ! [X20306,X20307,X20308] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20308),X20307))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20306),X20307))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_9425,plain,
    ! [X20060,X20061,X20062] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20062),X20061))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20060),X20061))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_9426,plain,
    ! [X20298,X20299,X20300] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20300),X20299))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20299),X20298))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_9427,plain,
    ! [X19910,X19911,X19912] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19912),X19911))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19911),X19910))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_9428,plain,
    ! [X20301,X20302,X20303] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20303),X20302))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20301),X20302))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_9429,plain,
    ! [X19913,X19914,X19915] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19915),X19914))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19915),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19913),X19914))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_9430,plain,
    ! [X24715,X24716,X24717,X24718] :
      ( ~ class_Divides_Osemiring__div(X24718)
      | c_Divides_Odiv__class_Omod(X24718,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24718),X24717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24718),X24716),X24715)),X24716) = c_Divides_Odiv__class_Omod(X24718,X24717,X24716) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).

fof(i_0_9431,plain,
    ! [X24719,X24720,X24721,X24722] :
      ( ~ class_Divides_Osemiring__div(X24722)
      | c_Divides_Odiv__class_Omod(X24722,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24722),X24721),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24722),X24720),X24719)),X24719) = c_Divides_Odiv__class_Omod(X24722,X24721,X24719) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).

fof(i_0_9432,plain,
    ! [X22457,X22458,X22460,X22461,X22462] :
      ( ( X22458 = hAPP(c_Nat_OSuc,esk123_2(X22457,X22458))
        | X22458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22458),hAPP(c_Nat_OSuc,X22457))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk123_2(X22457,X22458)),X22457))
        | X22458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22458),hAPP(c_Nat_OSuc,X22457))) )
      & ( X22461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22461),hAPP(c_Nat_OSuc,X22460))) )
      & ( X22461 != hAPP(c_Nat_OSuc,X22462)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22462),X22460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22461),hAPP(c_Nat_OSuc,X22460))) ) ),
    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_less__Suc__eq__0__disj])])])])])]) ).

cnf(i_0_9433,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_5885]) ).

fof(i_0_9434,plain,
    ! [X33256,X33257,X33258,X33260,X33261,X33262] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33257),X33258),c_Orderings_Otop__class_Otop(tc_fun(X33257,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X33256,X33258))
        | hBOOL(hAPP(X33256,esk511_1(X33256))) )
      & ( hBOOL(hAPP(hAPP(c_member(X33262),esk512_2(X33260,X33262)),c_Orderings_Otop__class_Otop(tc_fun(X33262,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X33260,X33261)) )
      & ( hBOOL(hAPP(X33260,esk512_2(X33260,X33262)))
        | ~ hBOOL(hAPP(X33260,X33261)) ) ),
    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_bex__UNIV])])])])])]) ).

fof(i_0_9435,plain,
    ! [X30726,X30727] :
      ( X30727 = c_List_Olist_ONil(X30726)
      | hAPP(c_List_Orotate1(X30726),X30727) = hAPP(hAPP(c_List_Oappend(X30726),hAPP(c_List_Otl(X30726),X30727)),hAPP(hAPP(c_List_Olist_OCons(X30726),hAPP(c_List_Ohd(X30726),X30727)),c_List_Olist_ONil(X30726))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).

cnf(i_0_9436,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5886]) ).

fof(i_0_9437,plain,
    ! [X31305,X31306,X31307,X31308] :
      ( ~ class_Groups_Ocomm__monoid__add(X31308)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X31308),X31307),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X31306,X31305))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31308),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X31308),X31307),c_List_Oupto(X31306,X31305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).

fof(i_0_9438,plain,
    ! [X31309,X31310,X31311,X31312] :
      ( ~ class_Groups_Ocomm__monoid__add(X31312)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31312),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X31312),X31311),c_List_Oupto(X31310,X31309))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X31312),X31311),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X31310,X31309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).

fof(i_0_9439,plain,
    ! [X20579,X20580,X20581,X20582] :
      ( ~ class_Lattices_Osemilattice__inf(X20582)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20582),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20582),X20581),X20580)),X20579) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20582),X20581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20582),X20580),X20579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).

fof(i_0_9440,plain,
    ! [X20571,X20572,X20573,X20574] :
      ( ~ class_Lattices_Osemilattice__inf(X20574)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20574),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20574),X20573),X20572)),X20571) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20574),X20573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20574),X20572),X20571)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).

fof(i_0_9441,plain,
    ! [X20575,X20576,X20577,X20578] :
      ( ~ class_Lattices_Olattice(X20578)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20578),X20577),X20576)),X20575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20578),X20577),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20578),X20576),X20575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).

fof(i_0_9442,plain,
    ! [X19480,X19481,X19482,X19483] :
      ( ~ class_Lattices_Osemilattice__sup(X19483)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19483),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19483),X19482),X19481)),X19480) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19483),X19482),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19483),X19481),X19480)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).

fof(i_0_9443,plain,
    ! [X19472,X19473,X19474,X19475] :
      ( ~ class_Lattices_Osemilattice__sup(X19475)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19475),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19475),X19474),X19473)),X19472) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19475),X19474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19475),X19473),X19472)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).

fof(i_0_9444,plain,
    ! [X19476,X19477,X19478,X19479] :
      ( ~ class_Lattices_Olattice(X19479)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19479),X19478),X19477)),X19476) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19479),X19478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19479),X19477),X19476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).

fof(i_0_9445,plain,
    ! [X18728,X18729,X18730,X18731] :
      ( ~ class_Orderings_Olinorder(X18731)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18731),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18731),X18730),X18729)),X18728) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18731),X18730),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18731),X18729),X18728)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).

fof(i_0_9446,plain,
    ! [X18724,X18725,X18726,X18727] :
      ( ~ class_Orderings_Olinorder(X18727)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18727),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18727),X18726),X18725)),X18724) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18727),X18726),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18727),X18725),X18724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).

fof(i_0_9447,plain,
    ! [X18720,X18721,X18722,X18723] :
      ( ~ class_Orderings_Olinorder(X18723)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18723),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18723),X18722),X18721)),X18720) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18723),X18722),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18723),X18721),X18720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).

fof(i_0_9448,plain,
    ! [X18716,X18717,X18718,X18719] :
      ( ~ class_Orderings_Olinorder(X18719)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18719),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18719),X18718),X18717)),X18716) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18719),X18718),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18719),X18717),X18716)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).

fof(i_0_9449,plain,
    ! [X20393,X20394,X20395] :
      ( ~ class_Groups_Omonoid__mult(X20395)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20395),hAPP(hAPP(c_Power_Opower__class_Opower(X20395),X20394),X20393)),X20394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20395),X20394),hAPP(hAPP(c_Power_Opower__class_Opower(X20395),X20394),X20393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).

fof(i_0_9450,plain,
    ! [X18614,X18615,X18616,X18617] :
      ( ~ class_Rings_Ocomm__semiring__1(X18617)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18616),X18615)),X18614) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18615),X18614)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).

fof(i_0_9451,plain,
    ! [X18251,X18252,X18253,X18254] :
      ( ~ class_Groups_Oab__semigroup__mult(X18254)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18254),X18253),X18252)),X18251) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18254),X18253),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18254),X18252),X18251)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).

fof(i_0_9452,plain,
    ! [X18580,X18581,X18582,X18583] :
      ( ~ class_Rings_Ocomm__semiring__1(X18583)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18583),X18582),X18581)),X18580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18583),X18582),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18583),X18581),X18580)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_9453,plain,
    ! [X18065,X18066,X18067,X18068] :
      ( ~ class_Groups_Oab__semigroup__add(X18068)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18068),X18067),X18066)),X18065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18068),X18067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18068),X18066),X18065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_9454,plain,
    ! [X23594,X23595,X23596,X23597] :
      ( ~ class_Rings_Odivision__ring(X23597)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23597),X23596),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23597),X23595),X23594)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23597),X23596),X23595)),X23594) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).

fof(i_0_9455,plain,
    ! [X18618,X18619,X18620,X18621] :
      ( ~ class_Rings_Ocomm__semiring__1(X18621)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18621),X18620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18621),X18619),X18618)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18621),X18620),X18619)),X18618) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).

fof(i_0_9456,plain,
    ! [X18584,X18585,X18586,X18587] :
      ( ~ class_Rings_Ocomm__semiring__1(X18587)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18587),X18586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18587),X18585),X18584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18587),X18586),X18585)),X18584) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_9457,plain,
    ! [X31649,X31650,X31651] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31651),X31650),hAPP(c_List_Oset(X31651),X31649)))
        | c_List_Oremdups(X31651,hAPP(hAPP(c_List_Olist_OCons(X31651),X31650),X31649)) = c_List_Oremdups(X31651,X31649) )
      & ( hBOOL(hAPP(hAPP(c_member(X31651),X31650),hAPP(c_List_Oset(X31651),X31649)))
        | c_List_Oremdups(X31651,hAPP(hAPP(c_List_Olist_OCons(X31651),X31650),X31649)) = hAPP(hAPP(c_List_Olist_OCons(X31651),X31650),c_List_Oremdups(X31651,X31649)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5887])]) ).

fof(i_0_9458,plain,
    ! [X30966,X30967] :
      ( X30967 = c_List_Olist_ONil(X30966)
      | c_List_Olast(X30966,X30967) = hAPP(hAPP(c_List_Onth(X30966),X30967),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30966)),X30967)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__conv__nth])]) ).

fof(i_0_9459,plain,
    ! [X24012,X24013] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24012),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X24013),X24012) = hAPP(c_Groups_Ouminus__class_Ouminus(X24013),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24013),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24012))))
        | ~ class_Rings_Oring__1(X24013) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24012),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X24013),X24012) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24013),hAPP(c_Int_Onat,X24012))
        | ~ class_Rings_Oring__1(X24013) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5888])])]) ).

fof(i_0_9460,plain,
    ! [X26399,X26400] :
      ( ~ class_Int_Onumber__ring(X26400)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X26399))
      | hBOOL(hAPP(hAPP(c_member(X26400),hAPP(c_Int_Onumber__class_Onumber__of(X26400),X26399)),c_Nat_Osemiring__1__class_ONats(X26400))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).

fof(i_0_9461,plain,
    ! [X24490,X24491] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24491),X24490))
      | hAPP(c_Finite__Set_Ocard(tc_fun(X24491,tc_HOL_Obool)),hAPP(c_Set_OPow(X24491),X24490)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X24491),X24490)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).

fof(i_0_9462,plain,
    ! [X24264] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24264)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X24264)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24264),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).

fof(i_0_9463,plain,
    ! [X20926,X20927,X20928] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20928,tc_HOL_Obool)),X20927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20928,tc_HOL_Obool)),X20926)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20928,tc_HOL_Obool)),X20927),X20926),
    inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).

fof(i_0_9464,plain,
    ! [X20929,X20930,X20931] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20931,tc_HOL_Obool)),X20930),X20929) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20931,tc_HOL_Obool)),X20930),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20931,tc_HOL_Obool)),X20929)),
    inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).

fof(i_0_9465,plain,
    ! [X22602] :
      ( ~ class_Rings_Olinordered__semidom(X22602)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22602),c_Groups_Ozero__class_Ozero(X22602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22602),c_Groups_Oone__class_Oone(X22602)),c_Groups_Oone__class_Oone(X22602)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_9466,plain,
    ! [X23748,X23749] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X23749,X23748)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23749),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(i_0_9467,plain,
    ! [X32927,X32928,X32929,X32930] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32930),X32929))
      | hAPP(hAPP(c_List_Onth(X32928),c_List_Oreplicate(X32928,X32929,X32927)),X32930) = X32927 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__replicate])]) ).

fof(i_0_9468,plain,
    ! [X19238,X19239,X19240] :
      ( ~ class_Orderings_Olinorder(X19240)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19240),X19239))
      | ~ hBOOL(hAPP(hAPP(c_member(X19240),X19238),X19239))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X19240),X19238),c_Big__Operators_Olattice_OInf__fin(X19240,c_Orderings_Oord__class_Omin(X19240),X19239)) = X19238 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).

fof(i_0_9469,plain,
    ! [X19235,X19236,X19237] :
      ( ~ class_Orderings_Olinorder(X19237)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19237),X19236))
      | ~ hBOOL(hAPP(hAPP(c_member(X19237),X19235),X19236))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X19237),X19235),c_Big__Operators_Olattice_OSup__fin(X19237,c_Orderings_Oord__class_Omax(X19237),X19236)) = X19235 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).

fof(i_0_9470,plain,
    ! [X22393,X22394] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22394),X22393),hAPP(c_Groups_Ouminus__class_Ouminus(X22394),X22393)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22394),X22393),c_Groups_Ozero__class_Ozero(X22394)))
        | ~ class_Rings_Olinordered__idom(X22394) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22394),X22393),c_Groups_Ozero__class_Ozero(X22394)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22394),X22393),hAPP(c_Groups_Ouminus__class_Ouminus(X22394),X22393)))
        | ~ class_Rings_Olinordered__idom(X22394) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_9471,plain,
    ! [X22387,X22388] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22388),X22387),hAPP(c_Groups_Ouminus__class_Ouminus(X22388),X22387)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22388),X22387),c_Groups_Ozero__class_Ozero(X22388)))
        | ~ class_Groups_Olinordered__ab__group__add(X22388) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22388),X22387),c_Groups_Ozero__class_Ozero(X22388)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22388),X22387),hAPP(c_Groups_Ouminus__class_Ouminus(X22388),X22387)))
        | ~ class_Groups_Olinordered__ab__group__add(X22388) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_9472,plain,
    ! [X20891,X20892,X20893] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20893,tc_HOL_Obool)),X20892),X20891) != c_Orderings_Obot__class_Obot(tc_fun(X20893,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20893,tc_HOL_Obool)),X20892),X20891) = X20892 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).

fof(i_0_9473,plain,
    ! [X30928,X30929,X30930,X30931,X30932] :
      ( ~ class_Orderings_Olinorder(X30932)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30931,X30932,X30930),X30929),X30928) != c_List_Olist_ONil(X30931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).

fof(i_0_9474,plain,
    ! [X20333,X20334,X20335,X20336] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20336)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20335),X20334))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20335,X20336),hAPP(c_COMBK(X20336,X20335),X20333)),X20334) = hAPP(hAPP(c_Power_Opower__class_Opower(X20336),X20333),hAPP(c_Finite__Set_Ocard(X20335),X20334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).

fof(i_0_9475,plain,
    ! [X32998,X32999] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32999),X32998))
        | c_Lazy__Sequence_Osmall__lazy_H(X32999,X32998) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32999),X32998))
        | c_Lazy__Sequence_Osmall__lazy_H(X32999,X32998) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X32998),c_Lazy__Sequence_Osmall__lazy_H(X32999,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32998),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5889])]) ).

fof(i_0_9476,plain,
    ! [X19152,X19153,X19154] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19154)
      | X19153 = c_Orderings_Obot__class_Obot(tc_fun(X19154,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19154),X19153))
      | hAPP(c_Finite__Set_Ofold1(X19154,c_Groups_Otimes__class_Otimes(X19154)),hAPP(hAPP(c_Set_Oinsert(X19154),X19152),X19153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19154),X19152),hAPP(c_Finite__Set_Ofold1(X19154,c_Groups_Otimes__class_Otimes(X19154)),X19153)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).

fof(i_0_9477,plain,
    ! [X23140,X23141,X23142,X23143] :
      ( ~ class_Orderings_Oorder(X23143)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23143,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23143,X23142),X23141)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23143,X23141),X23140)) = c_Orderings_Obot__class_Obot(tc_fun(X23143,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).

fof(i_0_9478,plain,
    ! [X24562,X24563] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24563),hAPP(c_Nat_OSuc,X24562)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24563),X24562)),
    inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).

fof(i_0_9479,plain,
    ! [X30428,X30429,X30430,X30431] : hAPP(hAPP(c_List_Oappend(X30431),hAPP(hAPP(c_List_Oappend(X30431),X30430),X30429)),X30428) = hAPP(hAPP(c_List_Oappend(X30431),X30430),hAPP(hAPP(c_List_Oappend(X30431),X30429),X30428)),
    inference(variable_rename,[status(thm)],[fact_append__assoc]) ).

fof(i_0_9480,plain,
    ! [X30386,X30387,X30388,X30389] : hAPP(hAPP(c_List_Oappend(X30389),hAPP(hAPP(c_List_Olist_OCons(X30389),X30388),X30387)),X30386) = hAPP(hAPP(c_List_Olist_OCons(X30389),X30388),hAPP(hAPP(c_List_Oappend(X30389),X30387),X30386)),
    inference(variable_rename,[status(thm)],[fact_append__Cons]) ).

fof(i_0_9481,plain,
    ! [X33989,X33990] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33990),X33989))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33989))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33990),X33989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).

fof(i_0_9482,plain,
    ! [X30797,X30798,X30799] :
      ( X30799 = c_List_Olist_ONil(X30798)
      | hAPP(hAPP(c_List_Otake(X30798),hAPP(c_Nat_OSuc,X30797)),X30799) = hAPP(hAPP(c_List_Olist_OCons(X30798),hAPP(c_List_Ohd(X30798),X30799)),hAPP(hAPP(c_List_Otake(X30798),X30797),hAPP(c_List_Otl(X30798),X30799))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).

fof(i_0_9483,plain,
    ! [X23569] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23569))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23569) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X23569))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).

fof(i_0_9484,plain,
    ! [X29785,X29786,X29787,X29788] :
      ( ( X29788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29787),hAPP(hAPP(c_List_Olist_OCons(X29787),X29786),X29785)),X29788) = X29786 )
      & ( X29788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29787),hAPP(hAPP(c_List_Olist_OCons(X29787),X29786),X29785)),X29788) = hAPP(hAPP(c_List_Onth(X29787),X29785),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29788),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons_H])]) ).

fof(i_0_9485,plain,
    ! [X17005,X17006,X17007,X17008] :
      ( ( X17008 != c_Orderings_Obot__class_Obot(tc_fun(X17007,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17007,X17006,hAPP(c_COMBK(X17006,X17007),X17005)),X17008) = c_Orderings_Obot__class_Obot(tc_fun(X17006,tc_HOL_Obool)) )
      & ( X17008 = c_Orderings_Obot__class_Obot(tc_fun(X17007,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17007,X17006,hAPP(c_COMBK(X17006,X17007),X17005)),X17008) = hAPP(hAPP(c_Set_Oinsert(X17006),X17005),c_Orderings_Obot__class_Obot(tc_fun(X17006,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).

cnf(i_0_9486,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5849]) ).

cnf(i_0_9487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5851]) ).

cnf(i_0_9488,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5850]) ).

cnf(i_0_9489,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5852]) ).

fof(i_0_9490,plain,
    ! [X31250,X31251,X31252,X31253] :
      ( ~ class_Groups_Ocomm__monoid__add(X31253)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31252),X31251))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31253),hAPP(hAPP(c_List_Omap(X31252,X31253),X31250),X31251)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X31252,X31253),X31250),hAPP(c_List_Oset(X31252),X31251)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).

fof(i_0_9491,plain,
    ! [X20402,X20403,X20404,X20405] :
      ( ~ class_Groups_Omonoid__mult(X20405)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20405),X20404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20403),X20402)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20405),hAPP(hAPP(c_Power_Opower__class_Opower(X20405),X20404),X20403)),X20402) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).

fof(i_0_9492,plain,
    ! [X20321,X20322,X20323,X20324] :
      ( ~ class_Rings_Ocomm__semiring__1(X20324)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20324),hAPP(hAPP(c_Power_Opower__class_Opower(X20324),X20323),X20322)),X20321) = hAPP(hAPP(c_Power_Opower__class_Opower(X20324),X20323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20322),X20321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).

fof(i_0_9493,plain,
    ! [X24655,X24656,X24657] :
      ( ~ class_Divides_Oring__div(X24657)
      | c_Divides_Odiv__class_Omod(X24657,hAPP(c_Groups_Ouminus__class_Ouminus(X24657),X24656),X24655) = c_Divides_Odiv__class_Omod(X24657,hAPP(c_Groups_Ouminus__class_Ouminus(X24657),c_Divides_Odiv__class_Omod(X24657,X24656,X24655)),X24655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).

fof(i_0_9494,plain,
    ! [X30794,X30795,X30796] : hAPP(c_List_Otl(X30796),hAPP(hAPP(c_List_Otake(X30796),X30795),X30794)) = hAPP(hAPP(c_List_Otake(X30796),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X30796),X30794)),
    inference(variable_rename,[status(thm)],[fact_tl__take]) ).

fof(i_0_9495,plain,
    ! [X25082,X25083,X25084] :
      ( ~ class_Rings_Olinordered__idom(X25084)
      | hAPP(c_Groups_Oabs__class_Oabs(X25084),hAPP(hAPP(c_Power_Opower__class_Opower(X25084),hAPP(c_Groups_Ouminus__class_Ouminus(X25084),X25083)),X25082)) = hAPP(c_Groups_Oabs__class_Oabs(X25084),hAPP(hAPP(c_Power_Opower__class_Opower(X25084),X25083),X25082)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).

cnf(i_0_9496,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId(X1)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_5890]) ).

cnf(i_0_9497,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Relation_OId(X1)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_5891]) ).

fof(i_0_9498,plain,
    ! [X22000,X22001,X22002] :
      ( ~ class_Lattices_Olattice(X22002)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22002),X22001))
      | hBOOL(hAPP(hAPP(c_member(X22002),X22000),X22001))
      | X22001 = c_Orderings_Obot__class_Obot(tc_fun(X22002,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X22002,hAPP(hAPP(c_Set_Oinsert(X22002),X22000),X22001)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X22002),X22000),c_Big__Operators_Olattice__class_OInf__fin(X22002,X22001)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5892])]) ).

fof(i_0_9499,plain,
    ! [X20354,X20355,X20356] :
      ( ~ class_Lattices_Olattice(X20356)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20356),X20355))
      | hBOOL(hAPP(hAPP(c_member(X20356),X20354),X20355))
      | X20355 = c_Orderings_Obot__class_Obot(tc_fun(X20356,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20356,hAPP(hAPP(c_Set_Oinsert(X20356),X20354),X20355)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20356),X20354),c_Big__Operators_Olattice__class_OSup__fin(X20356,X20355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5893])]) ).

fof(i_0_9500,plain,
    ! [X19161,X19162,X19163] :
      ( ~ class_Orderings_Olinorder(X19163)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19163),X19162))
      | hBOOL(hAPP(hAPP(c_member(X19163),X19161),X19162))
      | X19162 = c_Orderings_Obot__class_Obot(tc_fun(X19163,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X19163,hAPP(hAPP(c_Set_Oinsert(X19163),X19161),X19162)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19163),X19161),c_Big__Operators_Olinorder__class_OMin(X19163,X19162)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5894])]) ).

fof(i_0_9501,plain,
    ! [X19158,X19159,X19160] :
      ( ~ class_Orderings_Olinorder(X19160)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19160),X19159))
      | hBOOL(hAPP(hAPP(c_member(X19160),X19158),X19159))
      | X19159 = c_Orderings_Obot__class_Obot(tc_fun(X19160,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X19160,hAPP(hAPP(c_Set_Oinsert(X19160),X19158),X19159)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19160),X19158),c_Big__Operators_Olinorder__class_OMax(X19160,X19159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5895])]) ).

fof(i_0_9502,plain,
    ! [X19491,X19492] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19492),c_Orderings_Otop__class_Otop(tc_fun(X19492,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X19492),X19491) != hAPP(c_Finite__Set_Ocard(X19492),c_Orderings_Otop__class_Otop(tc_fun(X19492,tc_HOL_Obool)))
      | X19491 = c_Orderings_Otop__class_Otop(tc_fun(X19492,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_9503,plain,
    ! [X30664,X30665,X30666,X30667] :
      ( ( X30667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30666),X30667),hAPP(hAPP(c_List_Olist_OCons(X30666),X30665),X30664)) = hAPP(hAPP(c_List_Olist_OCons(X30666),X30665),X30664) )
      & ( X30667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30666),X30667),hAPP(hAPP(c_List_Olist_OCons(X30666),X30665),X30664)) = hAPP(hAPP(c_List_Odrop(X30666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30667),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30664) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).

fof(i_0_9504,plain,
    ! [X25572] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X25572))))),
    inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).

fof(i_0_9505,plain,
    ! [X17043,X17044,X17045,X17046] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17046),X17045),X17044),X17043))
        | X17045 = X17043
        | hBOOL(hAPP(X17044,X17043)) )
      & ( X17045 != X17043
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17046),X17045),X17044),X17043)) )
      & ( ~ hBOOL(hAPP(X17044,X17043))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17046),X17045),X17044),X17043)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_9506,plain,
    ! [X34126,X34127,X34128] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34128),X34127),hAPP(c_Groups_Ouminus__class_Ouminus(X34128),X34126)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34128),X34127),X34126))
        | ~ class_Rings_Ocomm__ring__1(X34128) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34128),X34127),X34126))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34128),X34127),hAPP(c_Groups_Ouminus__class_Ouminus(X34128),X34126)))
        | ~ class_Rings_Ocomm__ring__1(X34128) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).

fof(i_0_9507,plain,
    ! [X22768,X22769,X22770] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22770),X22769),hAPP(c_SetInterval_Oord__class_OlessThan(X22770),X22768)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22770),X22769),X22768))
        | ~ class_Orderings_Oord(X22770) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22770),X22769),X22768))
        | hBOOL(hAPP(hAPP(c_member(X22770),X22769),hAPP(c_SetInterval_Oord__class_OlessThan(X22770),X22768)))
        | ~ class_Orderings_Oord(X22770) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).

fof(i_0_9508,plain,
    ! [X24070,X24071,X24072] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24072),X24071),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24072),X24070)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24072),X24070),X24071))
        | ~ class_Orderings_Oord(X24072) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24072),X24070),X24071))
        | hBOOL(hAPP(hAPP(c_member(X24072),X24071),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24072),X24070)))
        | ~ class_Orderings_Oord(X24072) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).

fof(i_0_9509,plain,
    ! [X24300,X24301,X24302] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24302),X24301),hAPP(c_SetInterval_Oord__class_OatMost(X24302),X24300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24302),X24301),X24300))
        | ~ class_Orderings_Oord(X24302) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24302),X24301),X24300))
        | hBOOL(hAPP(hAPP(c_member(X24302),X24301),hAPP(c_SetInterval_Oord__class_OatMost(X24302),X24300)))
        | ~ class_Orderings_Oord(X24302) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).

fof(i_0_9510,plain,
    ! [X24303,X24304,X24305] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24305),X24304),hAPP(c_SetInterval_Oord__class_OatLeast(X24305),X24303)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24305),X24303),X24304))
        | ~ class_Orderings_Oord(X24305) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24305),X24303),X24304))
        | hBOOL(hAPP(hAPP(c_member(X24305),X24304),hAPP(c_SetInterval_Oord__class_OatLeast(X24305),X24303)))
        | ~ class_Orderings_Oord(X24305) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).

fof(i_0_9511,plain,
    ! [X23512,X23513,X23514] :
      ( ~ class_Groups_Oordered__ab__group__add(X23514)
      | hAPP(c_Set_Oimage(X23514,X23514,c_Groups_Ouminus__class_Ouminus(X23514)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23514,X23513,X23512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23514,hAPP(c_Groups_Ouminus__class_Ouminus(X23514),X23512)),hAPP(c_Groups_Ouminus__class_Ouminus(X23514),X23513)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).

fof(i_0_9512,plain,
    ! [X17216,X17217,X17218,X17219,X17220] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17220,X17219,X17218)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17220),X17217))
      | ~ hBOOL(hAPP(hAPP(c_member(X17220),X17216),X17217))
      | hAPP(hAPP(X17219,X17216),hAPP(X17218,X17217)) = hAPP(X17218,X17217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).

fof(i_0_9513,plain,
    ! [X18508,X18509,X18510] :
      ( ~ class_Orderings_Olinorder(X18510)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18510),X18509))
      | ~ hBOOL(hAPP(hAPP(c_member(X18510),X18508),X18509))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18510),X18508),c_Big__Operators_Olinorder__class_OMax(X18510,X18509))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).

cnf(i_0_9514,plain,
    ( c_List_Oall__interval__nat(X1,X2,X3)
    | ~ c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5896]) ).

fof(i_0_9515,plain,
    ! [X29981,X29982] :
      ( ~ class_Groups_Ocomm__monoid__add(X29982)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29982),X29981) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X29982),hAPP(c_List_Onth(X29982),X29981)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29982)),X29981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).

fof(i_0_9516,plain,
    ! [X22900,X22901] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22901),X22900))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22900)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22901)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22900),X22901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).

fof(i_0_9517,plain,
    ! [X23071] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23071)),X23071) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

fof(i_0_9518,plain,
    ! [X27757,X27758] : hAPP(c_Relation_OField(X27758),X27757) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27758,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27758,X27758),X27757)),hAPP(c_Relation_ORange(X27758,X27758),X27757)),
    inference(variable_rename,[status(thm)],[fact_Field__def]) ).

cnf(i_0_9519,plain,
    c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_5897]) ).

fof(i_0_9520,plain,
    ! [X24327,X24328] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24328,X24327) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24328),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24327))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(i_0_9521,plain,
    ! [X30293,X30294,X30295] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30295))
        | c_List_Osublist(X30294,hAPP(hAPP(c_List_Olist_OCons(X30294),X30293),c_List_Olist_ONil(X30294)),X30295) = hAPP(hAPP(c_List_Olist_OCons(X30294),X30293),c_List_Olist_ONil(X30294)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30295))
        | c_List_Osublist(X30294,hAPP(hAPP(c_List_Olist_OCons(X30294),X30293),c_List_Olist_ONil(X30294)),X30295) = c_List_Olist_ONil(X30294) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5898])]) ).

fof(i_0_9522,plain,
    ! [X23482,X23483] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23483))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23483),X23482)),X23483) = X23482 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).

fof(i_0_9523,plain,
    ! [X23484,X23485] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23485))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23484),X23485)),X23485) = X23484 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).

cnf(i_0_9524,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5899]) ).

cnf(i_0_9525,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5900]) ).

fof(i_0_9526,plain,
    ! [X24781,X24782] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24782,X24781) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24782,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24781)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24782,X24781) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24782,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24781)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24782,X24781)),X24781) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).

fof(i_0_9527,plain,
    ! [X19641,X19642] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19642,tc_HOL_Obool)),X19641),c_Orderings_Otop__class_Otop(tc_fun(X19642,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_9528,plain,
    ! [X25861] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25861)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25861)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25861)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25861)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25861))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5901])]) ).

cnf(i_0_9529,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5902]) ).

fof(i_0_9530,plain,
    ! [X23062,X23063,X23064] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23064),X23063))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23063),X23062))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23064),X23062)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_9531,plain,
    ! [X19919,X19920,X19921] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19921),X19920))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19920),X19919))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19921),X19919)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_9532,plain,
    ! [X34150,X34151,X34152,X34153] :
      ( ~ class_Divides_Osemiring__div(X34153)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34153),X34152),X34151))
      | c_Divides_Odiv__class_Omod(X34153,c_Divides_Odiv__class_Omod(X34153,X34150,X34151),X34152) = c_Divides_Odiv__class_Omod(X34153,X34150,X34152) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).

fof(i_0_9533,plain,
    ! [X20014,X20015] :
      ( ~ class_Rings_Ocomm__semiring__1(X20015)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20015),X20014),X20014) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20015),c_Groups_Oone__class_Oone(X20015)),c_Groups_Oone__class_Oone(X20015))),X20014) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_9534,plain,
    ! [X18390,X18391,X18392] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18392),X18391),X18390))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18392),X18391),X18390))
        | ~ class_Orderings_Opreorder(X18392) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18392),X18390),X18391))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18392),X18391),X18390))
        | ~ class_Orderings_Opreorder(X18392) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18392),X18391),X18390))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18392),X18390),X18391))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18392),X18391),X18390))
        | ~ class_Orderings_Opreorder(X18392) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5903])])]) ).

fof(i_0_9535,plain,
    ! [X20049,X20050,X20051,X20052] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20052),X20051))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20050),X20051) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20052),X20049)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20050),X20049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_9536,plain,
    ! [X34117,X34118,X34119] :
      ( ~ class_Divides_Oring__div(X34119)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34119),X34118),X34117))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34119),X34117),hAPP(c_Groups_Ouminus__class_Ouminus(X34119),X34118)) = hAPP(c_Groups_Ouminus__class_Ouminus(X34119),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34119),X34117),X34118)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).

fof(i_0_9537,plain,
    ! [X21548,X21549] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21549)),X21548))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21549),X21548)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_9538,plain,
    ! [X21800,X21801] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21801),X21800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21801)),X21800)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21801)),X21800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21801),X21800)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_9539,plain,
    ! [X21796,X21797] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21797)),X21796))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21797),X21796)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21797),X21796))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21797)),X21796)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_9540,plain,
    ! [X21788,X21789] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21789)),X21788))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21789),X21788)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_9541,plain,
    ! [X21575,X21576] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21576)),X21575))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21576),X21575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_9542,plain,
    ! [X20184,X20185,X20186] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20186),X20185))
      | hBOOL(hAPP(hAPP(c_member(X20186),X20184),X20185))
      | hAPP(c_Finite__Set_Ocard(X20186),hAPP(hAPP(c_Set_Oinsert(X20186),X20184),X20185)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X20186),X20185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5904])]) ).

fof(i_0_9543,plain,
    ! [X30615,X30616,X30617,X30618] : hAPP(hAPP(c_List_Odrop(X30618),X30617),hAPP(hAPP(c_List_Odrop(X30618),X30616),X30615)) = hAPP(hAPP(c_List_Odrop(X30618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30617),X30616)),X30615),
    inference(variable_rename,[status(thm)],[fact_drop__drop]) ).

fof(i_0_9544,plain,
    ! [X29851,X29852,X29853,X29854] : hAPP(hAPP(c_List_Otake(X29854),X29853),hAPP(hAPP(c_List_Otake(X29854),X29852),X29851)) = hAPP(hAPP(c_List_Otake(X29854),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X29853),X29852)),X29851),
    inference(variable_rename,[status(thm)],[fact_take__take]) ).

fof(i_0_9545,plain,
    ! [X23404,X23405,X23406] :
      ( ( ~ hBOOL(hAPP(X23406,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23405),X23404)))
        | epred1_3(X23406,X23405,X23404) )
      & ( ~ epred1_3(X23406,X23405,X23404)
        | hBOOL(hAPP(X23406,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23405),X23404))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5905])]) ).

fof(i_0_9546,plain,
    ! [X21899,X21900,X21901] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21901)
      | ~ hBOOL(hAPP(hAPP(c_member(X21901),X21900),X21899))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21901),c_Complete__Lattice_OInf__class_OInf(X21901,X21899)),X21900)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).

fof(i_0_9547,plain,
    ! [X22996,X22998,X22999,X23001] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk142_1(X22996)))
        | hBOOL(hAPP(X22996,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22998))) )
      & ( ~ hBOOL(hAPP(X22996,esk142_1(X22996)))
        | hBOOL(hAPP(X22996,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22998))) )
      & ( ~ hBOOL(hAPP(X22999,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk143_1(X22999))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23001))
        | hBOOL(hAPP(X22999,X23001)) ) ),
    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_transfer__int__nat__quantifiers_I1_J])])])])])]) ).

fof(i_0_9548,plain,
    ! [X23688,X23689] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23689))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23689),X23688)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X23689)),hAPP(c_Int_Onat,X23688)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).

fof(i_0_9549,plain,
    ! [X23722,X23723] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23723))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23723),X23722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X23723)),hAPP(c_Int_Onat,X23722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).

fof(i_0_9550,plain,
    ! [X24374,X24375] :
      ( ~ c_Nat__Transfer_Ois__nat(X24375)
      | ~ c_Nat__Transfer_Ois__nat(X24374)
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24375,X24374) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X24375),hAPP(c_Int_Onat,X24374))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).

fof(i_0_9551,plain,
    ! [X31881] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31881)),c_List_Otranspose__rel(X31881)),c_List_Olist_ONil(tc_List_Olist(X31881))))
      | c_List_Otranspose(X31881,c_List_Olist_ONil(tc_List_Olist(X31881))) = c_List_Olist_ONil(tc_List_Olist(X31881)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).

fof(i_0_9552,plain,
    ! [X24849,X24850,X24851] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24851),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24850,X24849)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24851),X24850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24851),X24849)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(i_0_9553,plain,
    ! [X23021,X23022] :
      ( ( X23022 != X23021
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23022) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23021) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23022) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23021)
        | X23022 = X23021 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).

fof(i_0_9554,plain,
    ! [X30444,X30445,X30446] : hAPP(c_List_Oset(X30446),hAPP(hAPP(c_List_Oappend(X30446),X30445),X30444)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30446,tc_HOL_Obool)),hAPP(c_List_Oset(X30446),X30445)),hAPP(c_List_Oset(X30446),X30444)),
    inference(variable_rename,[status(thm)],[fact_set__append]) ).

fof(i_0_9555,plain,
    ! [X21517,X21518] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21518),X21517))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21518)),hAPP(c_Nat_OSuc,X21517))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_9556,plain,
    ! [X17084,X17085,X17086,X17087] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X17087),X17086),X17085) != hAPP(hAPP(c_Set_Oinsert(X17087),X17086),X17084)
        | X17085 = X17084
        | hBOOL(hAPP(hAPP(c_member(X17087),X17086),X17084))
        | hBOOL(hAPP(hAPP(c_member(X17087),X17086),X17085)) )
      & ( X17085 != X17084
        | hAPP(hAPP(c_Set_Oinsert(X17087),X17086),X17085) = hAPP(hAPP(c_Set_Oinsert(X17087),X17086),X17084)
        | hBOOL(hAPP(hAPP(c_member(X17087),X17086),X17084))
        | hBOOL(hAPP(hAPP(c_member(X17087),X17086),X17085)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5906])])]) ).

fof(i_0_9557,plain,
    ! [X20411,X20412,X20413,X20414] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20414),X20413),X20412) != hAPP(hAPP(c_Power_Opower__class_Opower(X20414),X20413),X20411)
        | X20412 = X20411
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20414),c_Groups_Oone__class_Oone(X20414)),X20413))
        | ~ class_Rings_Olinordered__semidom(X20414) )
      & ( X20412 != X20411
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20414),X20413),X20412) = hAPP(hAPP(c_Power_Opower__class_Opower(X20414),X20413),X20411)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20414),c_Groups_Oone__class_Oone(X20414)),X20413))
        | ~ class_Rings_Olinordered__semidom(X20414) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).

fof(i_0_9558,plain,
    ! [X30331,X30332,X30333] : c_List_Olistset(X30333,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X30333,tc_HOL_Obool)),X30332),X30331)) = c_List_Oset__Cons(X30333,X30332,c_List_Olistset(X30333,X30331)),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(i_0_9559,plain,
    ! [X33243,X33244,X33245] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33244),X33245),c_Orderings_Obot__class_Obot(tc_fun(X33244,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X33243,X33245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__empty])]) ).

fof(i_0_9560,plain,
    ! [X24947,X24948] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X24948)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24948),X24947))
      | c_Complete__Lattice_OSup__class_OSup(X24948,X24947) = hAPP(hAPP(c_Finite__Set_Ofold(X24948,X24948,c_Lattices_Osemilattice__sup__class_Osup(X24948)),c_Orderings_Obot__class_Obot(X24948)),X24947) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).

fof(i_0_9561,plain,
    ! [X21459,X21460] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21460)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21460),X21459))
      | c_Complete__Lattice_OInf__class_OInf(X21460,X21459) = hAPP(hAPP(c_Finite__Set_Ofold(X21460,X21460,c_Lattices_Osemilattice__inf__class_Oinf(X21460)),c_Orderings_Otop__class_Otop(X21460)),X21459) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).

fof(i_0_9562,plain,
    ! [X22506,X22507] :
      ( ( X22507 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22506),X22507) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X22507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22506),X22507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22506),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22506),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22507),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).

fof(i_0_9563,plain,
    ! [X24168,X24169,X24170] :
      ( ~ class_Groups_Oordered__ab__group__add(X24170)
      | hAPP(c_Set_Oimage(X24170,X24170,c_Groups_Ouminus__class_Ouminus(X24170)),c_SetInterval_Oord__class_OatLeastAtMost(X24170,X24169,X24168)) = c_SetInterval_Oord__class_OatLeastAtMost(X24170,hAPP(c_Groups_Ouminus__class_Ouminus(X24170),X24168),hAPP(c_Groups_Ouminus__class_Ouminus(X24170),X24169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).

fof(i_0_9564,plain,
    ! [X23369,X23370,X23371] :
      ( ~ class_Groups_Oordered__ab__group__add(X23371)
      | hAPP(c_Set_Oimage(X23371,X23371,c_Groups_Ouminus__class_Ouminus(X23371)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23371,X23370,X23369)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23371,hAPP(c_Groups_Ouminus__class_Ouminus(X23371),X23369),hAPP(c_Groups_Ouminus__class_Ouminus(X23371),X23370)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).

fof(i_0_9565,plain,
    ! [X21966,X21967,X21968] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21968),X21966),X21967))
        | hAPP(c_Finite__Set_Ocard(X21968),hAPP(hAPP(c_Set_Oinsert(X21968),X21966),X21967)) = hAPP(c_Finite__Set_Ocard(X21968),X21967)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21968),X21967)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21968),X21966),X21967))
        | hAPP(c_Finite__Set_Ocard(X21968),hAPP(hAPP(c_Set_Oinsert(X21968),X21966),X21967)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21968),X21967))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21968),X21967)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5907])])]) ).

fof(i_0_9566,plain,
    ! [X22764] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22764)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22764))),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(i_0_9567,plain,
    ! [X26771,X26772] : c_Code__Numeral_Odiv__mod__code__numeral(X26772,X26771) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X26772),X26771)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X26772,X26771)),
    inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(i_0_9568,plain,
    ! [X26499,X26500] : c_Divides_Odivmod__int(X26500,X26499) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26500),X26499)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26500,X26499)),
    inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(i_0_9569,plain,
    ! [X24701,X24702] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24702,X24701)),X24701) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24702),X24701),
    inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).

fof(i_0_9570,plain,
    ! [X23642,X23643] :
      ( ( hAPP(c_Int_Onat,X23643) != hAPP(c_Int_Onat,X23642)
        | X23643 = X23642
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23643)) )
      & ( X23643 != X23642
        | hAPP(c_Int_Onat,X23643) = hAPP(c_Int_Onat,X23642)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23643)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).

fof(i_0_9571,plain,
    ! [X23640,X23641] :
      ( ( hAPP(c_Int_Onat,X23641) != hAPP(c_Int_Onat,X23640)
        | X23641 = X23640
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23641)) )
      & ( X23641 != X23640
        | hAPP(c_Int_Onat,X23641) = hAPP(c_Int_Onat,X23640)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23641)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).

fof(i_0_9572,plain,
    ! [X22860,X22861,X22863,X22864,X22865] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22861),X22860))
        | X22860 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22861),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk139_2(X22860,X22861)))) )
      & ( X22863 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22864),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X22865)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22864),X22863)) ) ),
    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_zless__iff__Suc__zadd])])])])]) ).

cnf(i_0_9573,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5908]) ).

fof(i_0_9574,plain,
    ! [X24904,X24905] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24905),X24904)),X24904) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24905),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24905,X24904)),
    inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).

fof(i_0_9575,plain,
    ! [X20150,X20151] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20151),X20150))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20150),X20151)),X20151) = X20150 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).

fof(i_0_9576,plain,
    ! [X22895] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22895)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22895)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22895))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22895))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).

fof(i_0_9577,plain,
    ! [X25887,X25888] :
      ( ( X25888 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25888) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25888) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887) )
      & ( X25888 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25888) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25887) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).

fof(i_0_9578,plain,
    ! [X24499,X24500] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X24500,tc_HOL_Obool)),hAPP(c_Set_OPow(X24500),X24499)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24500),X24499)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24500),X24499))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X24500,tc_HOL_Obool)),hAPP(c_Set_OPow(X24500),X24499))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).

fof(i_0_9579,plain,
    ! [X27780,X27781,X27782,X27783,X27784] :
      ( ~ hBOOL(hAPP(hAPP(X27784,X27783),X27782))
      | hBOOL(hAPP(c_Predicate_ODomainP(X27781,X27780,X27784),X27783)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).

fof(i_0_9580,plain,
    ! [X27682,X27683,X27684,X27685,X27686] :
      ( ~ hBOOL(hAPP(hAPP(X27686,X27685),X27684))
      | hBOOL(hAPP(c_Predicate_ORangeP(X27683,X27682,X27686),X27684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).

fof(i_0_9581,plain,
    ! [X32790,X32791,X32792] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32792)),c_List_Osplice(X32792,X32791,X32790)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32792)),X32791)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32792)),X32790)),
    inference(variable_rename,[status(thm)],[fact_length__splice]) ).

fof(i_0_9582,plain,
    ! [X30265,X30266] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30266)),X30265)))
        | X30265 != c_List_Olist_ONil(X30266) )
      & ( X30265 = c_List_Olist_ONil(X30266)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30266)),X30265))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).

fof(i_0_9583,plain,
    ! [X24337,X24338,X24339] :
      ( ~ class_Orderings_Oorder(X24339)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24339,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24339,X24338),X24337)),hAPP(c_SetInterval_Oord__class_OatLeast(X24339),X24337)) = c_Orderings_Obot__class_Obot(tc_fun(X24339,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).

fof(i_0_9584,plain,
    ! [X21790,X21791] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21790),hAPP(c_Nat_OSuc,X21791)))
        | X21790 = X21791
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21791),X21790)) )
      & ( X21790 != X21791
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21790),hAPP(c_Nat_OSuc,X21791)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21791),X21790)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

cnf(i_0_9585,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_5909]) ).

fof(i_0_9586,plain,
    ! [X24775,X24776] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24776))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24776),X24775))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24776,X24775) = X24776 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).

fof(i_0_9587,plain,
    ! [X24291,X24292] :
      ( ~ class_Orderings_Oorder(X24292)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24292,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24292),X24291)),hAPP(c_SetInterval_Oord__class_OatLeast(X24292),X24291)) = hAPP(hAPP(c_Set_Oinsert(X24292),X24291),c_Orderings_Obot__class_Obot(tc_fun(X24292,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).

fof(i_0_9588,plain,
    ! [X21567,X21568] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21568),X21567))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21567),hAPP(c_Nat_OSuc,X21568))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21567),hAPP(c_Nat_OSuc,X21568)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21568),X21567)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5910])]) ).

cnf(i_0_9589,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5911]) ).

fof(i_0_9590,plain,
    ! [X30435,X30436,X30437] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30437)),hAPP(hAPP(c_List_Oappend(X30437),X30436),X30435)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30437)),X30436)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30437)),X30435)),
    inference(variable_rename,[status(thm)],[fact_length__append]) ).

fof(i_0_9591,plain,
    ! [X23990,X23991] :
      ( ( X23991 != X23990
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23991) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23990)
        | ~ c_Nat__Transfer_Onat__set(X23990)
        | ~ c_Nat__Transfer_Onat__set(X23991) )
      & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23991) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23990)
        | X23991 = X23990
        | ~ c_Nat__Transfer_Onat__set(X23990)
        | ~ c_Nat__Transfer_Onat__set(X23991) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J])])]) ).

fof(i_0_9592,plain,
    ! [X16957,X16958,X16959,X16960,X16961,X16962,X16963] :
      ( ( X16962 = X16959
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16962),X16961),X16960) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16959),X16958),X16957) )
      & ( X16961 = X16958
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16962),X16961),X16960) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16959),X16958),X16957) )
      & ( X16960 = X16957
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16962),X16961),X16960) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16959),X16958),X16957) )
      & ( X16962 != X16959
        | X16961 != X16958
        | X16960 != X16957
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16962),X16961),X16960) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16963),X16959),X16958),X16957) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oinject])])]) ).

fof(i_0_9593,plain,
    ! [X22447,X22448,X22449,X22450,X22451] :
      ( ~ class_Rings_Ocomm__semiring__1(X22450)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22449),X22448))
      | ~ hBOOL(hAPP(hAPP(c_member(X22449),X22451),X22448))
      | hAPP(X22447,X22451) != c_Groups_Ozero__class_Ozero(X22450)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22449,X22450),X22447),X22448) = c_Groups_Ozero__class_Ozero(X22450) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).

fof(i_0_9594,plain,
    ! [X23452,X23453,X23454] :
      ( ( X23454 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23454),X23453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23454),X23452)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X23454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23454),X23453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23454),X23452)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23453),X23452) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).

fof(i_0_9595,plain,
    ! [X24506,X24507] : hBOOL(hAPP(hAPP(c_member(tc_fun(X24507,tc_HOL_Obool)),X24506),hAPP(c_Set_OPow(X24507),X24506))),
    inference(variable_rename,[status(thm)],[fact_Pow__top]) ).

fof(i_0_9596,plain,
    ! [X32200,X32201,X32202] : hAPP(c_List_Orev(X32202),hAPP(hAPP(c_List_Olist_OCons(X32202),X32201),X32200)) = hAPP(hAPP(c_List_Oappend(X32202),hAPP(c_List_Orev(X32202),X32200)),hAPP(hAPP(c_List_Olist_OCons(X32202),X32201),c_List_Olist_ONil(X32202))),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).

cnf(i_0_9597,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5912]) ).

fof(i_0_9598,plain,
    ! [X23350,X23351] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23351))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23351),X23350))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23351),X23350) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])]) ).

fof(i_0_9599,plain,
    ! [X23337,X23338] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23338),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23338))
        | X23337 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23337),X23338))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23338))
        | X23337 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23338),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23338),X23337))
        | X23337 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23337),X23338))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23338),X23337))
        | X23337 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X23337 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23338))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23338),X23337))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23338),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23337),X23338))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23338),X23337) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])]) ).

fof(i_0_9600,plain,
    ! [X21987,X21988] :
      ( ~ class_Lattices_Olattice(X21988)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21988),X21987))
      | X21987 = c_Orderings_Obot__class_Obot(tc_fun(X21988,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21988),c_Big__Operators_Olattice__class_OInf__fin(X21988,X21987)),c_Big__Operators_Olattice__class_OSup__fin(X21988,X21987))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).

fof(i_0_9601,plain,
    ! [X32868,X32869,X32870,X32871] : hAPP(hAPP(c_List_Omap(X32871,X32870),hAPP(c_COMBK(X32870,X32871),X32869)),X32868) = c_List_Oreplicate(X32870,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32871)),X32868),X32869),
    inference(variable_rename,[status(thm)],[fact_map__replicate__const]) ).

fof(i_0_9602,plain,
    ! [X33442,X33443,X33444,X33445,X33446] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33446,X33445)
      | ~ hBOOL(hAPP(hAPP(X33445,X33444),X33443))
      | ~ hBOOL(hAPP(hAPP(X33445,X33443),X33442))
      | hBOOL(hAPP(hAPP(X33445,X33444),X33442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__transp])]) ).

fof(i_0_9603,plain,
    ! [X33319,X33320,X33321,X33322,X33323] :
      ( ~ c_Predicate_Otransp(X33323,X33322)
      | ~ hBOOL(hAPP(hAPP(X33322,X33321),X33320))
      | ~ hBOOL(hAPP(hAPP(X33322,X33320),X33319))
      | hBOOL(hAPP(hAPP(X33322,X33321),X33319)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpE])]) ).

fof(i_0_9604,plain,
    ! [X27175,X27176,X27177,X27178,X27179] :
      ( ~ c_Equiv__Relations_Oequivp(X27179,X27178)
      | ~ hBOOL(hAPP(hAPP(X27178,X27177),X27176))
      | ~ hBOOL(hAPP(hAPP(X27178,X27176),X27175))
      | hBOOL(hAPP(hAPP(X27178,X27177),X27175)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).

fof(i_0_9605,plain,
    ! [X17186,X17187,X17188,X17189,X17190] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17190,X17189,X17188)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17190),X17187))
      | X17187 = c_Orderings_Obot__class_Obot(tc_fun(X17190,tc_HOL_Obool))
      | hAPP(X17188,hAPP(hAPP(c_Set_Oinsert(X17190),X17186),X17187)) = hAPP(hAPP(X17189,X17186),hAPP(X17188,X17187)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).

fof(i_0_9606,plain,
    ! [X24658,X24659,X24660,X24661] :
      ( ~ class_Divides_Oring__div(X24661)
      | c_Divides_Odiv__class_Omod(X24661,X24660,X24659) != c_Divides_Odiv__class_Omod(X24661,X24658,X24659)
      | c_Divides_Odiv__class_Omod(X24661,hAPP(c_Groups_Ouminus__class_Ouminus(X24661),X24660),X24659) = c_Divides_Odiv__class_Omod(X24661,hAPP(c_Groups_Ouminus__class_Ouminus(X24661),X24658),X24659) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).

fof(i_0_9607,plain,
    ! [X31554,X31555] : hAPP(c_Set_Oimage(tc_List_Olist(X31555),tc_fun(X31555,tc_HOL_Obool),c_List_Oset(X31555)),hAPP(c_List_Oset(tc_List_Olist(X31555)),c_Enum_Osublists(X31555,X31554))) = hAPP(c_Set_OPow(X31555),hAPP(c_List_Oset(X31555),X31554)),
    inference(variable_rename,[status(thm)],[fact_sublists__powset]) ).

fof(i_0_9608,plain,
    ! [X25214,X25215] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25215,tc_HOL_Obool),X25214) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X25215,tc_HOL_Obool),tc_fun(X25215,tc_HOL_Obool)),X25214),c_COMBI(tc_fun(X25215,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Union__def]) ).

fof(i_0_9609,plain,
    ! [X22033,X22034] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X22034,tc_HOL_Obool),X22033) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X22034,tc_HOL_Obool),tc_fun(X22034,tc_HOL_Obool)),X22033),c_COMBI(tc_fun(X22034,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Inter__def]) ).

fof(i_0_9610,plain,
    ! [X32279,X32280,X32281,X32282] :
      ( ( ~ hBOOL(hAPP(X32282,X32281))
        | c_List_OtakeWhile(X32280,X32282,hAPP(hAPP(c_List_Olist_OCons(X32280),X32281),X32279)) = hAPP(hAPP(c_List_Olist_OCons(X32280),X32281),c_List_OtakeWhile(X32280,X32282,X32279)) )
      & ( hBOOL(hAPP(X32282,X32281))
        | c_List_OtakeWhile(X32280,X32282,hAPP(hAPP(c_List_Olist_OCons(X32280),X32281),X32279)) = c_List_Olist_ONil(X32280) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5913])]) ).

fof(i_0_9611,plain,
    ! [X25159] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25159)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | X25159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X25159 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25159)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])]) ).

fof(i_0_9612,plain,
    ! [X22856] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22856)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X22856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22856 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22856)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])]) ).

fof(i_0_9613,plain,
    ! [X23733,X23734] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23734))
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X23734)),X23733) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23734),X23733)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).

fof(i_0_9614,plain,
    ! [X23735,X23736] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23736))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23736),X23735)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X23736)),X23735) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).

fof(i_0_9615,plain,
    ! [X20123,X20124,X20125] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20125),X20124)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20125),X20123)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20124),X20123),
    inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).

fof(i_0_9616,plain,
    ! [X20126,X20127,X20128] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20128),X20127)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20126),X20127)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20128),X20126),
    inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).

fof(i_0_9617,plain,
    ! [X22780,X22781,X22782] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22782),X22781)),X22780) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22781),X22780)),
    inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).

fof(i_0_9618,plain,
    ! [X22832,X22833,X22834] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22834),X22833)),X22832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22833),X22832)),
    inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).

fof(i_0_9619,plain,
    ! [X20245,X20246,X20247] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20247),X20246)),X20245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20246),X20245)),
    inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).

fof(i_0_9620,plain,
    ! [X23035,X23036,X23037] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23037),X23036)),X23035) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23037),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23036),X23035)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_9621,plain,
    ! [X19949,X19950,X19951] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19951),X19950)),X19949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19951),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19950),X19949)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_9622,plain,
    ! [X20117,X20118,X20119] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20119),X20118)),X20117) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20118),X20117)),
    inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).

fof(i_0_9623,plain,
    ! [X23441,X23442,X23443] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23442),X23441)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23443),X23442)),X23441),
    inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).

fof(i_0_9624,plain,
    ! [X28262,X28263,X28264] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28263),X28264),c_Orderings_Obot__class_Obot(tc_fun(X28263,tc_HOL_Obool))))
      | hBOOL(hAPP(X28262,X28264)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).

fof(i_0_9625,plain,
    ! [X24363,X24364,X24365] :
      ( ~ class_Orderings_Oorder(X24365)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24365,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24365),X24364)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24365,X24364,X24363)) = c_Orderings_Obot__class_Obot(tc_fun(X24365,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).

fof(i_0_9626,plain,
    ! [X24366,X24367,X24368] :
      ( ~ class_Orderings_Oorder(X24368)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24368,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24368),X24367)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24368,X24367,X24366)) = c_Orderings_Obot__class_Obot(tc_fun(X24368,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).

fof(i_0_9627,plain,
    ! [X24215,X24216,X24217] :
      ( ~ class_Orderings_Oorder(X24217)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24217),X24216)),c_SetInterval_Oord__class_OatLeastAtMost(X24217,X24216,X24215)) = c_Orderings_Obot__class_Obot(tc_fun(X24217,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).

fof(i_0_9628,plain,
    ! [X24769,X24770] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24769),X24770))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24770,X24769) = X24770 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).

fof(i_0_9629,plain,
    ! [X31157,X31158,X31159,X31160] : hAPP(c_List_Oset(X31160),hAPP(hAPP(c_List_Omap(X31159,X31160),X31158),X31157)) = hAPP(c_Set_Oimage(X31159,X31160,X31158),hAPP(c_List_Oset(X31159),X31157)),
    inference(variable_rename,[status(thm)],[fact_set__map]) ).

fof(i_0_9630,plain,
    ! [X30579,X30580,X30581] : hAPP(hAPP(c_List_Oappend(X30581),hAPP(hAPP(c_List_Otake(X30581),X30580),X30579)),hAPP(hAPP(c_List_Odrop(X30581),X30580),X30579)) = X30579,
    inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).

fof(i_0_9631,plain,
    ! [X22989] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22989)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[i_0_5914]) ).

fof(i_0_9632,plain,
    ! [X24844,X24845] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24845),X24844) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24845,X24844)),X24844),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(i_0_9633,plain,
    ! [X23288,X23289] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X23289,X23288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X23289)),c_Com_Ocom_Ocom__size(X23288))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I4_J]) ).

fof(i_0_9634,plain,
    ! [X25956] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25956)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25956)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25956))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

fof(i_0_9635,plain,
    ! [X32602,X32603,X32604,X32605] :
      ( ( ~ c_List_Olist__ex(X32605,X32604,hAPP(hAPP(c_List_Oappend(X32605),X32603),X32602))
        | c_List_Olist__ex(X32605,X32604,X32603)
        | c_List_Olist__ex(X32605,X32604,X32602) )
      & ( ~ c_List_Olist__ex(X32605,X32604,X32603)
        | c_List_Olist__ex(X32605,X32604,hAPP(hAPP(c_List_Oappend(X32605),X32603),X32602)) )
      & ( ~ c_List_Olist__ex(X32605,X32604,X32602)
        | c_List_Olist__ex(X32605,X32604,hAPP(hAPP(c_List_Oappend(X32605),X32603),X32602)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])]) ).

fof(i_0_9636,plain,
    ! [X23359,X23360] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23360),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23359),X23360))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23360),X23359) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial])]) ).

cnf(i_0_9637,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != c_Int_OBit1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5915]) ).

cnf(i_0_9638,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5916]) ).

fof(i_0_9639,plain,
    ! [X29844,X29845,X29846,X29847] : hAPP(hAPP(c_List_Otake(X29847),hAPP(c_Nat_OSuc,X29846)),hAPP(hAPP(c_List_Olist_OCons(X29847),X29845),X29844)) = hAPP(hAPP(c_List_Olist_OCons(X29847),X29845),hAPP(hAPP(c_List_Otake(X29847),X29846),X29844)),
    inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).

fof(i_0_9640,plain,
    ! [X32981,X32982,X32983] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X32983)
      | ~ class_Lazy__Sequence_Osmall__lazy(X32982)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X32983,X32982),X32981) = c_Lazy__Sequence_Oproduct(X32983,X32982,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32983,X32981),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32982,X32981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__prod__def])]) ).

fof(i_0_9641,plain,
    ! [X31102,X31103,X31104,X31105,X31106,X31107,X31108] :
      ( hAPP(hAPP(c_List_Omap(X31108,X31107),X31106),X31105) != hAPP(hAPP(c_List_Omap(X31104,X31107),X31103),X31102)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31108)),X31105) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31104)),X31102) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).

cnf(i_0_9642,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_5917]) ).

cnf(i_0_9643,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5918]) ).

fof(i_0_9644,plain,
    ! [X31556,X31557] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31557))),c_Enum_Osublists(X31557,X31556)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31557)),X31556)),
    inference(variable_rename,[status(thm)],[fact_length__sublists]) ).

fof(i_0_9645,plain,
    ! [X23661] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23661)) = X23661,
    inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(i_0_9646,plain,
    ! [X26995,X26996,X26997,X26998,X26999] :
      ( hAPP(c_Product__Type_Ofst(X26999,X26998),hAPP(hAPP(c_Product__Type_OPair(X26999,X26998),X26997),X26996)) != X26995
      | X26997 = X26995 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).

fof(i_0_9647,plain,
    ! [X26903,X26904,X26905,X26906,X26907] :
      ( hAPP(c_Product__Type_Osnd(X26907,X26906),hAPP(hAPP(c_Product__Type_OPair(X26907,X26906),X26905),X26904)) != X26903
      | X26904 = X26903 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).

cnf(i_0_9648,plain,
    c_Relation_Osym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5919]) ).

cnf(i_0_9649,plain,
    c_Relation_Oantisym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5920]) ).

cnf(i_0_9650,plain,
    c_Relation_Otrans(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5921]) ).

cnf(i_0_9651,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5899]) ).

cnf(i_0_9652,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5900]) ).

fof(i_0_9653,plain,
    ! [X23994] :
      ( ~ c_Nat__Transfer_Onat__set(X23994)
      | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23994)) = X23994 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).

fof(i_0_9654,plain,
    ! [X27253,X27254] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27254,X27254)),X27253))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27254),hAPP(c_Relation_OField(X27254),X27253))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).

fof(i_0_9655,plain,
    ! [X23509,X23510,X23511] :
      ( ~ class_Groups_Oordered__ab__group__add(X23511)
      | hAPP(c_Set_Oimage(X23511,X23511,c_Groups_Ouminus__class_Ouminus(X23511)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23511,X23510),X23509)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23511,hAPP(c_Groups_Ouminus__class_Ouminus(X23511),X23509),hAPP(c_Groups_Ouminus__class_Ouminus(X23511),X23510)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).

fof(i_0_9656,plain,
    ! [X21555,X21556] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21556),X21555))
      | hAPP(c_Nat_OSuc,X21556) = X21555
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21556)),X21555)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_9657,plain,
    ! [X20086,X20088,X20089,X20090] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20086))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20088),X20086))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20088),esk80_1(X20086))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk81_2(X20089,X20090)),X20089))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20089)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk81_2(X20089,X20090)),X20090))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20089)) ) ),
    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_finite__nat__set__iff__bounded])])])])])]) ).

fof(i_0_9658,plain,
    ! [X19937,X19939,X19940,X19941] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19937))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19939),X19937))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19939),esk77_1(X19937))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk78_2(X19940,X19941)),X19940))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19940)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk78_2(X19940,X19941)),X19941))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19940)) ) ),
    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_finite__nat__set__iff__bounded__le])])])])])]) ).

fof(i_0_9659,plain,
    ! [X25655,X25656] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25655)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25656),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25655)) = hAPP(c_Int_Onumber__class_Onumber__of(X25656),X25655)
        | ~ class_Int_Onumber__ring(X25656) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25655)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25656),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25655)) = c_Groups_Ozero__class_Ozero(X25656)
        | ~ class_Int_Onumber__ring(X25656) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5922])])]) ).

fof(i_0_9660,plain,
    ! [X25797,X25798,X25799] :
      ( ~ class_Int_Onumber__ring(X25799)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25799),hAPP(c_Int_Onumber__class_Onumber__of(X25799),X25798)),hAPP(c_Int_Onumber__class_Onumber__of(X25799),X25797)) = hAPP(c_Int_Onumber__class_Onumber__of(X25799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25798),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25797))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).

fof(i_0_9661,plain,
    ! [X31569,X31570,X31571] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31571),X31570))
      | hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31571)),c_Enum_On__lists(X31571,X31569,X31570))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__n__lists])]) ).

fof(i_0_9662,plain,
    ! [X21969,X21970,X21971] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21971),X21970))
      | hBOOL(hAPP(hAPP(c_member(X21971),X21969),X21970))
      | hAPP(c_Finite__Set_Ocard(X21971),hAPP(hAPP(c_Set_Oinsert(X21971),X21969),X21970)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21971),X21970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5923])]) ).

fof(i_0_9663,plain,
    ! [X23697] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X23697)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23697)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23697))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X23697))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).

fof(i_0_9664,plain,
    ! [X18363,X18364,X18365] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18365),X18364),X18363))
        | X18364 = X18363
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18365),X18364),X18363))
        | ~ class_Orderings_Olinorder(X18365) )
      & ( X18364 != X18363
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18365),X18364),X18363))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18365),X18364),X18363))
        | ~ class_Orderings_Olinorder(X18365) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5924])])]) ).

fof(i_0_9665,plain,
    ! [X30988,X30989,X30990] : c_List_Olast(X30990,hAPP(hAPP(c_List_Oappend(X30990),X30989),hAPP(hAPP(c_List_Olist_OCons(X30990),X30988),c_List_Olist_ONil(X30990)))) = X30988,
    inference(variable_rename,[status(thm)],[fact_last__snoc]) ).

fof(i_0_9666,plain,
    ! [X30505,X30506,X30507] : c_List_Obutlast(X30507,hAPP(hAPP(c_List_Oappend(X30507),X30506),hAPP(hAPP(c_List_Olist_OCons(X30507),X30505),c_List_Olist_ONil(X30507)))) = X30506,
    inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).

fof(i_0_9667,plain,
    ! [X28971,X28972] : hAPP(hAPP(c_Relation_Orel__comp(X28972,X28972,X28972),c_Transitive__Closure_Ortrancl(X28972,X28971)),c_Transitive__Closure_Ortrancl(X28972,X28971)) = c_Transitive__Closure_Ortrancl(X28972,X28971),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(i_0_9668,plain,
    ! [X26986,X26987,X26988] : hAPP(c_Product__Type_Ofst(X26988,X26987),X26986) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26988,X26987,X26988),c_COMBK(X26988,X26987)),X26986),
    inference(variable_rename,[status(thm)],[fact_fst__def]) ).

fof(i_0_9669,plain,
    ! [X29765] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29765)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X29765),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5925]) ).

fof(i_0_9670,plain,
    ! [X29185,X29186] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29186,X29186)),X29185))
      | ~ c_Wellfounded_Oacyclic(X29186,X29185)
      | c_Wellfounded_Owf(X29186,hAPP(c_Relation_Oconverse(X29186,X29186),X29185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).

fof(i_0_9671,plain,
    ! [X17631,X17632,X17633] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17633),X17632),X17631))
        | X17632 != X17631
        | ~ class_Orderings_Oorder(X17633) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17633),X17631),X17632))
        | X17632 != X17631
        | ~ class_Orderings_Oorder(X17633) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17633),X17632),X17631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17633),X17631),X17632))
        | X17632 = X17631
        | ~ class_Orderings_Oorder(X17633) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_9672,plain,
    ! [X17616,X17617,X17618] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17618),X17616),X17617))
        | X17616 = X17617
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17618),X17617),X17616))
        | ~ class_Orderings_Oorder(X17618) )
      & ( X17616 != X17617
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17618),X17616),X17617))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17618),X17617),X17616))
        | ~ class_Orderings_Oorder(X17618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_9673,plain,
    ! [X17593,X17594,X17595] :
      ( ~ class_Orderings_Oorder(X17595)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17595),X17594),X17593))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17595),X17593),X17594))
      | X17594 = X17593 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_9674,plain,
    ! [X17586,X17587,X17588] :
      ( ~ class_Orderings_Oorder(X17588)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17588),X17587),X17586))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17588),X17586),X17587))
      | X17586 = X17587 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_9675,plain,
    ! [X24880,X24881] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24881),X24880))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24880,X24881) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24880),X24881),X24881) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).

fof(i_0_9676,plain,
    ! [X34091,X34092] :
      ( X34092 != X34091
      | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34092,X34091) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34092),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H])]) ).

fof(i_0_9677,plain,
    ! [X32416,X32417,X32418] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32418),X32417),hAPP(c_List_Oset(X32418),X32416)))
      | c_List_Oinsert(X32418,X32417,X32416) = X32416 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__insert])]) ).

fof(i_0_9678,plain,
    ! [X32404,X32405,X32406] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32406),X32405),hAPP(c_List_Oset(X32406),X32404)))
        | c_List_Oinsert(X32406,X32405,X32404) = X32404 )
      & ( hBOOL(hAPP(hAPP(c_member(X32406),X32405),hAPP(c_List_Oset(X32406),X32404)))
        | c_List_Oinsert(X32406,X32405,X32404) = hAPP(hAPP(c_List_Olist_OCons(X32406),X32405),X32404) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5926])]) ).

fof(i_0_9679,plain,
    ! [X21842,X21843] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21843),X21842))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21842)),X21843) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21842),X21843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).

fof(i_0_9680,plain,
    ! [X18292,X18293,X18294] :
      ( ~ class_Orderings_Oorder(X18294)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18294),X18293),X18292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18294),X18292),X18293)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5927])]) ).

fof(i_0_9681,plain,
    ! [X18322,X18323,X18324] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18324),X18323),X18322))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18324),X18322),X18323))
        | X18323 = X18322
        | ~ class_Orderings_Olinorder(X18324) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18324),X18322),X18323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18324),X18323),X18322))
        | ~ class_Orderings_Olinorder(X18324) )
      & ( X18323 != X18322
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18324),X18323),X18322))
        | ~ class_Orderings_Olinorder(X18324) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5928])])]) ).

fof(i_0_9682,plain,
    ! [X18402,X18403,X18404] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18403),X18402))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18404),X18402),X18403))
        | ~ class_Orderings_Olinorder(X18404) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18404),X18402),X18403))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18403),X18402))
        | ~ class_Orderings_Olinorder(X18404) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5929])])]) ).

fof(i_0_9683,plain,
    ! [X18369,X18370,X18371] :
      ( ~ class_Orderings_Olinorder(X18371)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18371),X18370),X18369))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18371),X18369),X18370)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5930])]) ).

fof(i_0_9684,plain,
    ! [X18399,X18400,X18401] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18401),X18400),X18399))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18401),X18399),X18400))
        | ~ class_Orderings_Olinorder(X18401) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18401),X18399),X18400))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18401),X18400),X18399))
        | ~ class_Orderings_Olinorder(X18401) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5931])])]) ).

fof(i_0_9685,plain,
    ! [X18307,X18308,X18309] :
      ( ~ class_Orderings_Opreorder(X18309)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),X18308),X18307))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),X18307),X18308)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5932])]) ).

fof(i_0_9686,plain,
    ! [X18304,X18305,X18306] :
      ( ~ class_Orderings_Opreorder(X18306)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18306),X18305),X18304))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18306),X18304),X18305)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5933])]) ).

fof(i_0_9687,plain,
    ! [X18295,X18296,X18297] :
      ( ~ class_Orderings_Opreorder(X18297)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18297),X18296),X18295))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18297),X18295),X18296)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5934])]) ).

fof(i_0_9688,plain,
    ! [X18265,X18266,X18267] :
      ( ~ class_Orderings_Opreorder(X18267)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18267),X18266),X18265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18267),X18265),X18266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5935])]) ).

fof(i_0_9689,plain,
    ! [X25074,X25075] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25075)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25075),hAPP(c_Groups_Ouminus__class_Ouminus(X25075),X25074)),hAPP(c_Groups_Oabs__class_Oabs(X25075),X25074))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).

fof(i_0_9690,plain,
    ! [X22237,X22238] :
      ( ~ class_Rings_Olinordered__ring(X22238)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22238),c_Groups_Ozero__class_Ozero(X22238)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22238),X22237),X22237))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_9691,plain,
    ! [X20003,X20004] :
      ( ~ class_Rings_Olinordered__semidom(X20004)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20004),X20003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20004),X20003),c_Groups_Oone__class_Oone(X20004)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_9692,plain,
    ! [X25044,X25045] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25045),c_Groups_Ozero__class_Ozero(X25045)),hAPP(c_Groups_Oabs__class_Oabs(X25045),X25044)))
        | X25044 != c_Groups_Ozero__class_Ozero(X25045)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25045) )
      & ( X25044 = c_Groups_Ozero__class_Ozero(X25045)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25045),c_Groups_Ozero__class_Ozero(X25045)),hAPP(c_Groups_Oabs__class_Oabs(X25045),X25044)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25045) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).

fof(i_0_9693,plain,
    ! [X26963,X26964,X26965,X26966] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26966,X26965),X26964))
      | ~ hBOOL(hAPP(hAPP(X26965,X26963),X26964))
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X26966,X26965),X26963)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).

fof(i_0_9694,plain,
    ! [X25963,X25964] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25964),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25963)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25964),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25964),X25963)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5936])]) ).

fof(i_0_9695,plain,
    ! [X30722,X30723] :
      ( X30723 = c_List_Olist_ONil(X30722)
      | hBOOL(hAPP(hAPP(c_member(X30722),hAPP(c_List_Ohd(X30722),X30723)),hAPP(c_List_Oset(X30722),X30723))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).

fof(i_0_9696,plain,
    ! [X34093] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34093,X34093) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34093),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).

fof(i_0_9697,plain,
    ! [X33003,X33004,X33005] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33005)),c_Lazy__Sequence_Olazy__sequence_OInsert(X33005,X33004,X33003)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33005)),X33003)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I4_J]) ).

fof(i_0_9698,plain,
    ! [X21762,X21763,X21764] :
      ( ~ class_Rings_Ocomm__semiring__1(X21764)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21764),hAPP(hAPP(c_Power_Opower__class_Opower(X21764),X21763),X21762)),X21763) = hAPP(hAPP(c_Power_Opower__class_Opower(X21764),X21763),hAPP(c_Nat_OSuc,X21762)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).

fof(i_0_9699,plain,
    ! [X21765,X21766,X21767] :
      ( ~ class_Groups_Omonoid__mult(X21767)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21767),X21766),hAPP(c_Nat_OSuc,X21765)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(hAPP(c_Power_Opower__class_Opower(X21767),X21766),X21765)),X21766) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).

fof(i_0_9700,plain,
    ! [X31664,X31665] :
      ( ~ class_Orderings_Olinorder(X31665)
      | c_List_Olinorder__class_Osorted__list__of__set(X31665,hAPP(c_List_Oset(X31665),X31664)) = c_List_Olinorder__class_Osort__key(X31665,X31665,c_COMBI(X31665),c_List_Oremdups(X31665,X31664)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])]) ).

fof(i_0_9701,plain,
    ! [X29569,X29570,X29571] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29571)),hAPP(hAPP(c_List_Olist_OCons(X29571),X29570),X29569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29571)),X29569)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I4_J]) ).

fof(i_0_9702,plain,
    ! [X31576,X31577,X31578] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31578))),c_Enum_On__lists(X31578,X31577,X31576)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31578)),X31576)),X31577),
    inference(variable_rename,[status(thm)],[fact_length__n__lists]) ).

fof(i_0_9703,plain,
    ! [X23002,X23003,X23005,X23006] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23003))
        | ~ hBOOL(hAPP(X23002,X23003))
        | hBOOL(hAPP(X23002,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk144_1(X23002)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk145_1(X23005)))
        | ~ hBOOL(hAPP(X23005,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23006))) )
      & ( hBOOL(hAPP(X23005,esk145_1(X23005)))
        | ~ hBOOL(hAPP(X23005,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23006))) ) ),
    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_transfer__int__nat__quantifiers_I2_J])])])])])]) ).

fof(i_0_9704,plain,
    ! [X21792,X21793] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21793),X21792))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21793)),X21792)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_9705,plain,
    ! [X21956,X21957,X21958] :
      ( ~ class_Lattices_Olattice(X21958)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21958),X21957))
      | ~ hBOOL(hAPP(hAPP(c_member(X21958),X21956),X21957))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21958),X21956),c_Big__Operators_Olattice__class_OInf__fin(X21958,X21957)) = c_Big__Operators_Olattice__class_OInf__fin(X21958,X21957) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).

fof(i_0_9706,plain,
    ! [X20337,X20338,X20339] :
      ( ~ class_Lattices_Olattice(X20339)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20339),X20338))
      | ~ hBOOL(hAPP(hAPP(c_member(X20339),X20337),X20338))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20339),X20337),c_Big__Operators_Olattice__class_OSup__fin(X20339,X20338)) = c_Big__Operators_Olattice__class_OSup__fin(X20339,X20338) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).

fof(i_0_9707,plain,
    ! [X19098,X19099,X19100] :
      ( ~ class_Orderings_Olinorder(X19100)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19100),X19099))
      | ~ hBOOL(hAPP(hAPP(c_member(X19100),X19098),X19099))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X19100),X19098),c_Big__Operators_Olinorder__class_OMax(X19100,X19099)) = c_Big__Operators_Olinorder__class_OMax(X19100,X19099) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).

fof(i_0_9708,plain,
    ! [X19105,X19106,X19107] :
      ( ~ class_Orderings_Olinorder(X19107)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19107),X19106))
      | ~ hBOOL(hAPP(hAPP(c_member(X19107),X19105),X19106))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X19107),X19105),c_Big__Operators_Olinorder__class_OMin(X19107,X19106)) = c_Big__Operators_Olinorder__class_OMin(X19107,X19106) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).

fof(i_0_9709,plain,
    ! [X25153,X25154,X25155] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25155)
      | ~ hBOOL(hAPP(hAPP(c_member(X25155),X25154),X25153))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25155),X25154),c_Complete__Lattice_OSup__class_OSup(X25155,X25153))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).

cnf(i_0_9710,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X1,X2)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5937]) ).

fof(i_0_9711,plain,
    ! [X32617,X32618,X32619,X32620] :
      ( ( ~ c_List_Olist__ex(X32620,X32619,hAPP(hAPP(c_List_Olist_OCons(X32620),X32618),X32617))
        | hBOOL(hAPP(X32619,X32618))
        | c_List_Olist__ex(X32620,X32619,X32617) )
      & ( ~ hBOOL(hAPP(X32619,X32618))
        | c_List_Olist__ex(X32620,X32619,hAPP(hAPP(c_List_Olist_OCons(X32620),X32618),X32617)) )
      & ( ~ c_List_Olist__ex(X32620,X32619,X32617)
        | c_List_Olist__ex(X32620,X32619,hAPP(hAPP(c_List_Olist_OCons(X32620),X32618),X32617)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])]) ).

fof(i_0_9712,plain,
    ! [X23183,X23184,X23185] :
      ( ~ class_Orderings_Oorder(X23185)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23185,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23185),X23184)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23185,X23184),X23183)) = c_Orderings_Obot__class_Obot(tc_fun(X23185,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).

fof(i_0_9713,plain,
    ! [X22707,X22708] :
      ( ( X22707 != c_Orderings_Obot__class_Obot(tc_fun(X22708,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22708),X22707))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22708),X22707))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22708),X22707))) )
      & ( X22707 = c_Orderings_Obot__class_Obot(tc_fun(X22708,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22708),X22707))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22708),X22707))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).

fof(i_0_9714,plain,
    ! [X29777,X29778,X29779,X29780] : hAPP(hAPP(c_List_Onth(X29780),hAPP(hAPP(c_List_Olist_OCons(X29780),X29779),X29778)),hAPP(c_Nat_OSuc,X29777)) = hAPP(hAPP(c_List_Onth(X29780),X29778),X29777),
    inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(i_0_9715,plain,
    ! [X31031,X31032,X31033,X31034] : hAPP(hAPP(c_List_Omap(X31034,X31033),X31032),hAPP(c_List_Otl(X31034),X31031)) = hAPP(c_List_Otl(X31033),hAPP(hAPP(c_List_Omap(X31034,X31033),X31032),X31031)),
    inference(variable_rename,[status(thm)],[fact_map__tl]) ).

fof(i_0_9716,plain,
    ! [X32151,X32152,X32153,X32154] : hAPP(c_List_Orev(X32154),hAPP(hAPP(c_List_Omap(X32153,X32154),X32152),X32151)) = hAPP(hAPP(c_List_Omap(X32153,X32154),X32152),hAPP(c_List_Orev(X32153),X32151)),
    inference(variable_rename,[status(thm)],[fact_rev__map]) ).

fof(i_0_9717,plain,
    ! [X33848,X33849,X33850] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33850),X33849),c_Quotient_ORespects(X33850,X33848)))
        | hBOOL(hAPP(hAPP(X33848,X33849),X33849)) )
      & ( ~ hBOOL(hAPP(hAPP(X33848,X33849),X33849))
        | hBOOL(hAPP(hAPP(c_member(X33850),X33849),c_Quotient_ORespects(X33850,X33848))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__respects])]) ).

fof(i_0_9718,plain,
    ! [X17063,X17064] : ~ hBOOL(hAPP(hAPP(c_member(X17064),X17063),c_Orderings_Obot__class_Obot(tc_fun(X17064,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5938]) ).

fof(i_0_9719,plain,
    ! [X16998,X16999] : ~ hBOOL(hAPP(hAPP(c_member(X16999),X16998),c_Orderings_Obot__class_Obot(tc_fun(X16999,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5939]) ).

fof(i_0_9720,plain,
    ! [X34023,X34024,X34025] :
      ( ~ class_Divides_Osemiring__div(X34025)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34025),X34024),X34023))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34025),X34024),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34025),X34023),X34024)) = X34023 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).

fof(i_0_9721,plain,
    ! [X23650,X23651,X23653,X23654] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk160_1(X23650)))
        | ~ hBOOL(hAPP(X23650,X23651)) )
      & ( hBOOL(hAPP(X23650,hAPP(c_Int_Onat,esk160_1(X23650))))
        | ~ hBOOL(hAPP(X23650,X23651)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23654))
        | ~ hBOOL(hAPP(X23653,hAPP(c_Int_Onat,X23654)))
        | hBOOL(hAPP(X23653,esk161_1(X23653))) ) ),
    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_ex__nat])])])])])]) ).

fof(i_0_9722,plain,
    ! [X22617,X22618] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22618),X22617)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22618),X22617)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

cnf(i_0_9723,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5875]) ).

fof(i_0_9724,plain,
    ! [X32651,X32652,X32653,X32654] :
      ( ( c_List_Olist__all(X32654,X32653,X32652)
        | ~ c_List_Olist__all(X32654,X32653,hAPP(hAPP(c_List_Oappend(X32654),X32652),X32651)) )
      & ( c_List_Olist__all(X32654,X32653,X32651)
        | ~ c_List_Olist__all(X32654,X32653,hAPP(hAPP(c_List_Oappend(X32654),X32652),X32651)) )
      & ( ~ c_List_Olist__all(X32654,X32653,X32652)
        | ~ c_List_Olist__all(X32654,X32653,X32651)
        | c_List_Olist__all(X32654,X32653,hAPP(hAPP(c_List_Oappend(X32654),X32652),X32651)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])]) ).

fof(i_0_9725,plain,
    ! [X22621] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22621))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22621),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X22621 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).

fof(i_0_9726,plain,
    ! [X17119,X17120,X17121] :
      ( hAPP(hAPP(c_Set_Oinsert(X17121),X17120),c_Orderings_Obot__class_Obot(tc_fun(X17121,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X17121),X17119),c_Orderings_Obot__class_Obot(tc_fun(X17121,tc_HOL_Obool)))
      | X17120 = X17119 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).

fof(i_0_9727,plain,
    ! [X31343] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31343),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X31343)) = X31343 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).

fof(i_0_9728,plain,
    ! [X25778,X25779,X25780,X25781] :
      ( ( X25779 = c_Groups_Ozero__class_Ozero(X25781)
        | X25780 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25781),hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)),X25779)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) != hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) )
      & ( X25779 != c_Groups_Ozero__class_Ozero(X25781)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778) = c_Groups_Ozero__class_Ozero(X25781)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) != hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) )
      & ( X25779 = c_Groups_Ozero__class_Ozero(X25781)
        | X25779 != c_Groups_Ozero__class_Ozero(X25781)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) = hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778) != c_Groups_Ozero__class_Ozero(X25781)
        | X25779 != c_Groups_Ozero__class_Ozero(X25781)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) = hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) )
      & ( X25779 = c_Groups_Ozero__class_Ozero(X25781)
        | X25780 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25781),hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)),X25779)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) = hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778) != c_Groups_Ozero__class_Ozero(X25781)
        | X25780 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25781),hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)),X25779)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25781),X25780),X25779) = hAPP(c_Int_Onumber__class_Onumber__of(X25781),X25778)
        | ~ class_Fields_Ofield__inverse__zero(X25781)
        | ~ class_Int_Onumber(X25781) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).

fof(i_0_9729,plain,
    ! [X25782,X25783,X25784,X25785] :
      ( ( X25782 = c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25785),hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784)),X25782) = X25783
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) )
      & ( X25782 != c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) = c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) )
      & ( X25782 = c_Groups_Ozero__class_Ozero(X25785)
        | X25782 != c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) != c_Groups_Ozero__class_Ozero(X25785)
        | X25782 != c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) )
      & ( X25782 = c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25785),hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784)),X25782) != X25783
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) != c_Groups_Ozero__class_Ozero(X25785)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25785),hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784)),X25782) != X25783
        | hAPP(c_Int_Onumber__class_Onumber__of(X25785),X25784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25785),X25783),X25782)
        | ~ class_Fields_Ofield__inverse__zero(X25785)
        | ~ class_Int_Onumber(X25785) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).

fof(i_0_9730,plain,
    ! [X21583,X21584] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21584),hAPP(c_Nat_OSuc,X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21584),X21583))
        | X21584 = hAPP(c_Nat_OSuc,X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21584),X21583))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21584),hAPP(c_Nat_OSuc,X21583))) )
      & ( X21584 != hAPP(c_Nat_OSuc,X21583)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21584),hAPP(c_Nat_OSuc,X21583))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_9731,plain,
    ! [X21577,X21578] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21578),hAPP(c_Nat_OSuc,X21577)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21578),X21577))
      | X21578 = hAPP(c_Nat_OSuc,X21577) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5940])]) ).

fof(i_0_9732,plain,
    ! [X30994,X30995] :
      ( X30995 = c_List_Olist_ONil(X30994)
      | hAPP(hAPP(c_List_Oappend(X30994),c_List_Obutlast(X30994,X30995)),hAPP(hAPP(c_List_Olist_OCons(X30994),c_List_Olast(X30994,X30995)),c_List_Olist_ONil(X30994))) = X30995 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).

cnf(i_0_9733,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5941]) ).

fof(i_0_9734,plain,
    ! [X27011,X27012,X27013] : hAPP(hAPP(c_Product__Type_OPair(X27013,X27012),hAPP(c_Product__Type_Ofst(X27013,X27012),X27011)),hAPP(c_Product__Type_Osnd(X27013,X27012),X27011)) = X27011,
    inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).

fof(i_0_9735,plain,
    ! [X27008,X27009,X27010] : X27010 = hAPP(hAPP(c_Product__Type_OPair(X27009,X27008),hAPP(c_Product__Type_Ofst(X27009,X27008),X27010)),hAPP(c_Product__Type_Osnd(X27009,X27008),X27010)),
    inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).

fof(i_0_9736,plain,
    ! [X23195,X23196] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23196),X23195))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23196),hAPP(c_Nat_OSuc,X23195)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X23195),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23196),X23195)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23196),X23195))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23196),hAPP(c_Nat_OSuc,X23195)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5942])]) ).

fof(i_0_9737,plain,
    ! [X30894,X30895,X30896,X30897] :
      ( ~ class_Orderings_Olinorder(X30897)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30896,X30897,X30895),X30894),c_List_Olist_ONil(X30896)) = hAPP(hAPP(c_List_Olist_OCons(X30896),X30894),c_List_Olist_ONil(X30896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).

fof(i_0_9738,plain,
    ! [X32413,X32414,X32415] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32415),X32414))
      | hBOOL(hAPP(c_List_Odistinct(X32415),c_List_Oinsert(X32415,X32413,X32414))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).

fof(i_0_9739,plain,
    ! [X32288,X32289,X32290] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32290),X32289))
      | hBOOL(hAPP(c_List_Odistinct(X32290),c_List_OtakeWhile(X32290,X32288,X32289))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).

fof(i_0_9740,plain,
    ! [X30183,X30184,X30185] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30185),X30184))
      | hBOOL(hAPP(c_List_Odistinct(X30185),c_List_Oremove1(X30185,X30183,X30184))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).

fof(i_0_9741,plain,
    ! [X30127,X30128,X30129] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30129),X30128))
      | hBOOL(hAPP(c_List_Odistinct(X30129),c_List_Osublist(X30129,X30128,X30127))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).

fof(i_0_9742,plain,
    ! [X33006,X33007,X33008,X33009] : c_Lazy__Sequence_Oappend(X33009,c_Lazy__Sequence_Olazy__sequence_OInsert(X33009,X33008,X33007),X33006) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33009,X33008,c_Lazy__Sequence_Oappend(X33009,X33007,X33006)),
    inference(variable_rename,[status(thm)],[fact__01]) ).

fof(i_0_9743,plain,
    ! [X30212,X30213,X30214,X30215] : c_List_Oremove1(X30215,X30214,c_List_Oremove1(X30215,X30213,X30212)) = c_List_Oremove1(X30215,X30213,c_List_Oremove1(X30215,X30214,X30212)),
    inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).

fof(i_0_9744,plain,
    ! [X18039,X18040,X18041,X18042,X18043,X18044] :
      ( ~ c_Finite__Set_Ofun__left__comm(X18044,X18043,X18042)
      | hAPP(hAPP(X18042,X18041),hAPP(hAPP(X18042,X18040),X18039)) = hAPP(hAPP(X18042,X18040),hAPP(hAPP(X18042,X18041),X18039)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).

fof(i_0_9745,plain,
    ! [X20941,X20942,X20943] :
      ( ~ class_Lattices_Olattice(X20943)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20943),X20942))
      | ~ hBOOL(hAPP(hAPP(c_member(X20943),X20941),X20942))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20943),X20941),c_Big__Operators_Olattice__class_OSup__fin(X20943,X20942)) = X20941 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).

fof(i_0_9746,plain,
    ! [X21953,X21954,X21955] :
      ( ~ class_Lattices_Olattice(X21955)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21955),X21954))
      | ~ hBOOL(hAPP(hAPP(c_member(X21955),X21953),X21954))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21955),X21953),c_Big__Operators_Olattice__class_OInf__fin(X21955,X21954)) = X21953 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).

fof(i_0_9747,plain,
    ! [X28175] : c_Wellfounded_OwfP(X28175,hAPP(c_COMBK(tc_fun(X28175,tc_HOL_Obool),X28175),hAPP(c_COMBK(tc_HOL_Obool,X28175),c_fFalse))),
    inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).

fof(i_0_9748,plain,
    ! [X33604,X33605] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk536_2(X33604,X33605)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | hBOOL(hAPP(X33605,X33604)) )
      & ( ~ hBOOL(hAPP(X33605,hAPP(c_Code__Numeral_Oof__nat,esk536_2(X33604,X33605))))
        | hBOOL(hAPP(X33605,X33604)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__induct])])])]) ).

fof(i_0_9749,plain,
    ! [X31798,X31799,X31800,X31801] :
      ( ( ~ hBOOL(hAPP(X31801,X31800))
        | hAPP(c_List_Ofilter(X31799,X31801),hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),X31798)) = hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),hAPP(c_List_Ofilter(X31799,X31801),X31798)) )
      & ( hBOOL(hAPP(X31801,X31800))
        | hAPP(c_List_Ofilter(X31799,X31801),hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),X31798)) = hAPP(c_List_Ofilter(X31799,X31801),X31798) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5943])]) ).

fof(i_0_9750,plain,
    ! [X34042,X34043,X34044] :
      ( ~ class_Rings_Ocomm__semiring__1(X34044)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34044),X34043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34044),X34043),X34042))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).

fof(i_0_9751,plain,
    ! [X34045,X34046,X34047] :
      ( ~ class_Rings_Ocomm__semiring__1(X34047)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34047),X34046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34047),X34045),X34046))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).

fof(i_0_9752,plain,
    ! [X19504,X19505,X19506] :
      ( ~ class_Lattices_Osemilattice__sup(X19506)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19506),X19505),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19506),X19505),X19504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).

fof(i_0_9753,plain,
    ! [X19501,X19502,X19503] :
      ( ~ class_Lattices_Olattice(X19503)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19503),X19502),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19503),X19502),X19501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).

fof(i_0_9754,plain,
    ! [X19510,X19511,X19512] :
      ( ~ class_Lattices_Osemilattice__sup(X19512)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19512),X19511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19512),X19510),X19511))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).

fof(i_0_9755,plain,
    ! [X19507,X19508,X19509] :
      ( ~ class_Lattices_Olattice(X19509)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19509),X19508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19509),X19507),X19508))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).

fof(i_0_9756,plain,
    ! [X18848,X18849,X18850] :
      ( ~ class_Orderings_Olinorder(X18850)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18850),X18849),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18850),X18849),X18848))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).

fof(i_0_9757,plain,
    ! [X18845,X18846,X18847] :
      ( ~ class_Orderings_Olinorder(X18847)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18847),X18846),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18847),X18845),X18846))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).

fof(i_0_9758,plain,
    ! [X25287,X25288,X25289] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25289),X25288),hAPP(c_Set_OCollect(X25289),X25287)))
        | hBOOL(hAPP(X25287,X25288)) )
      & ( ~ hBOOL(hAPP(X25287,X25288))
        | hBOOL(hAPP(hAPP(c_member(X25289),X25288),hAPP(c_Set_OCollect(X25289),X25287))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).

fof(i_0_9759,plain,
    ! [X25284,X25285,X25286] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25286),X25285),hAPP(c_Set_OCollect(X25286),X25284)))
      | hBOOL(hAPP(X25284,X25285)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).

fof(i_0_9760,plain,
    ! [X25281,X25282,X25283] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25283),X25282),hAPP(c_Set_OCollect(X25283),X25281)))
      | hBOOL(hAPP(X25281,X25282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).

fof(i_0_9761,plain,
    ! [X23745] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23745))
      | hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X23745)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23745)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).

cnf(i_0_9762,plain,
    ( hAPP(c_List_Orotate(X2,X3),X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5855]) ).

fof(i_0_9763,plain,
    ! [X30197,X30198,X30199,X30200] :
      ( ( X30200 != X30199
        | c_List_Oremove1(X30198,X30200,hAPP(hAPP(c_List_Olist_OCons(X30198),X30199),X30197)) = X30197 )
      & ( X30200 = X30199
        | c_List_Oremove1(X30198,X30200,hAPP(hAPP(c_List_Olist_OCons(X30198),X30199),X30197)) = hAPP(hAPP(c_List_Olist_OCons(X30198),X30199),c_List_Oremove1(X30198,X30200,X30197)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).

fof(i_0_9764,plain,
    ! [X34014,X34015,X34016,X34017] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34017),X34015),X34016) != X34014
        | X34015 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34017),X34014),X34016)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34017),X34016),X34015))
        | X34016 = c_Groups_Ozero__class_Ozero(X34017)
        | ~ class_Divides_Osemiring__div(X34017) )
      & ( X34015 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34017),X34014),X34016)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X34017),X34015),X34016) = X34014
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34017),X34016),X34015))
        | X34016 = c_Groups_Ozero__class_Ozero(X34017)
        | ~ class_Divides_Osemiring__div(X34017) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).

fof(i_0_9765,plain,
    ! [X21565,X21566] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21566),hAPP(c_Nat_OSuc,X21565)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21566),X21565))
        | X21566 = X21565 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21566),X21565))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21566),hAPP(c_Nat_OSuc,X21565))) )
      & ( X21566 != X21565
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21566),hAPP(c_Nat_OSuc,X21565))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

fof(i_0_9766,plain,
    ! [X21561,X21562] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21562),hAPP(c_Nat_OSuc,X21561)))
        | X21562 = X21561
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21562),X21561)) )
      & ( X21562 != X21561
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21562),hAPP(c_Nat_OSuc,X21561)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21562),X21561)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5944])])]) ).

fof(i_0_9767,plain,
    ! [X21559,X21560] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21560),X21559))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21560),hAPP(c_Nat_OSuc,X21559)))
      | X21559 = X21560 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5945])]) ).

fof(i_0_9768,plain,
    ! [X21550,X21551] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21551),hAPP(c_Nat_OSuc,X21550)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21551),X21550))
      | X21551 = X21550 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5946])]) ).

cnf(i_0_9769,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5947]) ).

cnf(i_0_9770,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_5948]) ).

cnf(i_0_9771,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_5949]) ).

fof(i_0_9772,plain,
    ! [X27262,X27263,X27264] : hAPP(c_Relation_OImage(X27264,X27264,c_Relation_OId__on(X27264,X27263)),X27262) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27264,tc_HOL_Obool)),X27263),X27262),
    inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).

fof(i_0_9773,plain,
    ! [X20567,X20568,X20569,X20570] :
      ( ~ class_Lattices_Osemilattice__inf(X20570)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20570),X20569),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20570),X20568),X20567)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20570),X20568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20570),X20569),X20567)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).

fof(i_0_9774,plain,
    ! [X20559,X20560,X20561,X20562] :
      ( ~ class_Lattices_Osemilattice__inf(X20562)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20562),X20561),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20562),X20560),X20559)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20562),X20560),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20562),X20561),X20559)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).

fof(i_0_9775,plain,
    ! [X20563,X20564,X20565,X20566] :
      ( ~ class_Lattices_Olattice(X20566)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20566),X20565),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20566),X20564),X20563)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20566),X20564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20566),X20565),X20563)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).

fof(i_0_9776,plain,
    ! [X19468,X19469,X19470,X19471] :
      ( ~ class_Lattices_Osemilattice__sup(X19471)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19471),X19470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19471),X19469),X19468)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19471),X19469),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19471),X19470),X19468)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).

fof(i_0_9777,plain,
    ! [X19460,X19461,X19462,X19463] :
      ( ~ class_Lattices_Osemilattice__sup(X19463)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19463),X19462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19463),X19461),X19460)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19463),X19461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19463),X19462),X19460)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).

fof(i_0_9778,plain,
    ! [X19464,X19465,X19466,X19467] :
      ( ~ class_Lattices_Olattice(X19467)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19467),X19466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19467),X19465),X19464)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19467),X19465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19467),X19466),X19464)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).

fof(i_0_9779,plain,
    ! [X18755,X18756,X18757,X18758] :
      ( ~ class_Orderings_Olinorder(X18758)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18758),X18757),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18758),X18756),X18755)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18758),X18756),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18758),X18757),X18755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).

fof(i_0_9780,plain,
    ! [X18751,X18752,X18753,X18754] :
      ( ~ class_Orderings_Olinorder(X18754)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18754),X18753),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18754),X18752),X18751)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18754),X18752),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18754),X18753),X18751)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).

fof(i_0_9781,plain,
    ! [X18747,X18748,X18749,X18750] :
      ( ~ class_Orderings_Olinorder(X18750)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18750),X18749),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18750),X18748),X18747)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18750),X18748),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18750),X18749),X18747)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).

fof(i_0_9782,plain,
    ! [X18743,X18744,X18745,X18746] :
      ( ~ class_Orderings_Olinorder(X18746)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18746),X18745),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18746),X18744),X18743)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18746),X18744),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18746),X18745),X18743)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).

fof(i_0_9783,plain,
    ! [X18622,X18623,X18624,X18625] :
      ( ~ class_Rings_Ocomm__semiring__1(X18625)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18625),X18624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18625),X18623),X18622)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18625),X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18625),X18624),X18622)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).

fof(i_0_9784,plain,
    ! [X18588,X18589,X18590,X18591] :
      ( ~ class_Rings_Ocomm__semiring__1(X18591)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18591),X18590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18591),X18589),X18588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18591),X18589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18591),X18590),X18588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_9785,plain,
    ! [X18972,X18973,X18974] :
      ( ~ class_Groups_Ogroup__add(X18974)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18974),X18973),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18974),hAPP(c_Groups_Ouminus__class_Ouminus(X18974),X18973)),X18972)) = X18972 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_9786,plain,
    ! [X22501,X22502,X22503] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22503),X22502) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22503),X22501)
        | X22502 = X22501
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22503)) )
      & ( X22502 != X22501
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22503),X22502) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22503),X22501)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22503)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).

fof(i_0_9787,plain,
    ! [X21798,X21799] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21799),hAPP(c_Nat_OSuc,X21798)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21799),X21798)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21799),X21798))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21799),hAPP(c_Nat_OSuc,X21798))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_9788,plain,
    ! [X25862] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25862)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25862))),
    inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(i_0_9789,plain,
    ! [X23712,X23713,X23714,X23715,X23716] :
      ( ( X23712 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23714)
        | hBOOL(hAPP(X23713,X23714))
        | ~ hBOOL(hAPP(X23713,hAPP(c_Int_Onat,X23712))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(X23713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23713,hAPP(c_Int_Onat,X23712))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23715),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X23715 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk162_2(X23715,X23716))
        | hBOOL(hAPP(X23716,hAPP(c_Int_Onat,X23715))) )
      & ( ~ hBOOL(hAPP(X23716,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X23715 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk162_2(X23715,X23716))
        | hBOOL(hAPP(X23716,hAPP(c_Int_Onat,X23715))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23715),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X23716,esk162_2(X23715,X23716)))
        | hBOOL(hAPP(X23716,hAPP(c_Int_Onat,X23715))) )
      & ( ~ hBOOL(hAPP(X23716,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23716,esk162_2(X23715,X23716)))
        | hBOOL(hAPP(X23716,hAPP(c_Int_Onat,X23715))) ) ),
    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_split__nat])])])])])]) ).

fof(i_0_9790,plain,
    ! [X30594,X30595,X30596] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30596),X30595))
      | hBOOL(hAPP(c_List_Odistinct(X30596),hAPP(hAPP(c_List_Odrop(X30596),X30594),X30595))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).

fof(i_0_9791,plain,
    ! [X30124,X30125,X30126] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30126),X30125))
      | hBOOL(hAPP(c_List_Odistinct(X30126),hAPP(hAPP(c_List_Otake(X30126),X30124),X30125))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).

fof(i_0_9792,plain,
    ! [X16980,X16981,X16982] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16982),X16981))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16982),hAPP(hAPP(c_Set_Oinsert(X16982),X16980),X16981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_9793,plain,
    ! [X24171,X24172] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24172,X24171)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24172),hAPP(c_Nat_OSuc,X24171)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(i_0_9794,plain,
    ! [X21851,X21852,X21853] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21853,tc_fun(X21852,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X21853,tc_HOL_Obool))),X21851) = c_Orderings_Otop__class_Otop(tc_fun(X21852,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_INT__empty]) ).

fof(i_0_9795,plain,
    ! [X25884,X25885] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25885)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25884)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25884))),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(i_0_9796,plain,
    ! [X19744,X19745] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19745,tc_HOL_Obool)),X19744) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19745,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19745,tc_HOL_Obool))),X19744),
    inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(i_0_9797,plain,
    ! [X31153,X31154,X31155,X31156] : hAPP(hAPP(c_List_Omap(X31156,X31155),X31154),c_List_Obutlast(X31156,X31153)) = c_List_Obutlast(X31155,hAPP(hAPP(c_List_Omap(X31156,X31155),X31154),X31153)),
    inference(variable_rename,[status(thm)],[fact_map__butlast]) ).

fof(i_0_9798,plain,
    ! [X18511,X18512] :
      ( ~ class_Orderings_Olinorder(X18512)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18512),X18511))
      | X18511 = c_Orderings_Obot__class_Obot(tc_fun(X18512,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X18512),c_Big__Operators_Olinorder__class_OMin(X18512,X18511)),X18511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).

fof(i_0_9799,plain,
    ! [X18513,X18514] :
      ( ~ class_Orderings_Olinorder(X18514)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18514),X18513))
      | X18513 = c_Orderings_Obot__class_Obot(tc_fun(X18514,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X18514),c_Big__Operators_Olinorder__class_OMax(X18514,X18513)),X18513)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).

fof(i_0_9800,plain,
    ! [X33597] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33597),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | X33597 = hAPP(c_Code__Numeral_Onat__of,esk533_1(X33597)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__cases])])]) ).

fof(i_0_9801,plain,
    ! [X23644,X23646,X23647,X23649] :
      ( ( ~ hBOOL(hAPP(X23644,esk158_1(X23644)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23646))
        | hBOOL(hAPP(X23644,hAPP(c_Int_Onat,X23646))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk159_1(X23647)))
        | hBOOL(hAPP(X23647,X23649)) )
      & ( ~ hBOOL(hAPP(X23647,hAPP(c_Int_Onat,esk159_1(X23647))))
        | hBOOL(hAPP(X23647,X23649)) ) ),
    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_all__nat])])])])])]) ).

fof(i_0_9802,plain,
    ! [X17092,X17093,X17094] : hBOOL(hAPP(hAPP(c_member(X17094),X17093),hAPP(hAPP(c_Set_Oinsert(X17094),X17093),X17092))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_9803,plain,
    ! [X24862,X24863] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24863,X24862)) != X24862
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24863),X24862) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24863,X24862)) = X24862
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24863),X24862) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24863,X24862)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).

fof(i_0_9804,plain,
    ! [X33479] : c_Hilbert__Choice_Oinv__into(X33479,X33479,c_Orderings_Otop__class_Otop(tc_fun(X33479,tc_HOL_Obool)),c_Fun_Oid(X33479)) = c_Fun_Oid(X33479),
    inference(variable_rename,[status(thm)],[fact_inv__id]) ).

cnf(i_0_9805,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5950]) ).

cnf(i_0_9806,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5951]) ).

fof(i_0_9807,plain,
    ! [X17047,X17048,X17049,X17050] : hAPP(hAPP(c_Set_Oinsert(X17050),X17049),hAPP(hAPP(c_Set_Oinsert(X17050),X17048),X17047)) = hAPP(hAPP(c_Set_Oinsert(X17050),X17048),hAPP(hAPP(c_Set_Oinsert(X17050),X17049),X17047)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_9808,plain,
    ! [X17212,X17213,X17214,X17215] :
      ( ~ c_Finite__Set_Ofolding__one(X17215,X17214,X17213)
      | hAPP(X17213,hAPP(hAPP(c_Set_Oinsert(X17215),X17212),c_Orderings_Obot__class_Obot(tc_fun(X17215,tc_HOL_Obool)))) = X17212 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).

fof(i_0_9809,plain,
    ! [X22015,X22016] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22016),hAPP(c_Nat_OSuc,X22015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22016),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22015),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(i_0_9810,plain,
    ! [X17773,X17774,X17775,X17776] : hAPP(hAPP(c_Finite__Set_Ofold(X17776,X17775,X17774),X17773),c_Orderings_Obot__class_Obot(tc_fun(X17776,tc_HOL_Obool))) = X17773,
    inference(variable_rename,[status(thm)],[fact_fold__empty]) ).

cnf(i_0_9811,plain,
    ( c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))
    | ~ c_List_Oall__interval__nat(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5896]) ).

fof(i_0_9812,plain,
    ! [X30624,X30625,X30626] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30626)),hAPP(hAPP(c_List_Odrop(X30626),X30625),X30624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30626)),X30624)),X30625),
    inference(variable_rename,[status(thm)],[fact_length__drop]) ).

fof(i_0_9813,plain,
    ! [X29848,X29849,X29850] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29850)),hAPP(hAPP(c_List_Otake(X29850),X29849),X29848)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29850)),X29848)),X29849),
    inference(variable_rename,[status(thm)],[fact_length__take]) ).

cnf(i_0_9814,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Opred(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5952]) ).

fof(i_0_9815,plain,
    ! [X22931] :
      ( ~ class_Nat_Osemiring__char__0(X22931)
      | c_Fun_Oinj__on(tc_Nat_Onat,X22931,c_Nat_Osemiring__1__class_Oof__nat(X22931),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__of__nat])]) ).

fof(i_0_9816,plain,
    ! [X30771,X30772,X30773] : hAPP(hAPP(c_List_Otake(X30773),X30772),hAPP(c_List_Otl(X30773),X30771)) = hAPP(c_List_Otl(X30773),hAPP(hAPP(c_List_Otake(X30773),hAPP(c_Nat_OSuc,X30772)),X30771)),
    inference(variable_rename,[status(thm)],[fact_take__tl]) ).

fof(i_0_9817,plain,
    ! [X21775,X21776,X21778,X21779,X21780] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21776),X21775))
        | X21775 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21776),esk112_2(X21775,X21776))) )
      & ( X21778 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21779),X21780))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21779),X21778)) ) ),
    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_less__iff__Suc__add])])])])]) ).

fof(i_0_9818,plain,
    ! [X32882,X32883,X32884,X32885] : hAPP(hAPP(c_List_Odrop(X32885),X32884),c_List_Oreplicate(X32885,X32883,X32882)) = c_List_Oreplicate(X32885,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32883),X32884),X32882),
    inference(variable_rename,[status(thm)],[fact_drop__replicate]) ).

fof(i_0_9819,plain,
    ! [X32889,X32890,X32891,X32892] : hAPP(hAPP(c_List_Otake(X32892),X32891),c_List_Oreplicate(X32892,X32890,X32889)) = c_List_Oreplicate(X32892,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X32891),X32890),X32889),
    inference(variable_rename,[status(thm)],[fact_take__replicate]) ).

cnf(i_0_9820,plain,
    ( c_Transitive__Closure_Otrancl(X1,X2) = X2
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5953]) ).

fof(i_0_9821,plain,
    ! [X24145,X24146,X24147] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X24147,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X24147,X24146,X24145)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24147),X24146),X24145))
        | ~ class_Orderings_Oorder(X24147) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24147),X24146),X24145))
        | c_Orderings_Obot__class_Obot(tc_fun(X24147,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X24147,X24146,X24145)
        | ~ class_Orderings_Oorder(X24147) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5954])])]) ).

fof(i_0_9822,plain,
    ! [X23465,X23466,X23467] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X23467,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X23467,X23466,X23465)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23467),X23466),X23465))
        | ~ class_Orderings_Oorder(X23467) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23467),X23466),X23465))
        | c_Orderings_Obot__class_Obot(tc_fun(X23467,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23467,X23466,X23465)
        | ~ class_Orderings_Oorder(X23467) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5955])])]) ).

fof(i_0_9823,plain,
    ! [X24148,X24149,X24150] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(X24150,X24149,X24148) != c_Orderings_Obot__class_Obot(tc_fun(X24150,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24150),X24149),X24148))
        | ~ class_Orderings_Oorder(X24150) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24150),X24149),X24148))
        | c_SetInterval_Oord__class_OatLeastAtMost(X24150,X24149,X24148) = c_Orderings_Obot__class_Obot(tc_fun(X24150,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X24150) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5956])])]) ).

fof(i_0_9824,plain,
    ! [X23462,X23463,X23464] :
      ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X23464,X23463,X23462) != c_Orderings_Obot__class_Obot(tc_fun(X23464,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23464),X23463),X23462))
        | ~ class_Orderings_Oorder(X23464) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23464),X23463),X23462))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(X23464,X23463,X23462) = c_Orderings_Obot__class_Obot(tc_fun(X23464,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X23464) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5957])])]) ).

fof(i_0_9825,plain,
    ! [X24293] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24293) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24293))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9826,plain,
    ! [X32679,X32680,X32681,X32682] :
      ( ( hBOOL(hAPP(X32681,X32680))
        | ~ c_List_Olist__all(X32682,X32681,hAPP(hAPP(c_List_Olist_OCons(X32682),X32680),X32679)) )
      & ( c_List_Olist__all(X32682,X32681,X32679)
        | ~ c_List_Olist__all(X32682,X32681,hAPP(hAPP(c_List_Olist_OCons(X32682),X32680),X32679)) )
      & ( ~ hBOOL(hAPP(X32681,X32680))
        | ~ c_List_Olist__all(X32682,X32681,X32679)
        | c_List_Olist__all(X32682,X32681,hAPP(hAPP(c_List_Olist_OCons(X32682),X32680),X32679)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])]) ).

fof(i_0_9827,plain,
    ! [X25079,X25080,X25081] :
      ( ~ class_Fields_Olinordered__field(X25081)
      | X25080 = c_Groups_Ozero__class_Ozero(X25081)
      | hAPP(c_Groups_Oabs__class_Oabs(X25081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25081),X25079),X25080)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25081),hAPP(c_Groups_Oabs__class_Oabs(X25081),X25079)),hAPP(c_Groups_Oabs__class_Oabs(X25081),X25080)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).

fof(i_0_9828,plain,
    ! [X25584,X25585] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25585),esk251_2(X25584,X25585)),X25584))
        | hAPP(c_Finite__Set_Ocard(X25585),X25584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25585),X25584)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X25585),X25584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25585),X25584)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).

fof(i_0_9829,plain,
    ! [X20916,X20917] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20917,tc_HOL_Obool)),X20916),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20917,tc_HOL_Obool)),X20916)) = c_Orderings_Obot__class_Obot(tc_fun(X20917,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).

fof(i_0_9830,plain,
    ! [X19493,X19494] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19494,tc_HOL_Obool)),X19493),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19494,tc_HOL_Obool)),X19493)) = c_Orderings_Otop__class_Otop(tc_fun(X19494,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).

fof(i_0_9831,plain,
    ! [X17571,X17572,X17573] : c_Fun_Oinj__on(X17573,X17572,X17571,c_Orderings_Obot__class_Obot(tc_fun(X17573,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).

fof(i_0_9832,plain,
    ! [X23065,X23066] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23066),X23065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23065),X23066))
      | X23066 = X23065 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_9833,plain,
    ! [X19922,X19923] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19923),X19922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19922),X19923))
      | X19923 = X19922 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

cnf(i_0_9834,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | c_List_Oupt(X1,X2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5718]) ).

fof(i_0_9835,plain,
    ! [X26377] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26377))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X26377) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26377),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).

fof(i_0_9836,plain,
    ! [X33861,X33862,X33863,X33864] :
      ( ~ c_Equiv__Relations_Oequivp(X33864,X33863)
      | c_Quotient_OBabs(X33864,X33862,c_Quotient_ORespects(X33864,X33863),X33861) = X33861 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_babs__reg__eqv])]) ).

fof(i_0_9837,plain,
    ! [X21978,X21979,X21980] :
      ( ~ class_Lattices_Olattice(X21980)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21980),X21979))
      | X21979 = c_Orderings_Obot__class_Obot(tc_fun(X21980,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X21980,hAPP(hAPP(c_Set_Oinsert(X21980),X21978),X21979)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21980),X21978),c_Big__Operators_Olattice__class_OInf__fin(X21980,X21979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).

fof(i_0_9838,plain,
    ! [X20342,X20343,X20344] :
      ( ~ class_Lattices_Olattice(X20344)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20344),X20343))
      | X20343 = c_Orderings_Obot__class_Obot(tc_fun(X20344,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20344,hAPP(hAPP(c_Set_Oinsert(X20344),X20342),X20343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20344),X20342),c_Big__Operators_Olattice__class_OSup__fin(X20344,X20343)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).

fof(i_0_9839,plain,
    ! [X19132,X19133,X19134] :
      ( ~ class_Orderings_Olinorder(X19134)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19134),X19133))
      | X19133 = c_Orderings_Obot__class_Obot(tc_fun(X19134,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X19134,hAPP(hAPP(c_Set_Oinsert(X19134),X19132),X19133)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X19134),X19132),c_Big__Operators_Olinorder__class_OMin(X19134,X19133)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).

fof(i_0_9840,plain,
    ! [X19129,X19130,X19131] :
      ( ~ class_Orderings_Olinorder(X19131)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19131),X19130))
      | X19130 = c_Orderings_Obot__class_Obot(tc_fun(X19131,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X19131,hAPP(hAPP(c_Set_Oinsert(X19131),X19129),X19130)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X19131),X19129),c_Big__Operators_Olinorder__class_OMax(X19131,X19130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).

fof(i_0_9841,plain,
    ! [X19583,X19584,X19585] :
      ( ( X19584 = c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19585,tc_HOL_Obool)),X19584),X19583) != c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool)) )
      & ( X19583 = c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19585,tc_HOL_Obool)),X19584),X19583) != c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool)) )
      & ( X19584 != c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool))
        | X19583 != c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19585,tc_HOL_Obool)),X19584),X19583) = c_Orderings_Obot__class_Obot(tc_fun(X19585,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).

fof(i_0_9842,plain,
    ! [X30432,X30433,X30434] :
      ( ~ class_Groups_Omonoid__add(X30434)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30434),hAPP(hAPP(c_List_Oappend(X30434),X30433),X30432)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30434),hAPP(c_List_Omonoid__add__class_Olistsum(X30434),X30433)),hAPP(c_List_Omonoid__add__class_Olistsum(X30434),X30432)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).

fof(i_0_9843,plain,
    ! [X24993,X24994,X24995] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X24995)
      | hAPP(c_Groups_Oabs__class_Oabs(X24995),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24995),X24994),X24993)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24995),hAPP(c_Groups_Oabs__class_Oabs(X24995),X24994)),hAPP(c_Groups_Oabs__class_Oabs(X24995),X24993)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).

fof(i_0_9844,plain,
    ! [X24981,X24982,X24983] :
      ( ~ class_Rings_Olinordered__idom(X24983)
      | hAPP(c_Groups_Oabs__class_Oabs(X24983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24983),X24982),X24981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24983),hAPP(c_Groups_Oabs__class_Oabs(X24983),X24982)),hAPP(c_Groups_Oabs__class_Oabs(X24983),X24981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).

fof(i_0_9845,plain,
    ! [X20848,X20849,X20850] :
      ( ~ class_Lattices_Oboolean__algebra(X20850)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20850),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20850),X20849),X20848)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20850),hAPP(c_Groups_Ouminus__class_Ouminus(X20850),X20849)),hAPP(c_Groups_Ouminus__class_Ouminus(X20850),X20848)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).

fof(i_0_9846,plain,
    ! [X20851,X20852,X20853] :
      ( ~ class_Lattices_Oboolean__algebra(X20853)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20853),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20853),X20852),X20851)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20853),hAPP(c_Groups_Ouminus__class_Ouminus(X20853),X20852)),hAPP(c_Groups_Ouminus__class_Ouminus(X20853),X20851)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).

fof(i_0_9847,plain,
    ! [X18695,X18696,X18697] :
      ( ~ class_Groups_Olinordered__ab__group__add(X18697)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18697),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18697),X18696),X18695)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18697),hAPP(c_Groups_Ouminus__class_Ouminus(X18697),X18696)),hAPP(c_Groups_Ouminus__class_Ouminus(X18697),X18695)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).

fof(i_0_9848,plain,
    ! [X18692,X18693,X18694] :
      ( ~ class_Groups_Olinordered__ab__group__add(X18694)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18694),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18694),X18693),X18692)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18694),hAPP(c_Groups_Ouminus__class_Ouminus(X18694),X18693)),hAPP(c_Groups_Ouminus__class_Ouminus(X18694),X18692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).

fof(i_0_9849,plain,
    ! [X18966,X18967,X18968] :
      ( ~ class_Groups_Oab__group__add(X18968)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18968),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18968),X18967),X18966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18968),hAPP(c_Groups_Ouminus__class_Ouminus(X18968),X18967)),hAPP(c_Groups_Ouminus__class_Ouminus(X18968),X18966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_9850,plain,
    ! [X18969,X18970,X18971] :
      ( ~ class_Groups_Ogroup__add(X18971)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18971),X18970),X18969)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18971),hAPP(c_Groups_Ouminus__class_Ouminus(X18971),X18969)),hAPP(c_Groups_Ouminus__class_Ouminus(X18971),X18970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

cnf(i_0_9851,plain,
    ( c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5531]) ).

cnf(i_0_9852,plain,
    ( c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5958]) ).

fof(i_0_9853,plain,
    ! [X24508,X24509,X24510] : hAPP(c_Set_Oimage(X24509,tc_fun(X24509,tc_HOL_Obool),X24510),X24508) != hAPP(c_Set_OPow(X24509),X24508),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).

fof(i_0_9854,plain,
    ! [X17649,X17650,X17651] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17649,tc_HOL_Obool)),X17651),X17650))
        | X17651 != X17650 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17649,tc_HOL_Obool)),X17650),X17651))
        | X17651 != X17650 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5959])])]) ).

fof(i_0_9855,plain,
    ! [X17659,X17660,X17661] :
      ( X17661 != X17660
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17659,tc_HOL_Obool)),X17661),X17660)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_9856,plain,
    ! [X17656,X17657,X17658] :
      ( X17658 != X17657
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17656,tc_HOL_Obool)),X17657),X17658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_9857,plain,
    ! [X21587] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21587)),X21587)),
    inference(variable_rename,[status(thm)],[i_0_5960]) ).

fof(i_0_9858,plain,
    ! [X23423,X23424] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23424))
        | c_SMT_Oz3div(X23423,X23424) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23423),X23424) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23424))
        | c_SMT_Oz3div(X23423,X23424) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23424))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5961])]) ).

fof(i_0_9859,plain,
    ! [X30986,X30987] :
      ( X30987 = c_List_Olist_ONil(X30986)
      | hBOOL(hAPP(hAPP(c_member(X30986),c_List_Olast(X30986,X30987)),hAPP(c_List_Oset(X30986),X30987))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).

fof(i_0_9860,plain,
    ! [X21593,X21594,X21595] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21595)),X21594) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21595)),X21593)
        | X21594 = X21593 )
      & ( X21594 != X21593
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21595)),X21594) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21595)),X21593) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).

fof(i_0_9861,plain,
    ! [X26705,X26706,X26707,X26708,X26709,X26710] :
      ( ( X26708 = X26706
        | hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26708),X26707) != hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26706),X26705) )
      & ( X26707 = X26705
        | hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26708),X26707) != hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26706),X26705) )
      & ( X26708 != X26706
        | X26707 != X26705
        | hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26708),X26707) = hAPP(hAPP(c_Product__Type_OPair(X26710,X26709),X26706),X26705) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).

fof(i_0_9862,plain,
    ! [X26699,X26700,X26701,X26702,X26703,X26704] :
      ( ( X26702 = X26700
        | hAPP(hAPP(c_Product__Type_OPair(X26704,X26703),X26702),X26701) != hAPP(hAPP(c_Product__Type_OPair(X26704,X26703),X26700),X26699) )
      & ( X26701 = X26699
        | hAPP(hAPP(c_Product__Type_OPair(X26704,X26703),X26702),X26701) != hAPP(hAPP(c_Product__Type_OPair(X26704,X26703),X26700),X26699) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).

fof(i_0_9863,plain,
    ! [X24783,X24784] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24784,X24783) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24784),X24783) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24784,X24783) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24784),X24783) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24783),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24784,X24783)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).

fof(i_0_9864,plain,
    ! [X24875,X24876] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24876),X24875))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24876,X24875) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24876),X24875),X24875) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5962])]) ).

fof(i_0_9865,plain,
    ! [X24873,X24874] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24874),X24873))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24874,X24873) = X24874 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24874),X24873))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24874,X24873) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24874),X24873),X24873) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5963])]) ).

fof(i_0_9866,plain,
    ! [X32407,X32408,X32409] :
      ( hBOOL(hAPP(hAPP(c_member(X32409),X32408),hAPP(c_List_Oset(X32409),X32407)))
      | c_List_Oinsert(X32409,X32408,X32407) = hAPP(hAPP(c_List_Olist_OCons(X32409),X32408),X32407) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5964])]) ).

fof(i_0_9867,plain,
    ! [X17665,X17666] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17666,tc_HOL_Obool)),X17665),X17665)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_9868,plain,
    ! [X23107,X23108] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23108),X23107)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23108)),hAPP(c_Nat_OSuc,X23107)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_9869,plain,
    ! [X32146,X32147,X32148] : hAPP(c_List_Orev(X32148),hAPP(hAPP(c_List_Oappend(X32148),X32147),X32146)) = hAPP(hAPP(c_List_Oappend(X32148),hAPP(c_List_Orev(X32148),X32146)),hAPP(c_List_Orev(X32148),X32147)),
    inference(variable_rename,[status(thm)],[fact_rev__append]) ).

fof(i_0_9870,plain,
    ! [X30680,X30681,X30682,X30683] :
      ( hAPP(c_List_Orotate1(X30683),c_List_Olist_ONil(X30683)) = c_List_Olist_ONil(X30683)
      & hAPP(c_List_Orotate1(X30682),hAPP(hAPP(c_List_Olist_OCons(X30682),X30681),X30680)) = hAPP(hAPP(c_List_Oappend(X30682),X30680),hAPP(hAPP(c_List_Olist_OCons(X30682),X30681),c_List_Olist_ONil(X30682))) ),
    inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).

fof(i_0_9871,plain,
    ! [X21557,X21558] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21558),X21557))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21558),hAPP(c_Nat_OSuc,X21557))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_9872,plain,
    ! [X21794,X21795] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21795),X21794))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21795),hAPP(c_Nat_OSuc,X21794))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_9873,plain,
    ! [X21579,X21580] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21580),X21579))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21580),hAPP(c_Nat_OSuc,X21579))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_9874,plain,
    ! [X29998,X29999] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X29999,X29998) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29999),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29998)),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(i_0_9875,plain,
    ! [X22963,X22964] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22964),X22963),X22963) != c_Groups_Ozero__class_Ozero(X22964)
        | X22963 = c_Groups_Ozero__class_Ozero(X22964)
        | ~ hBOOL(hAPP(hAPP(c_member(X22964),X22963),c_Int_Oring__1__class_OInts(X22964)))
        | ~ class_Int_Oring__char__0(X22964) )
      & ( X22963 != c_Groups_Ozero__class_Ozero(X22964)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22964),X22963),X22963) = c_Groups_Ozero__class_Ozero(X22964)
        | ~ hBOOL(hAPP(hAPP(c_member(X22964),X22963),c_Int_Oring__1__class_OInts(X22964)))
        | ~ class_Int_Oring__char__0(X22964) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_9876,plain,
    ! [X26374] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26374))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X26374) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq__minus1])]) ).

fof(i_0_9877,plain,
    ! [X20500,X20501,X20502] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20502,tc_HOL_Obool)),X20501),X20500) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20502,tc_HOL_Obool)),X20500),X20501),
    inference(variable_rename,[status(thm)],[fact_Int__commute]) ).

fof(i_0_9878,plain,
    ! [X19376,X19377,X19378] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19378,tc_HOL_Obool)),X19377),X19376) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19378,tc_HOL_Obool)),X19376),X19377),
    inference(variable_rename,[status(thm)],[fact_Un__commute]) ).

fof(i_0_9879,plain,
    ! [X22734,X22735,X22736,X22737,X22738] : c_Hoare__Mirabelle_Otriple_Otriple__size(X22738,X22737,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X22738),X22736),X22735),X22734)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_triple_Osize_I1_J]) ).

fof(i_0_9880,plain,
    ! [X24476] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk205_1(X24476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24476)) )
      & ( X24476 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk205_1(X24476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24476)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int])])])]) ).

fof(i_0_9881,plain,
    ! [X23824,X23825,X23826,X23827,X23828] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23828),X23825),X23827) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23828),X23824),X23826)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23828),X23825),X23826) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23828),X23824),X23827)
        | X23826 = c_Groups_Ozero__class_Ozero(X23828)
        | X23827 = c_Groups_Ozero__class_Ozero(X23828)
        | ~ class_Fields_Ofield(X23828) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23828),X23825),X23826) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23828),X23824),X23827)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23828),X23825),X23827) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23828),X23824),X23826)
        | X23826 = c_Groups_Ozero__class_Ozero(X23828)
        | X23827 = c_Groups_Ozero__class_Ozero(X23828)
        | ~ class_Fields_Ofield(X23828) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

fof(i_0_9882,plain,
    ! [X24796,X24797] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24797),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24796),X24797)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24796),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24796,X24797)),
    inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).

fof(i_0_9883,plain,
    ! [X24906,X24907] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24907),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24906),X24907)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24906),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24906,X24907)),
    inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).

fof(i_0_9884,plain,
    ! [X31346,X31347] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X31347),X31346) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31347)),hAPP(c_Code__Numeral_Onat__of,X31346))),
    inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).

fof(i_0_9885,plain,
    ! [X31322,X31323] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X31323),X31322) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31323)),hAPP(c_Code__Numeral_Onat__of,X31322))),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).

fof(i_0_9886,plain,
    ! [X31344,X31345] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X31345),X31344) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31345)),hAPP(c_Code__Numeral_Onat__of,X31344))),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(i_0_9887,plain,
    ! [X31341,X31342] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X31342),X31341) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31342)),hAPP(c_Code__Numeral_Onat__of,X31341))),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(i_0_9888,plain,
    ! [X20158,X20159] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20159),X20158))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20158),X20159)) = X20158 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).

fof(i_0_9889,plain,
    ! [X20160,X20161] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20161),X20160))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20160),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20160),X20161)) = X20161 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).

fof(i_0_9890,plain,
    ! [X24528,X24529,X24530,X24531] : c_Nat_Onat_Onat__case(X24531,X24530,X24529,hAPP(c_Nat_OSuc,X24528)) = hAPP(X24529,X24528),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_9891,plain,
    ! [X29987,X29988,X29989] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29987) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X29988),hAPP(c_List_Oset(tc_Nat_Onat),X29987)))
        | X29988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk397_1(X29989)),hAPP(c_List_Oset(tc_Nat_Onat),X29989)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk397_1(X29989) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    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_listsum__eq__0__nat__iff__nat])])])])])]) ).

fof(i_0_9892,plain,
    ! [X18393,X18394,X18395] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18395),X18394),X18393))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18395),X18394),X18393))
        | ~ class_Orderings_Oorder(X18395) )
      & ( X18394 != X18393
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18395),X18394),X18393))
        | ~ class_Orderings_Oorder(X18395) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18395),X18394),X18393))
        | X18394 = X18393
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18395),X18394),X18393))
        | ~ class_Orderings_Oorder(X18395) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_9893,plain,
    ! [X18387,X18388,X18389] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18389),X18388),X18387))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18389),X18388),X18387))
        | X18388 = X18387
        | ~ class_Orderings_Oorder(X18389) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18389),X18388),X18387))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18389),X18388),X18387))
        | ~ class_Orderings_Oorder(X18389) )
      & ( X18388 != X18387
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18389),X18388),X18387))
        | ~ class_Orderings_Oorder(X18389) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_9894,plain,
    ! [X18375,X18376,X18377] :
      ( ~ class_Orderings_Oorder(X18377)
      | X18376 = X18375
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18377),X18376),X18375))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18377),X18376),X18375)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_9895,plain,
    ! [X18360,X18361,X18362] :
      ( ~ class_Orderings_Oorder(X18362)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18362),X18361),X18360))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18362),X18361),X18360))
      | X18361 = X18360 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_9896,plain,
    ! [X18357,X18358,X18359] :
      ( ~ class_Orderings_Oorder(X18359)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18359),X18358),X18357))
      | X18358 = X18357
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18359),X18358),X18357)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_9897,plain,
    ! [X18354,X18355,X18356] :
      ( ~ class_Orderings_Oorder(X18356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18356),X18355),X18354))
      | X18354 = X18355
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18356),X18355),X18354)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_9898,plain,
    ! [X18378,X18379,X18380] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18380),X18379),X18378))
        | X18379 = X18378
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18380),X18379),X18378))
        | ~ class_Orderings_Olinorder(X18380) )
      & ( X18379 != X18378
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18380),X18379),X18378))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18380),X18379),X18378))
        | ~ class_Orderings_Olinorder(X18380) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5965])])]) ).

fof(i_0_9899,plain,
    ! [X18372,X18373,X18374] :
      ( ~ class_Orderings_Oorder(X18374)
      | X18373 = X18372
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18374),X18372),X18373))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18374),X18372),X18373)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_9900,plain,
    ! [X25756,X25757,X25758] :
      ( ~ class_Int_Onumber__ring(X25758)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25758),hAPP(c_Int_Onumber__class_Onumber__of(X25758),X25757)),hAPP(c_Int_Onumber__class_Onumber__of(X25758),X25756)) = hAPP(c_Int_Onumber__class_Onumber__of(X25758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25757),X25756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_9901,plain,
    ! [X25746,X25747,X25748] :
      ( ~ class_Int_Onumber__ring(X25748)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25748),hAPP(c_Int_Onumber__class_Onumber__of(X25748),X25747)),hAPP(c_Int_Onumber__class_Onumber__of(X25748),X25746)) = hAPP(c_Int_Onumber__class_Onumber__of(X25748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25747),X25746)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_9902,plain,
    ! [X25759,X25760,X25761] :
      ( ~ class_Int_Onumber__ring(X25761)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25760),X25759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25761),hAPP(c_Int_Onumber__class_Onumber__of(X25761),X25760)),hAPP(c_Int_Onumber__class_Onumber__of(X25761),X25759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_9903,plain,
    ! [X25749,X25750,X25751] :
      ( ~ class_Int_Onumber__ring(X25751)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25750),X25749)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25751),hAPP(c_Int_Onumber__class_Onumber__of(X25751),X25750)),hAPP(c_Int_Onumber__class_Onumber__of(X25751),X25749)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_9904,plain,
    ! [X25762,X25763,X25764] :
      ( ~ class_Int_Onumber__ring(X25764)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25763),X25762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25764),hAPP(c_Int_Onumber__class_Onumber__of(X25764),X25763)),hAPP(c_Int_Onumber__class_Onumber__of(X25764),X25762)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).

fof(i_0_9905,plain,
    ! [X24053,X24054,X24055] :
      ( ~ class_Rings_Oring__1(X24055)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24054),X24053)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24055),hAPP(c_Int_Oring__1__class_Oof__int(X24055),X24054)),hAPP(c_Int_Oring__1__class_Oof__int(X24055),X24053)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).

fof(i_0_9906,plain,
    ! [X24050,X24051,X24052] :
      ( ~ class_Rings_Oring__1(X24052)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24051),X24050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24052),hAPP(c_Int_Oring__1__class_Oof__int(X24052),X24051)),hAPP(c_Int_Oring__1__class_Oof__int(X24052),X24050)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).

fof(i_0_9907,plain,
    ! [X24057,X24058,X24059] :
      ( ~ class_Rings_Oring__1(X24059)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24058),X24057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24059),hAPP(c_Int_Oring__1__class_Oof__int(X24059),X24058)),hAPP(c_Int_Oring__1__class_Oof__int(X24059),X24057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).

fof(i_0_9908,plain,
    ! [X22920,X22921,X22922] :
      ( ~ class_Rings_Osemiring__1(X22922)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22921),X22920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22922),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22922),X22921)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22922),X22920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).

fof(i_0_9909,plain,
    ! [X22917,X22918,X22919] :
      ( ~ class_Rings_Osemiring__1(X22919)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22918),X22917)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22919),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22919),X22918)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22919),X22917)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).

fof(i_0_9910,plain,
    ! [X31503,X31504,X31505] : c_Enum_Oproduct(X31505,X31504,c_List_Olist_ONil(X31505),X31503) = c_List_Olist_ONil(tc_prod(X31505,X31504)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(i_0_9911,plain,
    ! [X26370,X26371] :
      ( ~ class_Fields_Ofield__inverse__zero(X26371)
      | ~ class_Int_Onumber__ring(X26371)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26371),hAPP(c_Int_Onumber__class_Onumber__of(X26371),c_Int_OMin)),X26370) = hAPP(c_Groups_Ouminus__class_Ouminus(X26371),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26371),c_Groups_Oone__class_Oone(X26371)),X26370)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).

fof(i_0_9912,plain,
    ! [X20000,X20001,X20002] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20002)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20001,X20002),hAPP(c_COMBK(X20002,X20001),c_Groups_Oone__class_Oone(X20002))),X20000) = c_Groups_Oone__class_Oone(X20002) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).

fof(i_0_9913,plain,
    ! [X22193,X22194,X22195] :
      ( ~ class_Groups_Ocomm__monoid__add(X22195)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22194,X22195),hAPP(c_COMBK(X22195,X22194),c_Groups_Ozero__class_Ozero(X22195))),X22193) = c_Groups_Ozero__class_Ozero(X22195) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).

fof(i_0_9914,plain,
    ! [X23402,X23403] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23403),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23402) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X23403,X23402),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(i_0_9915,plain,
    ! [X18366,X18367,X18368] :
      ( ~ class_Orderings_Opreorder(X18368)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18368),X18367),X18366))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18368),X18367),X18366)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_9916,plain,
    ! [X32859,X32860,X32861] :
      ( X32861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Otl(X32860),c_List_Oreplicate(X32860,X32861,X32859)) = c_List_Oreplicate(X32860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32861),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__replicate])]) ).

fof(i_0_9917,plain,
    ! [X26818,X26819] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26819),X26818)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X26819),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26818)),
    inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).

fof(i_0_9918,plain,
    ! [X26372,X26373] :
      ( ~ class_Int_Onumber__ring(X26373)
      | ~ class_Rings_Olinordered__idom(X26373)
      | hAPP(c_Groups_Oabs__class_Oabs(X26373),hAPP(hAPP(c_Power_Opower__class_Opower(X26373),hAPP(c_Int_Onumber__class_Onumber__of(X26373),c_Int_OMin)),X26372)) = c_Groups_Oone__class_Oone(X26373) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).

fof(i_0_9919,plain,
    ! [X23112,X23113,X23114] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23114,X23113),X23112) != c_Orderings_Obot__class_Obot(tc_fun(X23114,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23114),X23113),X23112))
        | ~ class_Orderings_Oorder(X23114) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23114),X23113),X23112))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23114,X23113),X23112) = c_Orderings_Obot__class_Obot(tc_fun(X23114,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X23114) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5966])])]) ).

fof(i_0_9920,plain,
    ! [X23115,X23116,X23117] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X23117,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23117,X23116),X23115)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23117),X23116),X23115))
        | ~ class_Orderings_Oorder(X23117) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23117),X23116),X23115))
        | c_Orderings_Obot__class_Obot(tc_fun(X23117,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23117,X23116),X23115)
        | ~ class_Orderings_Oorder(X23117) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5967])])]) ).

cnf(i_0_9921,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5968]) ).

fof(i_0_9922,plain,
    ! [X23981,X23982] :
      ( ~ c_Nat__Transfer_Onat__set(X23982)
      | ~ c_Nat__Transfer_Onat__set(X23981)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23982),X23981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).

fof(i_0_9923,plain,
    ! [X23983,X23984] :
      ( ~ c_Nat__Transfer_Onat__set(X23984)
      | ~ c_Nat__Transfer_Onat__set(X23983)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23984),X23983)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).

fof(i_0_9924,plain,
    ! [X22990,X22991,X22993,X22994,X22995] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22991),X22990))
        | X22990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22991),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk141_2(X22990,X22991))) )
      & ( X22993 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22994),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22995))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22994),X22993)) ) ),
    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_zle__iff__zadd])])])])]) ).

fof(i_0_9925,plain,
    ! [X32953,X32954,X32955,X32956,X32957] : hAPP(hAPP(c_List_Omap(X32957,X32956),X32955),c_List_Oreplicate(X32957,X32954,X32953)) = c_List_Oreplicate(X32956,X32954,hAPP(X32955,X32953)),
    inference(variable_rename,[status(thm)],[fact_map__replicate]) ).

fof(i_0_9926,plain,
    ! [X31776,X31777,X31778,X31779] : hAPP(c_List_Ofilter(X31779,X31778),c_List_Oremove1(X31779,X31777,X31776)) = c_List_Oremove1(X31779,X31777,hAPP(c_List_Ofilter(X31779,X31778),X31776)),
    inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).

fof(i_0_9927,plain,
    ! [X30996,X30997,X30998,X30999] :
      ( ( X30996 != c_List_Olist_ONil(X30999)
        | hAPP(hAPP(c_List_Oappend(X30999),X30998),hAPP(hAPP(c_List_Olist_OCons(X30999),X30997),c_List_Olist_ONil(X30999))) != X30996 )
      & ( c_List_Obutlast(X30999,X30996) = X30998
        | hAPP(hAPP(c_List_Oappend(X30999),X30998),hAPP(hAPP(c_List_Olist_OCons(X30999),X30997),c_List_Olist_ONil(X30999))) != X30996 )
      & ( c_List_Olast(X30999,X30996) = X30997
        | hAPP(hAPP(c_List_Oappend(X30999),X30998),hAPP(hAPP(c_List_Olist_OCons(X30999),X30997),c_List_Olist_ONil(X30999))) != X30996 )
      & ( X30996 = c_List_Olist_ONil(X30999)
        | c_List_Obutlast(X30999,X30996) != X30998
        | c_List_Olast(X30999,X30996) != X30997
        | hAPP(hAPP(c_List_Oappend(X30999),X30998),hAPP(hAPP(c_List_Olist_OCons(X30999),X30997),c_List_Olist_ONil(X30999))) = X30996 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).

fof(i_0_9928,plain,
    ! [X24276] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24276),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | X24276 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk174_1(X24276)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).

fof(i_0_9929,plain,
    ! [X25769,X25770] :
      ( ~ class_Int_Onumber__ring(X25770)
      | hBOOL(hAPP(hAPP(c_member(X25770),hAPP(c_Int_Onumber__class_Onumber__of(X25770),X25769)),c_Int_Oring__1__class_OInts(X25770))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).

fof(i_0_9930,plain,
    ! [X24064,X24065] :
      ( ~ class_Rings_Oring__1(X24065)
      | hBOOL(hAPP(hAPP(c_member(X24065),hAPP(c_Int_Oring__1__class_Oof__int(X24065),X24064)),c_Int_Oring__1__class_OInts(X24065))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).

fof(i_0_9931,plain,
    ! [X26508,X26509] :
      ( ~ class_Rings_Osemiring__1(X26509)
      | hBOOL(hAPP(hAPP(c_member(X26509),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26509),X26508)),c_Nat_Osemiring__1__class_ONats(X26509))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).

fof(i_0_9932,plain,
    ! [X22828,X22829] :
      ( ~ class_Rings_Oring__1(X22829)
      | hBOOL(hAPP(hAPP(c_member(X22829),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22829),X22828)),c_Int_Oring__1__class_OInts(X22829))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).

fof(i_0_9933,plain,
    ! [X22718] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22718))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22718),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X22718 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).

fof(i_0_9934,plain,
    ! [X22519] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22519))
      | X22519 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22519),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).

fof(i_0_9935,plain,
    ! [X31333] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31333)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_nat__of]) ).

fof(i_0_9936,plain,
    ! [X24725,X24726,X24727] :
      ( ~ class_Divides_Osemiring__div(X24727)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X24727),c_Divides_Odiv__class_Omod(X24727,X24726,X24725)),X24725) = c_Groups_Ozero__class_Ozero(X24727) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).

fof(i_0_9937,plain,
    ! [X26778] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X26778) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26778),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(i_0_9938,plain,
    ! [X32974,X32975,X32976] : hAPP(c_List_Oset(X32976),c_List_Oreplicate(X32976,hAPP(c_Nat_OSuc,X32975),X32974)) = hAPP(hAPP(c_Set_Oinsert(X32976),X32974),c_Orderings_Obot__class_Obot(tc_fun(X32976,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_set__replicate__Suc]) ).

fof(i_0_9939,plain,
    ! [X24312,X24313] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24313))
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24313,X24312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).

fof(i_0_9940,plain,
    ! [X19215,X19216] :
      ( ~ class_Orderings_Olinorder(X19216)
      | c_Big__Operators_Olattice_OInf__fin(X19216,c_Orderings_Oord__class_Omin(X19216),hAPP(hAPP(c_Set_Oinsert(X19216),X19215),c_Orderings_Obot__class_Obot(tc_fun(X19216,tc_HOL_Obool)))) = X19215 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).

fof(i_0_9941,plain,
    ! [X19217,X19218] :
      ( ~ class_Orderings_Olinorder(X19218)
      | c_Big__Operators_Olattice_OSup__fin(X19218,c_Orderings_Oord__class_Omax(X19218),hAPP(hAPP(c_Set_Oinsert(X19218),X19217),c_Orderings_Obot__class_Obot(tc_fun(X19218,tc_HOL_Obool)))) = X19217 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).

fof(i_0_9942,plain,
    ! [X23074] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23074))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23074)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23074))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23074)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_9943,plain,
    ! [X20722,X20723] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20723,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X20723,tc_HOL_Obool))),X20722) = c_Orderings_Obot__class_Obot(tc_fun(X20723,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).

fof(i_0_9944,plain,
    ! [X19370,X19371] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19371,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19371,tc_HOL_Obool))),X19370) = c_Orderings_Otop__class_Otop(tc_fun(X19371,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).

fof(i_0_9945,plain,
    ! [X17332,X17333] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17333,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17333,tc_HOL_Obool))),X17332) = c_Orderings_Obot__class_Obot(tc_fun(X17333,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).

fof(i_0_9946,plain,
    ! [X27791,X27792,X27793] : hAPP(hAPP(c_Product__Type_OSigma(X27793,X27792),c_Orderings_Obot__class_Obot(tc_fun(X27793,tc_HOL_Obool))),X27791) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27793,X27792),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).

fof(i_0_9947,plain,
    ! [X19982] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19982),X19982))),
    inference(variable_rename,[status(thm)],[fact_le__square]) ).

fof(i_0_9948,plain,
    ! [X19893,X19894] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19894),X19893))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_9949,plain,
    ! [X19891,X19892] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19891),X19892))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_9950,plain,
    ! [X25774,X25775,X25776,X25777] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) = c_Groups_Ozero__class_Ozero(X25777)
        | X25776 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25777),X25774),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) != X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) != c_Groups_Ozero__class_Ozero(X25777)
        | X25774 = c_Groups_Ozero__class_Ozero(X25777)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) != X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) = c_Groups_Ozero__class_Ozero(X25777)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) != c_Groups_Ozero__class_Ozero(X25777)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) = X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) )
      & ( X25774 != c_Groups_Ozero__class_Ozero(X25777)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) != c_Groups_Ozero__class_Ozero(X25777)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) = X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775) = c_Groups_Ozero__class_Ozero(X25777)
        | X25776 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25777),X25774),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) = X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) )
      & ( X25774 != c_Groups_Ozero__class_Ozero(X25777)
        | X25776 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25777),X25774),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25777),X25776),hAPP(c_Int_Onumber__class_Onumber__of(X25777),X25775)) = X25774
        | ~ class_Fields_Ofield__inverse__zero(X25777)
        | ~ class_Int_Onumber(X25777) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).

fof(i_0_9951,plain,
    ! [X25786,X25787,X25788,X25789] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) = c_Groups_Ozero__class_Ozero(X25789)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25789),X25788),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786)) = X25787
        | X25788 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) != c_Groups_Ozero__class_Ozero(X25789)
        | X25788 = c_Groups_Ozero__class_Ozero(X25789)
        | X25788 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) = c_Groups_Ozero__class_Ozero(X25789)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) != c_Groups_Ozero__class_Ozero(X25789)
        | X25788 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) )
      & ( X25788 != c_Groups_Ozero__class_Ozero(X25789)
        | hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) != c_Groups_Ozero__class_Ozero(X25789)
        | X25788 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786) = c_Groups_Ozero__class_Ozero(X25789)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25789),X25788),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786)) != X25787
        | X25788 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) )
      & ( X25788 != c_Groups_Ozero__class_Ozero(X25789)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25789),X25788),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786)) != X25787
        | X25788 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25789),X25787),hAPP(c_Int_Onumber__class_Onumber__of(X25789),X25786))
        | ~ class_Fields_Ofield__inverse__zero(X25789)
        | ~ class_Int_Onumber(X25789) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).

fof(i_0_9952,plain,
    ! [X20083,X20084,X20085] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | X20085 = X20084
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20085),X20084)) )
      & ( ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | X20085 = X20084
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20085),X20084)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20085),X20084)) )
      & ( ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20085),X20084)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | X20085 = X20084
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085)) )
      & ( ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | X20085 = X20084
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085)) )
      & ( ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085))
        | ~ hBOOL(hAPP(hAPP(X20083,X20084),X20085)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_9953,plain,
    ! [X23197] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23197) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23197)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9954,plain,
    ! [X30400,X30401,X30402,X30403,X30404,X30405] :
      ( hAPP(hAPP(c_List_Oappend(X30405),X30404),X30403) != X30402
      | X30401 != hAPP(hAPP(c_List_Oappend(X30405),X30403),X30400)
      | hAPP(hAPP(c_List_Oappend(X30405),X30404),X30401) = hAPP(hAPP(c_List_Oappend(X30405),X30402),X30400) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).

fof(i_0_9955,plain,
    ! [X30390,X30391,X30392,X30393,X30394,X30395] :
      ( hAPP(hAPP(c_List_Olist_OCons(X30395),X30394),X30393) != X30392
      | X30391 != hAPP(hAPP(c_List_Oappend(X30395),X30393),X30390)
      | hAPP(hAPP(c_List_Olist_OCons(X30395),X30394),X30391) = hAPP(hAPP(c_List_Oappend(X30395),X30392),X30390) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).

fof(i_0_9956,plain,
    ! [X23032,X23033,X23034] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23034),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23033),X23032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23034),X23032)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_9957,plain,
    ! [X19952,X19953,X19954] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19954),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19953),X19952)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19953),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19954),X19952)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_9958,plain,
    ! [X29996,X29997] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X29997),X29996) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29997,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29996),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(i_0_9959,plain,
    ! [X20102,X20103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20103),X20102)),X20102) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X20103),X20102),
    inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).

fof(i_0_9960,plain,
    ! [X19181] :
      ( ~ class_Orderings_Olinorder(X19181)
      | c_Orderings_Oord_Omax(X19181,hAPP(c_COMBC(X19181,X19181,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X19181))) = c_Orderings_Oord__class_Omin(X19181) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).

fof(i_0_9961,plain,
    ! [X19180] :
      ( ~ class_Orderings_Olinorder(X19180)
      | c_Orderings_Oord_Omin(X19180,hAPP(c_COMBC(X19180,X19180,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X19180))) = c_Orderings_Oord__class_Omax(X19180) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).

fof(i_0_9962,plain,
    ! [X30837] :
      ( ~ class_Groups_Omonoid__add(X30837)
      | c_List_Omonoid__add__class_Olistsum(X30837) = c_List_Ofoldl(X30837,X30837,c_Groups_Oplus__class_Oplus(X30837),c_Groups_Ozero__class_Ozero(X30837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).

fof(i_0_9963,plain,
    ! [X23321,X23322,X23323] :
      ( ~ class_Divides_Osemiring__div(X23323)
      | X23322 = c_Groups_Ozero__class_Ozero(X23323)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23323),X23322),X23321)),X23322) = X23321 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).

fof(i_0_9964,plain,
    ! [X23318,X23319,X23320] :
      ( ~ class_Divides_Osemiring__div(X23320)
      | X23319 = c_Groups_Ozero__class_Ozero(X23320)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23320),X23318),X23319)),X23319) = X23318 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).

fof(i_0_9965,plain,
    ! [X20147,X20148,X20149] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20148),X20149) != X20147
        | X20148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20147),X20149)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20149),X20148)) )
      & ( X20148 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20147),X20149)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20148),X20149) = X20147
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20149),X20148)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).

fof(i_0_9966,plain,
    ! [X24705,X24706] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X24706,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24705)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24706),X24705)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).

fof(i_0_9967,plain,
    ! [X31640,X31641,X31642] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31642),X31641))
      | c_List_Oremove1(X31642,X31640,c_List_Oremdups(X31642,X31641)) = c_List_Oremdups(X31642,c_List_Oremove1(X31642,X31640,X31641)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__remdups])]) ).

fof(i_0_9968,plain,
    ! [X28239,X28240] :
      ( ( c_Wellfounded_Oacyclic(X28240,X28239)
        | ~ c_Nitpick_Owf_H(X28240,X28239) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28240,X28240)),X28239))
        | c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Nitpick_Owf_H(X28240,X28239) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28240,X28240)),X28239))
        | ~ c_Wellfounded_Oacyclic(X28240,X28239)
        | c_Nitpick_Owf_H(X28240,X28239) )
      & ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Wellfounded_Oacyclic(X28240,X28239)
        | c_Nitpick_Owf_H(X28240,X28239) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).

fof(i_0_9969,plain,
    ! [X28235,X28236] :
      ( ( ~ c_Wellfounded_Owf(X28236,X28235)
        | c_Wellfounded_Oacyclic(X28236,X28235)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28236,X28236)),X28235)) )
      & ( ~ c_Wellfounded_Oacyclic(X28236,X28235)
        | c_Wellfounded_Owf(X28236,X28235)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28236,X28236)),X28235)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).

fof(i_0_9970,plain,
    ! [X28237,X28238] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28238,X28238)),X28237))
      | ~ c_Wellfounded_Oacyclic(X28238,X28237)
      | c_Wellfounded_Owf(X28238,X28237) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).

fof(i_0_9971,plain,
    ! [X32131,X32132] : c_Fun_Oinj__on(tc_List_Olist(X32132),tc_List_Olist(X32132),c_List_Orev(X32132),X32131),
    inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).

fof(i_0_9972,plain,
    ! [X31749,X31750,X31751] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31751),X31750))
      | hBOOL(hAPP(c_List_Odistinct(X31751),hAPP(c_List_Ofilter(X31751,X31749),X31750))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).

fof(i_0_9973,plain,
    ! [X22741,X22742,X22743,X22744] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X22744)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X22744),X22743),X22742),X22741)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_triple_Osize_I2_J]) ).

fof(i_0_9974,plain,
    ! [X27158,X27159,X27160,X27161,X27162,X27163,X27164,X27167] :
      ( ( ~ hBOOL(hAPP(hAPP(X27158,X27160),X27161))
        | hAPP(X27158,X27160) = hAPP(X27158,X27161)
        | ~ c_Equiv__Relations_Oequivp(X27159,X27158) )
      & ( hAPP(X27158,X27162) != hAPP(X27158,X27163)
        | hBOOL(hAPP(hAPP(X27158,X27162),X27163))
        | ~ c_Equiv__Relations_Oequivp(X27159,X27158) )
      & ( ~ hBOOL(hAPP(hAPP(X27164,esk278_1(X27164)),esk279_1(X27164)))
        | hAPP(X27164,esk278_1(X27164)) != hAPP(X27164,esk279_1(X27164))
        | c_Equiv__Relations_Oequivp(X27167,X27164) )
      & ( hBOOL(hAPP(hAPP(X27164,esk278_1(X27164)),esk279_1(X27164)))
        | hAPP(X27164,esk278_1(X27164)) = hAPP(X27164,esk279_1(X27164))
        | c_Equiv__Relations_Oequivp(X27167,X27164) ) ),
    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_equivp__def])])])])])]) ).

fof(i_0_9975,plain,
    ! [X18101,X18102,X18103] :
      ( ~ class_Groups_Ogroup__add(X18103)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18103),X18102),X18101)),X18101) = X18102 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

fof(i_0_9976,plain,
    ! [X18098,X18099,X18100] :
      ( ~ class_Groups_Ogroup__add(X18100)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18100),X18099),X18098)),X18098) = X18099 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(i_0_9977,plain,
    ! [X31666,X31667,X31668] :
      ( ~ class_Orderings_Olinorder(X31668)
      | c_List_Olinorder__class_Osort__key(X31667,X31668,X31666,c_List_Olist_ONil(X31667)) = c_List_Olist_ONil(X31667) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])]) ).

fof(i_0_9978,plain,
    ! [X27731,X27732,X27733] : hAPP(c_Set_Oimage(tc_prod(X27733,X27732),X27733,c_Product__Type_Ofst(X27733,X27732)),X27731) = hAPP(c_Relation_ODomain(X27733,X27732),X27731),
    inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).

fof(i_0_9979,plain,
    ! [X27653,X27654,X27655] : hAPP(c_Set_Oimage(tc_prod(X27655,X27654),X27654,c_Product__Type_Osnd(X27655,X27654)),X27653) = hAPP(c_Relation_ORange(X27655,X27654),X27653),
    inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).

fof(i_0_9980,plain,
    ! [X29330,X29331,X29332] :
      ( ( ~ c_Relation_Ototal__on(X29332,X29331,hAPP(c_Relation_Oconverse(X29332,X29332),X29330))
        | c_Relation_Ototal__on(X29332,X29331,X29330) )
      & ( ~ c_Relation_Ototal__on(X29332,X29331,X29330)
        | c_Relation_Ototal__on(X29332,X29331,hAPP(c_Relation_Oconverse(X29332,X29332),X29330)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).

fof(i_0_9981,plain,
    ! [X29132,X29133,X29134] :
      ( ( ~ c_Relation_Orefl__on(X29134,X29133,hAPP(c_Relation_Oconverse(X29134,X29134),X29132))
        | c_Relation_Orefl__on(X29134,X29133,X29132) )
      & ( ~ c_Relation_Orefl__on(X29134,X29133,X29132)
        | c_Relation_Orefl__on(X29134,X29133,hAPP(c_Relation_Oconverse(X29134,X29134),X29132)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).

fof(i_0_9982,plain,
    ! [X25842,X25843,X25844] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X25844,X25843,X25842)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X25842)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I11_J]) ).

fof(i_0_9983,plain,
    ! [X23996] :
      ( ~ c_Nat__Transfer_Onat__set(X23996)
      | hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X23996) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23996)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).

fof(i_0_9984,plain,
    ! [X23992,X23993] :
      ( ~ c_Nat__Transfer_Onat__set(X23993)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23992),X23993))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).

fof(i_0_9985,plain,
    ! [X23985,X23986,X23987] :
      ( ( ~ c_Nat__Transfer_Onat__set(X23985)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23986),X23985))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23986)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk163_1(X23987)),X23987))
        | c_Nat__Transfer_Onat__set(X23987) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk163_1(X23987)))
        | c_Nat__Transfer_Onat__set(X23987) ) ),
    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_nat__set__def])])])])])]) ).

fof(i_0_9986,plain,
    ! [X28190] : c_Relation_Orefl__on(X28190,c_Orderings_Obot__class_Obot(tc_fun(X28190,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28190,X28190),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).

fof(i_0_9987,plain,
    ! [X20034,X20035] : hAPP(c_Finite__Set_Ocard(X20035),X20034) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20035,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X20035),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20034),
    inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).

fof(i_0_9988,plain,
    ! [X26852,X26853,X26854,X26855] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26855,X26854),X26853))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26855,X26854),X26852))
      | X26853 = X26852 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).

fof(i_0_9989,plain,
    ! [X18681,X18682] :
      ( ~ class_Groups_Oordered__ab__group__add(X18682)
      | c_Fun_Oinj__on(X18682,X18682,c_Groups_Ouminus__class_Ouminus(X18682),X18681) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).

fof(i_0_9990,plain,
    ! [X31350,X31351] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X31351,X31350) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X31351),hAPP(c_Code__Numeral_Onat__of,X31350))),
    inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(i_0_9991,plain,
    ! [X29774,X29775,X29776] : hAPP(hAPP(c_List_Onth(X29776),hAPP(hAPP(c_List_Olist_OCons(X29776),X29775),X29774)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X29775,
    inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).

fof(i_0_9992,plain,
    ! [X33463,X33464] :
      ( ( hBOOL(hAPP(hAPP(X33463,esk526_2(X33463,X33464)),esk526_2(X33463,X33464)))
        | ~ c_Equiv__Relations_Opart__equivp(X33464,X33463) )
      & ( c_Predicate_Osymp(X33464,X33463)
        | ~ c_Equiv__Relations_Opart__equivp(X33464,X33463) )
      & ( c_Predicate_Otransp(X33464,X33463)
        | ~ c_Equiv__Relations_Opart__equivp(X33464,X33463) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5969])])])]) ).

fof(i_0_9993,plain,
    ! [X33434,X33435,X33437,X33438,X33439] :
      ( ( hBOOL(hAPP(hAPP(X33434,esk522_2(X33434,X33435)),esk522_2(X33434,X33435)))
        | ~ c_Equiv__Relations_Opart__equivp(X33435,X33434) )
      & ( c_Predicate_Osymp(X33435,X33434)
        | ~ c_Equiv__Relations_Opart__equivp(X33435,X33434) )
      & ( c_Predicate_Otransp(X33435,X33434)
        | ~ c_Equiv__Relations_Opart__equivp(X33435,X33434) )
      & ( ~ hBOOL(hAPP(hAPP(X33437,X33439),X33439))
        | ~ c_Predicate_Osymp(X33438,X33437)
        | ~ c_Predicate_Otransp(X33438,X33437)
        | c_Equiv__Relations_Opart__equivp(X33438,X33437) ) ),
    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_part__equivp__refl__symp__transp])])])])])]) ).

fof(i_0_9994,plain,
    ! [X17136,X17137,X17138,X17139] :
      ( ( hAPP(c_Set_Oimage(X17139,X17138,X17137),X17136) != c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool))
        | X17136 = c_Orderings_Obot__class_Obot(tc_fun(X17139,tc_HOL_Obool)) )
      & ( X17136 != c_Orderings_Obot__class_Obot(tc_fun(X17139,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17139,X17138,X17137),X17136) = c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).

fof(i_0_9995,plain,
    ! [X17143,X17144,X17145,X17146] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X17146,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X17145,X17146,X17144),X17143)
        | X17143 = c_Orderings_Obot__class_Obot(tc_fun(X17145,tc_HOL_Obool)) )
      & ( X17143 != c_Orderings_Obot__class_Obot(tc_fun(X17145,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X17146,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X17145,X17146,X17144),X17143) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).

fof(i_0_9996,plain,
    ! [X30220,X30221] : c_List_Olistrelp(X30221,X30220,c_List_Olist_ONil(X30221),c_List_Olist_ONil(X30221)),
    inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).

fof(i_0_9997,plain,
    ! [X30218,X30219] : c_List_Olistrelp(X30219,X30218,c_List_Olist_ONil(X30219),c_List_Olist_ONil(X30219)),
    inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(i_0_9998,plain,
    ! [X31171,X31172,X31173,X31174] :
      ( X31174 = c_List_Olist_ONil(X31173)
      | hAPP(c_List_Ohd(X31172),hAPP(hAPP(c_List_Omap(X31173,X31172),X31171),X31174)) = hAPP(X31171,hAPP(c_List_Ohd(X31173),X31174)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).

fof(i_0_9999,plain,
    ! [X23157,X23158,X23159] :
      ( ~ class_Rings_Osemiring__1(X23159)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X23159,X23158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23157) = X23157 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).

fof(i_0_10000,plain,
    ! [X24162,X24163,X24164,X24165] :
      ( ( X24164 = X24163
        | c_SetInterval_Oord__class_OatLeastAtMost(X24165,X24164,X24163) != hAPP(hAPP(c_Set_Oinsert(X24165),X24162),c_Orderings_Obot__class_Obot(tc_fun(X24165,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24165) )
      & ( X24163 = X24162
        | c_SetInterval_Oord__class_OatLeastAtMost(X24165,X24164,X24163) != hAPP(hAPP(c_Set_Oinsert(X24165),X24162),c_Orderings_Obot__class_Obot(tc_fun(X24165,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24165) )
      & ( X24164 != X24163
        | X24163 != X24162
        | c_SetInterval_Oord__class_OatLeastAtMost(X24165,X24164,X24163) = hAPP(hAPP(c_Set_Oinsert(X24165),X24162),c_Orderings_Obot__class_Obot(tc_fun(X24165,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24165) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).

fof(i_0_10001,plain,
    ! [X32785,X32786,X32787,X32788,X32789] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X32789),X32788),X32787),X32786),X32785) = c_New__DSequence_Opos__single(X32789,X32788),
    inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).

fof(i_0_10002,plain,
    ! [X32766,X32767,X32768,X32769,X32770] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X32770),X32769),X32768),X32767),X32766) = c_New__DSequence_Oneg__single(X32770,X32769),
    inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).

fof(i_0_10003,plain,
    ! [X24976,X24977,X24978] :
      ( ~ class_Rings_Olinordered__idom(X24978)
      | hAPP(c_Groups_Oabs__class_Oabs(X24978),hAPP(hAPP(c_Power_Opower__class_Opower(X24978),X24977),X24976)) = hAPP(hAPP(c_Power_Opower__class_Opower(X24978),hAPP(c_Groups_Oabs__class_Oabs(X24978),X24977)),X24976) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).

fof(i_0_10004,plain,
    ! [X23585,X23586,X23587] :
      ( ~ class_Rings_Odivision__ring(X23587)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X23587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23587),X23586),X23585)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23587),hAPP(c_Groups_Ouminus__class_Ouminus(X23587),X23586)),X23585) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_10005,plain,
    ! [X18981,X18982,X18983] :
      ( ~ class_Rings_Oring(X18983)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18983),X18982),X18981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18983),hAPP(c_Groups_Ouminus__class_Ouminus(X18983),X18982)),X18981) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_10006,plain,
    ! [X22196,X22197,X22198,X22199] : hAPP(hAPP(c_Power_Opower_Opower(X22199,X22198,X22197),X22196),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22198,
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(i_0_10007,plain,
    ! [X33974,X33975,X33976] : c_Lazy__Sequence_Omap(X33976,X33975,X33974,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33976)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X33975),
    inference(variable_rename,[status(thm)],[fact__07]) ).

fof(i_0_10008,plain,
    ! [X32432,X32433,X32434] : c_List_Omaps(X32434,X32433,X32432,c_List_Olist_ONil(X32434)) = c_List_Olist_ONil(X32433),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).

cnf(i_0_10009,plain,
    ( X1 = X2
    | c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5970]) ).

fof(i_0_10010,plain,
    ! [X24151,X24152,X24153] :
      ( ~ class_Orderings_Oorder(X24153)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24153),X24152),X24151))
      | c_SetInterval_Oord__class_OatLeastAtMost(X24153,X24151,X24152) = c_Orderings_Obot__class_Obot(tc_fun(X24153,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).

fof(i_0_10011,plain,
    ! [X23459,X23460,X23461] :
      ( ~ class_Orderings_Oorder(X23461)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23461),X23460),X23459))
      | c_SetInterval_Oord__class_OgreaterThanAtMost(X23461,X23459,X23460) = c_Orderings_Obot__class_Obot(tc_fun(X23461,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).

fof(i_0_10012,plain,
    ! [X23334,X23335,X23336] :
      ( ~ class_Orderings_Oorder(X23336)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23336),X23335),X23334))
      | c_SetInterval_Oord__class_OgreaterThanLessThan(X23336,X23334,X23335) = c_Orderings_Obot__class_Obot(tc_fun(X23336,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).

fof(i_0_10013,plain,
    ! [X34129] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34129),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X34129 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X34129 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34129),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).

fof(i_0_10014,plain,
    ! [X30768,X30769,X30770] :
      ( X30770 = c_List_Olist_ONil(X30769)
      | hAPP(c_List_Otl(X30769),hAPP(hAPP(c_List_Oappend(X30769),X30770),X30768)) = hAPP(hAPP(c_List_Oappend(X30769),hAPP(c_List_Otl(X30769),X30770)),X30768) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).

fof(i_0_10015,plain,
    ! [X24746,X24747] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24747,X24746)),X24746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(i_0_10016,plain,
    ! [X27004,X27005,X27006,X27007] :
      ( hAPP(c_Product__Type_Ofst(X27007,X27006),X27005) != hAPP(c_Product__Type_Ofst(X27007,X27006),X27004)
      | hAPP(c_Product__Type_Osnd(X27007,X27006),X27005) != hAPP(c_Product__Type_Osnd(X27007,X27006),X27004)
      | X27005 = X27004 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).

fof(i_0_10017,plain,
    ! [X27000,X27001,X27002,X27003] :
      ( ( hAPP(c_Product__Type_Ofst(X27001,X27000),X27003) = hAPP(c_Product__Type_Ofst(X27001,X27000),X27002)
        | X27003 != X27002 )
      & ( hAPP(c_Product__Type_Osnd(X27001,X27000),X27003) = hAPP(c_Product__Type_Osnd(X27001,X27000),X27002)
        | X27003 != X27002 )
      & ( hAPP(c_Product__Type_Ofst(X27001,X27000),X27003) != hAPP(c_Product__Type_Ofst(X27001,X27000),X27002)
        | hAPP(c_Product__Type_Osnd(X27001,X27000),X27003) != hAPP(c_Product__Type_Osnd(X27001,X27000),X27002)
        | X27003 = X27002 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).

fof(i_0_10018,plain,
    ! [X28021,X28022] : c_Fun_Oinj__on(X28022,X28022,c_Fun_Oid(X28022),X28021),
    inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).

fof(i_0_10019,plain,
    ! [X17684,X17685] : c_Fun_Oinj__on(X17685,X17685,c_COMBI(X17685),X17684),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_10020,plain,
    ! [X24859,X24860,X24861] :
      ( ~ class_Rings_Olinordered__idom(X24861)
      | c_Groups_Osgn__class_Osgn(X24861,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24861),X24860),X24859)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24861),c_Groups_Osgn__class_Osgn(X24861,X24860)),c_Groups_Osgn__class_Osgn(X24861,X24859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_10021,plain,
    ! [X32046,X32047,X32048] :
      ( ~ class_Orderings_Olinorder(X32048)
      | ~ c_List_Olinorder__class_Osorted(X32048,X32047)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32048),X32047))
      | ~ c_List_Olinorder__class_Osorted(X32048,X32046)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32048),X32046))
      | hAPP(c_List_Oset(X32048),X32047) != hAPP(c_List_Oset(X32048),X32046)
      | X32047 = X32046 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).

fof(i_0_10022,plain,
    ! [X30585,X30586,X30587,X30588] : hAPP(hAPP(c_List_Odrop(X30588),hAPP(c_Nat_OSuc,X30587)),hAPP(hAPP(c_List_Olist_OCons(X30588),X30586),X30585)) = hAPP(hAPP(c_List_Odrop(X30588),X30587),X30585),
    inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).

cnf(i_0_10023,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(split_conjunct,[status(thm)],[fact_less__than__def]) ).

fof(i_0_10024,plain,
    ! [X24963,X24964,X24965] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24965)
      | hAPP(c_Groups_Oabs__class_Oabs(X24965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24965),X24964),X24963)) = hAPP(c_Groups_Oabs__class_Oabs(X24965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24965),X24963),X24964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

cnf(i_0_10025,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_5971]) ).

fof(i_0_10026,plain,
    ! [X33173,X33174,X33175] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X33175,X33174,X33173,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X33174,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(i_0_10027,plain,
    ! [X27331,X27332,X27333] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X27333,X27332,X27331,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X27332,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(i_0_10028,plain,
    ! [X24525,X24526,X24527] : c_Nat_Onat_Onat__case(X24527,X24526,X24525,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24526,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_10029,plain,
    ! [X23457,X23458] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23458)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23457)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23458),X23457)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10030,plain,
    ! [X25867,X25868] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25868)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25867)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25868),X25867)),
    inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(i_0_10031,plain,
    ! [X22980,X22981] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22981)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22980)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22981),X22980)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10032,plain,
    ! [X22880,X22881] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22881)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22880)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22881),X22880)),
    inference(variable_rename,[status(thm)],[fact_zmult__int]) ).

fof(i_0_10033,plain,
    ! [X25869,X25870] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25870)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25869)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25870),X25869)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(i_0_10034,plain,
    ! [X23167,X23168] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23168)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23167)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23168),X23167)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10035,plain,
    ! [X22871,X22872] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22872)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22871)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22872),X22871)),
    inference(variable_rename,[status(thm)],[fact_zadd__int]) ).

fof(i_0_10036,plain,
    ! [X23455,X23456] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23456),X23455)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23455)),
    inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).

fof(i_0_10037,plain,
    ! [X22878,X22879] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22879),X22878)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22879)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22878)),
    inference(variable_rename,[status(thm)],[fact_int__mult]) ).

cnf(i_0_10038,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X1)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5972]) ).

fof(i_0_10039,plain,
    ! [X23042,X23043] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23043),X23042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23043)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23042)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_10040,plain,
    ! [X32939,X32940,X32941,X32942] :
      ( ( ~ hBOOL(hAPP(X32942,X32941))
        | hAPP(c_List_Ofilter(X32940,X32942),c_List_Oreplicate(X32940,X32939,X32941)) = c_List_Oreplicate(X32940,X32939,X32941) )
      & ( hBOOL(hAPP(X32942,X32941))
        | hAPP(c_List_Ofilter(X32940,X32942),c_List_Oreplicate(X32940,X32939,X32941)) = c_List_Olist_ONil(X32940) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5973])]) ).

fof(i_0_10041,plain,
    ! [X20774,X20775] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20775,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20775,tc_HOL_Obool))),X20774) = X20774,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).

fof(i_0_10042,plain,
    ! [X19579,X19580] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19580,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X19580,tc_HOL_Obool))),X19579) = X19579,
    inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).

fof(i_0_10043,plain,
    ! [X22823,X22824] :
      ( ( X22824 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22824),X22823) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22824)) )
      & ( X22823 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22824),X22823) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22824)) )
      & ( X22824 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X22823 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22824),X22823) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22824)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).

cnf(i_0_10044,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).

fof(i_0_10045,plain,
    ! [X19087,X19088,X19089] : hAPP(c_Finite__Set_Ofold1(X19089,X19088),hAPP(hAPP(c_Set_Oinsert(X19089),X19087),c_Orderings_Obot__class_Obot(tc_fun(X19089,tc_HOL_Obool)))) = X19087,
    inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).

fof(i_0_10046,plain,
    ! [X31109,X31110,X31111,X31112] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31112)),hAPP(hAPP(c_List_Omap(X31111,X31112),X31110),X31109)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31111)),X31109),
    inference(variable_rename,[status(thm)],[fact_length__map]) ).

fof(i_0_10047,plain,
    ! [X30024,X30025,X30026,X30027] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30027)),hAPP(hAPP(c_List_Olist__update(X30027,X30026),X30025),X30024)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30027)),X30026),
    inference(variable_rename,[status(thm)],[fact_length__list__update]) ).

fof(i_0_10048,plain,
    ! [X24066,X24067,X24068] :
      ( ~ class_Rings_Oring__1(X24068)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24068),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24067),X24066)) = hAPP(hAPP(c_Power_Opower__class_Opower(X24068),hAPP(c_Int_Oring__1__class_Oof__int(X24068),X24067)),X24066) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).

fof(i_0_10049,plain,
    ! [X22924,X22925,X22926] :
      ( ~ class_Rings_Osemiring__1(X22926)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22926),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22925),X22924)) = hAPP(hAPP(c_Power_Opower__class_Opower(X22926),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22926),X22925)),X22924) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).

fof(i_0_10050,plain,
    ! [X23051,X23052] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23052),X23051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23052),X23051)) )
      & ( X23052 != X23051
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23052),X23051)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23052),X23051))
        | X23052 = X23051
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23052),X23051)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_10051,plain,
    ! [X20042,X20043] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20043),X20042))
      | X20043 = X20042
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20043),X20042)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_10052,plain,
    ! [X20038,X20039] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20039),X20038))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20039),X20038))
        | X20039 = X20038 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20039),X20038))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20039),X20038)) )
      & ( X20039 != X20038
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20039),X20038)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_10053,plain,
    ! [X20036,X20037] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20037),X20036))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20037),X20036)) )
      & ( X20037 != X20036
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20037),X20036)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20037),X20036))
        | X20037 = X20036
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20037),X20036)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

cnf(i_0_10054,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(X1)) = X1
    | ~ c_List_Onat__list(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5974]) ).

fof(i_0_10055,plain,
    ! [X19083,X19084,X19085,X19086] :
      ( X19086 != c_Finite__Set_Ofold1(X19085,X19084)
      | hAPP(X19086,hAPP(hAPP(c_Set_Oinsert(X19085),X19083),c_Orderings_Obot__class_Obot(tc_fun(X19085,tc_HOL_Obool)))) = X19083 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).

fof(i_0_10056,plain,
    ! [X30792,X30793] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30793)),hAPP(c_List_Otl(X30793),X30792)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30793)),X30792)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__tl]) ).

fof(i_0_10057,plain,
    ! [X17477,X17478,X17479,X17480,X17481] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17481,X17480,X17479)
      | hAPP(hAPP(X17479,X17478),hAPP(hAPP(X17479,X17478),X17477)) = hAPP(hAPP(X17479,X17478),X17477) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).

fof(i_0_10058,plain,
    ! [X23989] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23989)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(i_0_10059,plain,
    ! [X24278,X24279] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24279,X24278))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(i_0_10060,plain,
    ! [X23439,X23440] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23440,X23439))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(i_0_10061,plain,
    ! [X23292,X23293] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X23293,X23292))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(i_0_10062,plain,
    ! [X24125,X24126] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24126,X24125))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(i_0_10063,plain,
    ! [X23437,X23438] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23438,X23437))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(i_0_10064,plain,
    ! [X23290,X23291] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X23291,X23290))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(i_0_10065,plain,
    ! [X22456] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22456),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X22456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22456 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22456),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).

fof(i_0_10066,plain,
    ! [X21755] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X21755),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_10067,plain,
    ! [X20304,X20305] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20305),X20304))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20305),X20304)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_10068,plain,
    ! [X20044,X20045] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20045),X20044))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20045),X20044)) )
      & ( X20045 != X20044
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20045),X20044)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_10069,plain,
    ! [X20040,X20041] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20041),X20040))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20041),X20040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_10070,plain,
    ! [X23109,X23110,X23111] :
      ( ~ class_Orderings_Oorder(X23111)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23111),X23110),X23109))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23111,X23109),X23110) = c_Orderings_Obot__class_Obot(tc_fun(X23111,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).

fof(i_0_10071,plain,
    ! [X17209,X17210,X17211] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17211),X17210),hAPP(c_fequal,X17209)))
        | X17210 = X17209 )
      & ( X17210 != X17209
        | hBOOL(hAPP(hAPP(c_member(X17211),X17210),hAPP(c_fequal,X17209))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_10072,plain,
    ! [X31015,X31016,X31017,X31018] :
      ( X31018 = c_List_Olist_ONil(X31017)
      | c_List_Olast(X31016,hAPP(hAPP(c_List_Omap(X31017,X31016),X31015),X31018)) = hAPP(X31015,c_List_Olast(X31017,X31018)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).

cnf(i_0_10073,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5975]) ).

fof(i_0_10074,plain,
    ! [X18975,X18976,X18977] :
      ( ~ class_Groups_Ogroup__add(X18977)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18977),hAPP(c_Groups_Ouminus__class_Ouminus(X18977),X18976)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18977),X18976),X18975)) = X18975 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_10075,plain,
    ! [X17065,X17066,X17067,X17068,X17069] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17066),X17067),X17065))
        | X17065 != c_Orderings_Obot__class_Obot(tc_fun(X17066,tc_HOL_Obool)) )
      & ( X17068 = c_Orderings_Obot__class_Obot(tc_fun(X17069,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X17069),esk2_2(X17068,X17069)),X17068)) ) ),
    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_ex__in__conv])])])])]) ).

fof(i_0_10076,plain,
    ! [X17071,X17072,X17074,X17075,X17076] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17072),esk3_2(X17071,X17072)),X17071))
        | X17071 = c_Orderings_Obot__class_Obot(tc_fun(X17072,tc_HOL_Obool)) )
      & ( X17074 != c_Orderings_Obot__class_Obot(tc_fun(X17075,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X17075),X17076),X17074)) ) ),
    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_5976])])])])]) ).

fof(i_0_10077,plain,
    ! [X30249,X30250,X30251] :
      ( hBOOL(hAPP(hAPP(c_member(X30251),X30250),hAPP(c_List_Oset(X30251),X30249)))
      | c_List_Oremove1(X30251,X30250,X30249) = X30249 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5977])]) ).

cnf(i_0_10078,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_5978]) ).

fof(i_0_10079,plain,
    ! [X24094,X24095] :
      ( ~ class_Rings_Oring__1(X24095)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24094))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24095),hAPP(c_Int_Onat,X24094)) = hAPP(c_Int_Oring__1__class_Oof__int(X24095),X24094) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).

fof(i_0_10080,plain,
    ! [X24882,X24883] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24883),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24882)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24883,X24882)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10081,plain,
    ! [X24703,X24704] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24704),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24703)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24704,X24703)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(i_0_10082,plain,
    ! [X24884,X24885] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24885,X24884)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24885),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24884)),
    inference(variable_rename,[status(thm)],[fact_zmod__int]) ).

fof(i_0_10083,plain,
    ! [X24840,X24841] :
      ( ( X24840 != c_Groups_Ozero__class_Ozero(X24841)
        | c_Groups_Osgn__class_Osgn(X24841,X24840) = c_Groups_Ozero__class_Ozero(X24841)
        | ~ class_Groups_Osgn__if(X24841) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24841),c_Groups_Ozero__class_Ozero(X24841)),X24840))
        | c_Groups_Osgn__class_Osgn(X24841,X24840) = c_Groups_Oone__class_Oone(X24841)
        | X24840 = c_Groups_Ozero__class_Ozero(X24841)
        | ~ class_Groups_Osgn__if(X24841) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24841),c_Groups_Ozero__class_Ozero(X24841)),X24840))
        | c_Groups_Osgn__class_Osgn(X24841,X24840) = hAPP(c_Groups_Ouminus__class_Ouminus(X24841),c_Groups_Oone__class_Oone(X24841))
        | X24840 = c_Groups_Ozero__class_Ozero(X24841)
        | ~ class_Groups_Osgn__if(X24841) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5979])])]) ).

fof(i_0_10084,plain,
    ! [X30157,X30158] :
      ( ~ class_Groups_Ocomm__monoid__add(X30158)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30158),X30157))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30158),X30157) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30158,X30158),c_COMBI(X30158)),hAPP(c_List_Oset(X30158),X30157)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).

fof(i_0_10085,plain,
    ! [X21759,X21760,X21761] :
      ( ~ class_Rings_Ocomm__semiring__1(X21761)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21760),hAPP(hAPP(c_Power_Opower__class_Opower(X21761),X21760),X21759)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21761),X21760),hAPP(c_Nat_OSuc,X21759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).

fof(i_0_10086,plain,
    ! [X21768,X21769,X21770] :
      ( ~ class_Power_Opower(X21770)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21770),X21769),hAPP(c_Nat_OSuc,X21768)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21770),X21769),hAPP(hAPP(c_Power_Opower__class_Opower(X21770),X21769),X21768)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).

fof(i_0_10087,plain,
    ! [X21756,X21757,X21758] :
      ( ~ class_Rings_Ocomm__semiring__1(X21758)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21758),X21757),hAPP(c_Nat_OSuc,X21756)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21758),X21757),hAPP(hAPP(c_Power_Opower__class_Opower(X21758),X21757),X21756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).

fof(i_0_10088,plain,
    ! [X24287,X24288] :
      ( ~ class_Groups_Oordered__ab__group__add(X24288)
      | hAPP(c_Set_Oimage(X24288,X24288,c_Groups_Ouminus__class_Ouminus(X24288)),hAPP(c_SetInterval_Oord__class_OatMost(X24288),X24287)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24288),hAPP(c_Groups_Ouminus__class_Ouminus(X24288),X24287)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).

fof(i_0_10089,plain,
    ! [X24289,X24290] :
      ( ~ class_Groups_Oordered__ab__group__add(X24290)
      | hAPP(c_Set_Oimage(X24290,X24290,c_Groups_Ouminus__class_Ouminus(X24290)),hAPP(c_SetInterval_Oord__class_OatLeast(X24290),X24289)) = hAPP(c_SetInterval_Oord__class_OatMost(X24290),hAPP(c_Groups_Ouminus__class_Ouminus(X24290),X24289)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).

fof(i_0_10090,plain,
    ! [X24101,X24102] :
      ( ~ class_Groups_Oordered__ab__group__add(X24102)
      | hAPP(c_Set_Oimage(X24102,X24102,c_Groups_Ouminus__class_Ouminus(X24102)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24102),X24101)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24102),hAPP(c_Groups_Ouminus__class_Ouminus(X24102),X24101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).

fof(i_0_10091,plain,
    ! [X24099,X24100] :
      ( ~ class_Groups_Oordered__ab__group__add(X24100)
      | hAPP(c_Set_Oimage(X24100,X24100,c_Groups_Ouminus__class_Ouminus(X24100)),hAPP(c_SetInterval_Oord__class_OlessThan(X24100),X24099)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24100),hAPP(c_Groups_Ouminus__class_Ouminus(X24100),X24099)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).

fof(i_0_10092,plain,
    ! [X32876,X32877,X32878] : c_List_Oreplicate(X32878,hAPP(c_Nat_OSuc,X32877),X32876) = hAPP(hAPP(c_List_Olist_OCons(X32878),X32876),c_List_Oreplicate(X32878,X32877,X32876)),
    inference(variable_rename,[status(thm)],[fact_replicate__Suc]) ).

cnf(i_0_10093,plain,
    ( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5980]) ).

cnf(i_0_10094,plain,
    ( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5981]) ).

cnf(i_0_10095,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
    | c_List_Oupt(X1,X2) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5981]) ).

fof(i_0_10096,plain,
    ! [X24834,X24835] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24835))
        | c_SMT_Oz3mod(X24834,X24835) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X24834,X24835) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24835))
        | c_SMT_Oz3mod(X24834,X24835) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X24834,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24835)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5982])]) ).

fof(i_0_10097,plain,
    ! [X32971,X32972,X32973] :
      ( ( X32973 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X32972),c_List_Oreplicate(X32972,X32973,X32971)) = c_Orderings_Obot__class_Obot(tc_fun(X32972,tc_HOL_Obool)) )
      & ( X32973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X32972),c_List_Oreplicate(X32972,X32973,X32971)) = hAPP(hAPP(c_Set_Oinsert(X32972),X32971),c_Orderings_Obot__class_Obot(tc_fun(X32972,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate__conv__if])]) ).

fof(i_0_10098,plain,
    ! [X32968,X32969,X32970] :
      ( X32970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Oset(X32969),c_List_Oreplicate(X32969,X32970,X32968)) = hAPP(hAPP(c_Set_Oinsert(X32969),X32968),c_Orderings_Obot__class_Obot(tc_fun(X32969,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate])]) ).

fof(i_0_10099,plain,
    ! [X25042,X25043] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25043)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25043),c_Groups_Ozero__class_Ozero(X25043)),X25042))
      | hAPP(c_Groups_Oabs__class_Oabs(X25043),X25042) = X25042 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(i_0_10100,plain,
    ! [X25040,X25041] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25041)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25041),c_Groups_Ozero__class_Ozero(X25041)),X25040))
      | hAPP(c_Groups_Oabs__class_Oabs(X25041),X25040) = X25040 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

fof(i_0_10101,plain,
    ! [X25143,X25144] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25144),X25143),c_Groups_Ozero__class_Ozero(X25144)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25144),X25143) = hAPP(c_Groups_Ouminus__class_Ouminus(X25144),X25143)
        | ~ class_Groups_Oabs__if(X25144) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25144),X25143),c_Groups_Ozero__class_Ozero(X25144)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25144),X25143) = X25143
        | ~ class_Groups_Oabs__if(X25144) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5983])])]) ).

fof(i_0_10102,plain,
    ! [X25145,X25146] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25146)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25146),X25145),c_Groups_Ozero__class_Ozero(X25146)))
      | hAPP(c_Groups_Oabs__class_Oabs(X25146),X25145) = hAPP(c_Groups_Ouminus__class_Ouminus(X25146),X25145) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_10103,plain,
    ! [X25139,X25140] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25140)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25140),X25139),c_Groups_Ozero__class_Ozero(X25140)))
      | hAPP(c_Groups_Oabs__class_Oabs(X25140),X25139) = hAPP(c_Groups_Ouminus__class_Ouminus(X25140),X25139) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

fof(i_0_10104,plain,
    ! [X24838,X24839] :
      ( ( c_Groups_Osgn__class_Osgn(X24839,X24838) != hAPP(c_Groups_Ouminus__class_Ouminus(X24839),c_Groups_Oone__class_Oone(X24839))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24839),X24838),c_Groups_Ozero__class_Ozero(X24839)))
        | ~ class_Rings_Olinordered__idom(X24839) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24839),X24838),c_Groups_Ozero__class_Ozero(X24839)))
        | c_Groups_Osgn__class_Osgn(X24839,X24838) = hAPP(c_Groups_Ouminus__class_Ouminus(X24839),c_Groups_Oone__class_Oone(X24839))
        | ~ class_Rings_Olinordered__idom(X24839) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_10105,plain,
    ! [X24836,X24837] :
      ( ~ class_Rings_Olinordered__idom(X24837)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24837),X24836),c_Groups_Ozero__class_Ozero(X24837)))
      | c_Groups_Osgn__class_Osgn(X24837,X24836) = hAPP(c_Groups_Ouminus__class_Ouminus(X24837),c_Groups_Oone__class_Oone(X24837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_10106,plain,
    ! [X33447,X33448,X33449,X33450] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33450,X33449)
      | ~ hBOOL(hAPP(hAPP(X33449,X33448),X33447))
      | hBOOL(hAPP(hAPP(X33449,X33447),X33448)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__symp])]) ).

fof(i_0_10107,plain,
    ! [X33328,X33329,X33330,X33331] :
      ( ~ c_Predicate_Osymp(X33331,X33330)
      | ~ hBOOL(hAPP(hAPP(X33330,X33329),X33328))
      | hBOOL(hAPP(hAPP(X33330,X33328),X33329)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sympE])]) ).

fof(i_0_10108,plain,
    ! [X27171,X27172,X27173,X27174] :
      ( ~ c_Equiv__Relations_Oequivp(X27174,X27173)
      | ~ hBOOL(hAPP(hAPP(X27173,X27172),X27171))
      | hBOOL(hAPP(hAPP(X27173,X27171),X27172)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).

fof(i_0_10109,plain,
    ! [X34133,X34134,X34135] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34135),X34134),X34133))
        | c_Divides_Odiv__class_Omod(X34135,X34133,X34134) = c_Groups_Ozero__class_Ozero(X34135)
        | ~ class_Divides_Osemiring__div(X34135) )
      & ( c_Divides_Odiv__class_Omod(X34135,X34133,X34134) != c_Groups_Ozero__class_Ozero(X34135)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34135),X34134),X34133))
        | ~ class_Divides_Osemiring__div(X34135) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).

fof(i_0_10110,plain,
    ! [X34130,X34131,X34132] :
      ( ~ class_Divides_Osemiring__div(X34132)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34132),X34131),X34130))
      | c_Divides_Odiv__class_Omod(X34132,X34130,X34131) = c_Groups_Ozero__class_Ozero(X34132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).

fof(i_0_10111,plain,
    ! [X30098,X30099] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30099)),c_List_Obutlast(X30099,X30098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30099)),X30098)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__butlast]) ).

fof(i_0_10112,plain,
    ! [X22384] :
      ( ~ class_Rings_Olinordered__semidom(X22384)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22384),c_Groups_Oone__class_Oone(X22384)),c_Groups_Ozero__class_Ozero(X22384))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5984])]) ).

fof(i_0_10113,plain,
    ! [X22382] :
      ( ~ class_Rings_Olinordered__semidom(X22382)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22382),c_Groups_Oone__class_Oone(X22382)),c_Groups_Ozero__class_Ozero(X22382))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5985])]) ).

fof(i_0_10114,plain,
    ! [X19885,X19886] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19886),X19885))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19886),X19885)) = X19886 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5986])]) ).

fof(i_0_10115,plain,
    ! [X30173,X30174] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30174)),c_List_Olist_ONil(X30174)),c_List_Olists(X30174,X30173))),
    inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).

fof(i_0_10116,plain,
    ! [X24932,X24933] :
      ( ( c_Groups_Osgn__class_Osgn(X24933,X24932) != c_Groups_Oone__class_Oone(X24933)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24933),c_Groups_Ozero__class_Ozero(X24933)),X24932))
        | ~ class_Rings_Olinordered__idom(X24933) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24933),c_Groups_Ozero__class_Ozero(X24933)),X24932))
        | c_Groups_Osgn__class_Osgn(X24933,X24932) = c_Groups_Oone__class_Oone(X24933)
        | ~ class_Rings_Olinordered__idom(X24933) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).

fof(i_0_10117,plain,
    ! [X24930,X24931] :
      ( ~ class_Rings_Olinordered__idom(X24931)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24931),c_Groups_Ozero__class_Ozero(X24931)),X24930))
      | c_Groups_Osgn__class_Osgn(X24931,X24930) = c_Groups_Oone__class_Oone(X24931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_10118,plain,
    ! [X23630,X23631,X23632] :
      ( ~ class_Rings_Odivision__ring(X23632)
      | X23631 = c_Groups_Ozero__class_Ozero(X23632)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23632),hAPP(c_Groups_Ouminus__class_Ouminus(X23632),X23630)),hAPP(c_Groups_Ouminus__class_Ouminus(X23632),X23631)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23632),X23630),X23631) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_10119,plain,
    ! [X30315] : c_List_Olistset(X30315,c_List_Olist_ONil(tc_fun(X30315,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30315)),c_List_Olist_ONil(X30315)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30315),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(i_0_10120,plain,
    ! [X30296] : c_List_Olists(X30296,c_Orderings_Obot__class_Obot(tc_fun(X30296,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30296)),c_List_Olist_ONil(X30296)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30296),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_lists__empty]) ).

fof(i_0_10121,plain,
    ! [X25267,X25268,X25269] :
      ( ~ hBOOL(hAPP(X25269,X25268))
      | hBOOL(hAPP(hAPP(c_member(X25267),X25268),hAPP(c_Set_OCollect(X25267),X25269))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).

fof(i_0_10122,plain,
    ! [X32133,X32134] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X32134),hAPP(c_List_Orev(X32134),X32133)))
        | hBOOL(hAPP(c_List_Odistinct(X32134),X32133)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X32134),X32133))
        | hBOOL(hAPP(c_List_Odistinct(X32134),hAPP(c_List_Orev(X32134),X32133))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])]) ).

fof(i_0_10123,plain,
    ! [X30597,X30598] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30598),hAPP(c_List_Orotate1(X30598),X30597)))
        | hBOOL(hAPP(c_List_Odistinct(X30598),X30597)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30598),X30597))
        | hBOOL(hAPP(c_List_Odistinct(X30598),hAPP(c_List_Orotate1(X30598),X30597))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).

fof(i_0_10124,plain,
    ! [X25484,X25485] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X25485),c_Orderings_Obot__class_Obot(tc_fun(X25485,tc_HOL_Obool))),X25484) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25485,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).

fof(i_0_10125,plain,
    ! [X28034,X28035] : hAPP(c_Product__Type_Oprod_Oprod__case(X28035,X28034,tc_prod(X28035,X28034)),c_Product__Type_OPair(X28035,X28034)) = c_Fun_Oid(tc_prod(X28035,X28034)),
    inference(variable_rename,[status(thm)],[fact_split__Pair]) ).

fof(i_0_10126,plain,
    ! [X20627,X20628,X20629] :
      ( ~ class_Lattices_Osemilattice__inf(X20629)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20629),X20628),X20627))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20629),X20628),X20627) = X20628 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).

fof(i_0_10127,plain,
    ! [X20612,X20613,X20614] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20614),X20613),X20612))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20614),X20613),X20612) = X20613
        | ~ class_Lattices_Osemilattice__inf(X20614) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20614),X20613),X20612) != X20613
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20614),X20613),X20612))
        | ~ class_Lattices_Osemilattice__inf(X20614) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).

fof(i_0_10128,plain,
    ! [X20630,X20631,X20632] :
      ( ~ class_Lattices_Osemilattice__inf(X20632)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20632),X20631),X20630))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20632),X20630),X20631) = X20631 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).

fof(i_0_10129,plain,
    ! [X19528,X19529,X19530] :
      ( ~ class_Lattices_Osemilattice__sup(X19530)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19530),X19529),X19528))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19530),X19529),X19528) = X19528 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).

fof(i_0_10130,plain,
    ! [X19513,X19514,X19515] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19515),X19514),X19513))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19515),X19514),X19513) = X19513
        | ~ class_Lattices_Osemilattice__sup(X19515) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19515),X19514),X19513) != X19513
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19515),X19514),X19513))
        | ~ class_Lattices_Osemilattice__sup(X19515) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).

fof(i_0_10131,plain,
    ! [X19531,X19532,X19533] :
      ( ~ class_Lattices_Osemilattice__sup(X19533)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19533),X19532),X19531))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19533),X19531),X19532) = X19531 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).

fof(i_0_10132,plain,
    ! [X18842,X18843,X18844] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18844),X18843),X18842))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18844),X18843),X18842) = X18842
        | ~ class_Orderings_Olinorder(X18844) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X18844),X18843),X18842) != X18842
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18844),X18843),X18842))
        | ~ class_Orderings_Olinorder(X18844) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).

fof(i_0_10133,plain,
    ! [X18827,X18828,X18829] :
      ( ~ class_Orderings_Olinorder(X18829)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18829),X18828),X18827))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18829),X18828),X18827) = X18827 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).

fof(i_0_10134,plain,
    ! [X18824,X18825,X18826] :
      ( ~ class_Orderings_Olinorder(X18826)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18826),X18825),X18824))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18826),X18824),X18825) = X18824 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).

fof(i_0_10135,plain,
    ! [X18908,X18909,X18910] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18910),X18909),X18908))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18910),X18909),X18908) = X18909
        | ~ class_Orderings_Olinorder(X18910) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X18910),X18909),X18908) != X18909
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18910),X18909),X18908))
        | ~ class_Orderings_Olinorder(X18910) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).

fof(i_0_10136,plain,
    ! [X18893,X18894,X18895] :
      ( ~ class_Orderings_Olinorder(X18895)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18895),X18894),X18893))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18895),X18894),X18893) = X18894 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).

fof(i_0_10137,plain,
    ! [X18890,X18891,X18892] :
      ( ~ class_Orderings_Olinorder(X18892)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18892),X18891),X18890))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18892),X18890),X18891) = X18891 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).

fof(i_0_10138,plain,
    ! [X25157,X25158] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25158)
      | c_Complete__Lattice_OSup__class_OSup(X25158,hAPP(hAPP(c_Set_Oinsert(X25158),X25157),c_Orderings_Obot__class_Obot(tc_fun(X25158,tc_HOL_Obool)))) = X25157 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).

fof(i_0_10139,plain,
    ! [X21907,X21908] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21908)
      | c_Complete__Lattice_OInf__class_OInf(X21908,hAPP(hAPP(c_Set_Oinsert(X21908),X21907),c_Orderings_Obot__class_Obot(tc_fun(X21908,tc_HOL_Obool)))) = X21907 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])]) ).

fof(i_0_10140,plain,
    ! [X21896,X21897] :
      ( ~ class_Lattices_Olattice(X21897)
      | c_Big__Operators_Olattice__class_OInf__fin(X21897,hAPP(hAPP(c_Set_Oinsert(X21897),X21896),c_Orderings_Obot__class_Obot(tc_fun(X21897,tc_HOL_Obool)))) = X21896 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).

fof(i_0_10141,plain,
    ! [X20331,X20332] :
      ( ~ class_Lattices_Olattice(X20332)
      | c_Big__Operators_Olattice__class_OSup__fin(X20332,hAPP(hAPP(c_Set_Oinsert(X20332),X20331),c_Orderings_Obot__class_Obot(tc_fun(X20332,tc_HOL_Obool)))) = X20331 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).

fof(i_0_10142,plain,
    ! [X18496,X18497] :
      ( ~ class_Orderings_Olinorder(X18497)
      | c_Big__Operators_Olinorder__class_OMin(X18497,hAPP(hAPP(c_Set_Oinsert(X18497),X18496),c_Orderings_Obot__class_Obot(tc_fun(X18497,tc_HOL_Obool)))) = X18496 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).

fof(i_0_10143,plain,
    ! [X18498,X18499] :
      ( ~ class_Orderings_Olinorder(X18499)
      | c_Big__Operators_Olinorder__class_OMax(X18499,hAPP(hAPP(c_Set_Oinsert(X18499),X18498),c_Orderings_Obot__class_Obot(tc_fun(X18499,tc_HOL_Obool)))) = X18498 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).

fof(i_0_10144,plain,
    ! [X21829,X21830] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21830)),X21829) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21830),X21829)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).

fof(i_0_10145,plain,
    ! [X16964,X16965,X16966,X16967] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16967,X16966,X16965)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16967,X16964,X16966)
      | c_Hoare__Mirabelle_Ohoare__derivs(X16967,X16964,X16965) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).

cnf(i_0_10146,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5916]) ).

cnf(i_0_10147,plain,
    ( c_Int_OMin = c_Int_OBit1(X1)
    | c_Int_OMin != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_5915]) ).

cnf(i_0_10148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5764]) ).

fof(i_0_10149,plain,
    ! [X20115,X20116] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20116),X20115)),X20116) = X20115,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).

fof(i_0_10150,plain,
    ! [X20113,X20114] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20114),X20113)),X20113) = X20114,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).

fof(i_0_10151,plain,
    ! [X32984,X32985,X32986,X32987] : hAPP(c_New__DSequence_Opos__union(X32987,X32986,X32985),X32984) = c_Lazy__Sequence_Oappend(X32987,hAPP(X32986,X32984),hAPP(X32985,X32984)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def]) ).

fof(i_0_10152,plain,
    ! [X25771,X25772,X25773] :
      ( ~ c_Equiv__Relations_Oequiv(X25773,X25772,X25771)
      | c_Complete__Lattice_OSup__class_OSup(tc_fun(X25773,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25773),X25772),X25771)) = X25772 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).

fof(i_0_10153,plain,
    ! [X23778,X23779,X23780] :
      ( ~ class_Fields_Ofield__inverse__zero(X23780)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23780),hAPP(c_Groups_Ouminus__class_Ouminus(X23780),X23779)),hAPP(c_Groups_Ouminus__class_Ouminus(X23780),X23778)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23780),X23779),X23778) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_10154,plain,
    ! [X24984,X24985] :
      ( ~ class_Rings_Olinordered__idom(X24985)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24985),hAPP(c_Groups_Oabs__class_Oabs(X24985),X24984)),hAPP(c_Groups_Oabs__class_Oabs(X24985),X24984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24985),X24984),X24984) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).

fof(i_0_10155,plain,
    ! [X18987,X18988,X18989] :
      ( ~ class_Rings_Oring(X18989)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18989),hAPP(c_Groups_Ouminus__class_Ouminus(X18989),X18988)),hAPP(c_Groups_Ouminus__class_Ouminus(X18989),X18987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18989),X18988),X18987) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_10156,plain,
    ! [X18984,X18985,X18986] :
      ( ~ class_Rings_Oring(X18986)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18986),hAPP(c_Groups_Ouminus__class_Ouminus(X18986),X18985)),X18984) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18986),X18985),hAPP(c_Groups_Ouminus__class_Ouminus(X18986),X18984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

fof(i_0_10157,plain,
    ! [X28178,X28179,X28180,X28181,X28182] :
      ( ( ~ c_Wellfounded_OwfP(X28179,X28178)
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X28179,X28178),X28180)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X28182,X28181),esk311_2(X28181,X28182)))
        | c_Wellfounded_OwfP(X28182,X28181) ) ),
    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_wfP__accp__iff])])])])]) ).

fof(i_0_10158,plain,
    ! [X23633,X23634,X23635] :
      ( ~ class_Rings_Odivision__ring(X23635)
      | X23634 = c_Groups_Ozero__class_Ozero(X23635)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X23635),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23635),X23633),X23634)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23635),X23633),hAPP(c_Groups_Ouminus__class_Ouminus(X23635),X23634)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

cnf(i_0_10159,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_5987]) ).

fof(i_0_10160,plain,
    ! [X25481,X25482,X25483] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25483,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X25483),X25482),X25481)
        | X25482 = c_Orderings_Obot__class_Obot(tc_fun(X25483,tc_HOL_Obool)) )
      & ( X25482 != c_Orderings_Obot__class_Obot(tc_fun(X25483,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25483,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X25483),X25482),X25481) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).

fof(i_0_10161,plain,
    ! [X25478,X25479,X25480] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X25480),X25479),X25478) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25480,tc_HOL_Obool),tc_HOL_Obool))
        | X25479 = c_Orderings_Obot__class_Obot(tc_fun(X25480,tc_HOL_Obool)) )
      & ( X25479 != c_Orderings_Obot__class_Obot(tc_fun(X25480,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X25480),X25479),X25478) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25480,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).

fof(i_0_10162,plain,
    ! [X23667,X23668] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23668,X23667)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23667),X23668)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(i_0_10163,plain,
    ! [X18325,X18326,X18327] :
      ( ( X18326 = X18325
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18327),X18326),X18325))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18327),X18325),X18326))
        | ~ class_Orderings_Olinorder(X18327) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18327),X18326),X18325))
        | X18326 != X18325
        | ~ class_Orderings_Olinorder(X18327) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18327),X18325),X18326))
        | X18326 != X18325
        | ~ class_Orderings_Olinorder(X18327) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_10164,plain,
    ! [X18568,X18569,X18570] :
      ( ~ class_Rings_Olinordered__idom(X18570)
      | X18569 = X18568
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18570),X18569),X18568))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18570),X18568),X18569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5988])]) ).

fof(i_0_10165,plain,
    ! [X18319,X18320,X18321] :
      ( ~ class_Orderings_Olinorder(X18321)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18321),X18320),X18319))
      | X18320 = X18319
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18321),X18319),X18320)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_10166,plain,
    ! [X18316,X18317,X18318] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18318),X18316),X18317))
        | X18316 = X18317
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18318),X18317),X18316))
        | ~ class_Orderings_Olinorder(X18318) )
      & ( X18316 != X18317
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18318),X18316),X18317))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18318),X18317),X18316))
        | ~ class_Orderings_Olinorder(X18318) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5989])])]) ).

fof(i_0_10167,plain,
    ! [X18313,X18314,X18315] :
      ( ~ class_Orderings_Olinorder(X18315)
      | X18314 = X18313
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18314),X18313))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18313),X18314)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5990])]) ).

fof(i_0_10168,plain,
    ! [X18262,X18263,X18264] :
      ( ~ class_Orderings_Olinorder(X18264)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18264),X18263),X18262))
      | X18263 = X18262
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18264),X18262),X18263)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5991])]) ).

fof(i_0_10169,plain,
    ! [X24668,X24669,X24670] :
      ( ~ class_Divides_Osemiring__div(X24670)
      | c_Divides_Odiv__class_Omod(X24670,c_Divides_Odiv__class_Omod(X24670,X24669,X24668),X24668) = c_Divides_Odiv__class_Omod(X24670,X24669,X24668) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).

fof(i_0_10170,plain,
    ! [X20724,X20725] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20725,tc_HOL_Obool)),X20724),c_Orderings_Obot__class_Obot(tc_fun(X20725,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X20725,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).

fof(i_0_10171,plain,
    ! [X19372,X19373] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19373,tc_HOL_Obool)),X19372),c_Orderings_Otop__class_Otop(tc_fun(X19373,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19373,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).

fof(i_0_10172,plain,
    ! [X19730,X19731] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19731,tc_HOL_Obool)),X19730),c_Orderings_Otop__class_Otop(tc_fun(X19731,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X19731,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).

fof(i_0_10173,plain,
    ! [X27718,X27719] : hAPP(c_Relation_ODomain(X27719,X27718),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27719,X27718),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27719,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).

fof(i_0_10174,plain,
    ! [X27644,X27645] : hAPP(c_Relation_ORange(X27645,X27644),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27645,X27644),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27644,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__empty]) ).

fof(i_0_10175,plain,
    ! [X26991,X26992,X26993,X26994] : hAPP(c_Product__Type_Ofst(X26994,X26993),hAPP(hAPP(c_Product__Type_OPair(X26994,X26993),X26992),X26991)) = X26992,
    inference(variable_rename,[status(thm)],[fact_fst__conv]) ).

fof(i_0_10176,plain,
    ! [X26899,X26900,X26901,X26902] : hAPP(c_Product__Type_Osnd(X26902,X26901),hAPP(hAPP(c_Product__Type_OPair(X26902,X26901),X26900),X26899)) = X26899,
    inference(variable_rename,[status(thm)],[fact_snd__conv]) ).

cnf(i_0_10177,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_minus__Min]) ).

fof(i_0_10178,plain,
    ! [X19897,X19898,X19900,X19901,X19902] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19898),X19897))
        | X19897 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19898),esk76_2(X19897,X19898)) )
      & ( X19900 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19901),X19902)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19901),X19900)) ) ),
    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_le__iff__add])])])])]) ).

fof(i_0_10179,plain,
    ! [X17077,X17078,X17079] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17079),X17078),X17077))
      | hAPP(hAPP(c_Set_Oinsert(X17079),X17078),X17077) = X17077 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_10180,plain,
    ! [X17152,X17153] : c_Set_Othe__elem(X17153,hAPP(hAPP(c_Set_Oinsert(X17153),X17152),c_Orderings_Obot__class_Obot(tc_fun(X17153,tc_HOL_Obool)))) = X17152,
    inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).

fof(i_0_10181,plain,
    ! [X18396,X18397,X18398] :
      ( ~ class_Orderings_Olinorder(X18398)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18398),X18397),X18396))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18398),X18396),X18397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_10182,plain,
    ! [X18381,X18382,X18383] :
      ( ~ class_Orderings_Olinorder(X18383)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18383),X18382),X18381))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18383),X18381),X18382)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5992])]) ).

fof(i_0_10183,plain,
    ! [X18384,X18385,X18386] :
      ( ~ class_Orderings_Olinorder(X18386)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18386),X18385),X18384))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18386),X18384),X18385)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5993])]) ).

fof(i_0_10184,plain,
    ! [X17634,X17635,X17636] :
      ( ~ class_Orderings_Olinorder(X17636)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17636),X17635),X17634))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17636),X17634),X17635)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_10185,plain,
    ! [X17574,X17575,X17576] :
      ( ~ class_Orderings_Olinorder(X17576)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17576),X17575),X17574))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17576),X17574),X17575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5994])]) ).

cnf(i_0_10186,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_5995]) ).

cnf(i_0_10187,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5996]) ).

fof(i_0_10188,plain,
    ! [X29993,X29994,X29995] :
      ( ~ class_Groups_Omonoid__add(X29995)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29995),hAPP(hAPP(c_List_Olist_OCons(X29995),X29994),X29993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29995),X29994),hAPP(c_List_Omonoid__add__class_Olistsum(X29995),X29993)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).

fof(i_0_10189,plain,
    ! [X23781,X23782,X23783] :
      ( ~ class_Fields_Ofield__inverse__zero(X23783)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X23783),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23783),X23782),X23781)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23783),X23782),hAPP(c_Groups_Ouminus__class_Ouminus(X23783),X23781)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

fof(i_0_10190,plain,
    ! [X18978,X18979,X18980] :
      ( ~ class_Rings_Oring(X18980)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18980),X18979),X18978)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18980),X18979),hAPP(c_Groups_Ouminus__class_Ouminus(X18980),X18978)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_10191,plain,
    ! [X31411,X31412] : c_List_Opartition(X31412,X31411,c_List_Olist_ONil(X31412)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31412),tc_List_Olist(X31412)),c_List_Olist_ONil(X31412)),c_List_Olist_ONil(X31412)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).

cnf(i_0_10192,plain,
    c_Int_Osucc(c_Int_Opred(X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_5997]) ).

fof(i_0_10193,plain,
    ! [X30267,X30268,X30269] : hAPP(hAPP(c_List_Otake(X30269),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X30269),X30268),X30267)) = hAPP(hAPP(c_List_Olist_OCons(X30269),X30268),c_List_Olist_ONil(X30269)),
    inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).

fof(i_0_10194,plain,
    ! [X33414,X33415,X33416,X33417] :
      ( ~ c_Relation_Osym(X33417,X33416)
      | c_Relation_Osym(X33415,hAPP(hAPP(c_Relation_Oinv__image(X33417,X33415),X33416),X33414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__inv__image])]) ).

fof(i_0_10195,plain,
    ! [X33267,X33268,X33269,X33270] :
      ( ~ c_Relation_Otrans(X33270,X33269)
      | c_Relation_Otrans(X33268,hAPP(hAPP(c_Relation_Oinv__image(X33270,X33268),X33269),X33267)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__inv__image])]) ).

fof(i_0_10196,plain,
    ! [X27500,X27501,X27502,X27503] :
      ( ~ c_Wellfounded_Owf(X27503,X27502)
      | c_Wellfounded_Owf(X27501,hAPP(hAPP(c_Relation_Oinv__image(X27503,X27501),X27502),X27500)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).

fof(i_0_10197,plain,
    ! [X27283,X27284,X27285,X27286] :
      ( ~ c_FunDef_Oreduction__pair(X27286,X27285)
      | c_FunDef_Oreduction__pair(X27284,hAPP(hAPP(c_FunDef_Orp__inv__image(X27286,X27284),X27285),X27283)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).

fof(i_0_10198,plain,
    ! [X34140,X34141] :
      ( ~ class_Rings_Ocomm__semiring__1(X34141)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34141),c_Groups_Ozero__class_Ozero(X34141)),X34140))
      | X34140 = c_Groups_Ozero__class_Ozero(X34141) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).

fof(i_0_10199,plain,
    ! [X24649,X24650,X24651] :
      ( ~ class_Divides_Osemiring__div(X24651)
      | c_Divides_Odiv__class_Omod(X24651,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24651),X24650),X24649),X24650) = c_Divides_Odiv__class_Omod(X24651,X24649,X24650) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).

fof(i_0_10200,plain,
    ! [X24652,X24653,X24654] :
      ( ~ class_Divides_Osemiring__div(X24654)
      | c_Divides_Odiv__class_Omod(X24654,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24654),X24653),X24652),X24652) = c_Divides_Odiv__class_Omod(X24654,X24653,X24652) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).

fof(i_0_10201,plain,
    ! [X30589,X30590,X30591,X30592,X30593] :
      ( hAPP(hAPP(c_List_Odrop(X30593),X30592),X30591) != hAPP(hAPP(c_List_Olist_OCons(X30593),X30590),X30589)
      | hAPP(hAPP(c_List_Onth(X30593),X30591),X30592) = X30590 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).

fof(i_0_10202,plain,
    ! [X21732,X21733] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21733)),hAPP(c_Nat_OSuc,X21732)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X21733),X21732)),
    inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).

fof(i_0_10203,plain,
    ! [X21730,X21731] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21731)),hAPP(c_Nat_OSuc,X21730)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21731),X21730)),
    inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).

fof(i_0_10204,plain,
    ! [X31270,X31271] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31271)),hAPP(c_Code__Numeral_Oof__nat,X31270)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31271),X31270)),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).

fof(i_0_10205,plain,
    ! [X31289,X31290] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31290)),hAPP(c_Code__Numeral_Oof__nat,X31289)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31290),X31289)),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(i_0_10206,plain,
    ! [X22972,X22973] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22973)),X22972) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22973),X22972)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(i_0_10207,plain,
    ! [X22882,X22883] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22883)),X22882) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22883),X22882)),
    inference(variable_rename,[status(thm)],[fact_zpower__int]) ).

fof(i_0_10208,plain,
    ! [X22830,X22831] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22831)),X22830) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22831),X22830)),
    inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).

fof(i_0_10209,plain,
    ! [X22884,X22885] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22885),X22884)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22885)),X22884),
    inference(variable_rename,[status(thm)],[fact_int__power]) ).

fof(i_0_10210,plain,
    ! [X32419,X32420,X32421] : hAPP(c_List_Oset(X32421),c_List_Oinsert(X32421,X32420,X32419)) = hAPP(hAPP(c_Set_Oinsert(X32421),X32420),hAPP(c_List_Oset(X32421),X32419)),
    inference(variable_rename,[status(thm)],[fact_List_Oset__insert]) ).

cnf(i_0_10211,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Osucc(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5998]) ).

fof(i_0_10212,plain,
    ! [X32802,X32803,X32804] : c_List_Osplice(X32804,hAPP(hAPP(c_List_Olist_OCons(X32804),X32803),X32802),c_List_Olist_ONil(X32804)) = hAPP(hAPP(c_List_Olist_OCons(X32804),X32803),X32802),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(i_0_10213,plain,
    ! [X25036,X25037] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25037)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25037),c_Groups_Ozero__class_Ozero(X25037)),hAPP(c_Groups_Oabs__class_Oabs(X25037),X25036))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).

fof(i_0_10214,plain,
    ! [X22898,X22899] :
      ( ~ class_Rings_Olinordered__semidom(X22899)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22899),c_Groups_Ozero__class_Ozero(X22899)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22899),X22898))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).

fof(i_0_10215,plain,
    ! [X22896,X22897] :
      ( ~ class_Rings_Olinordered__semidom(X22897)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22897),c_Groups_Ozero__class_Ozero(X22897)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22897),X22896))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).

fof(i_0_10216,plain,
    ! [X20556,X20557,X20558] :
      ( ~ class_Lattices_Osemilattice__inf(X20558)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20558),X20557),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20558),X20557),X20556)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20558),X20557),X20556) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).

fof(i_0_10217,plain,
    ! [X20550,X20551,X20552] :
      ( ~ class_Lattices_Osemilattice__inf(X20552)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20552),X20551),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20552),X20551),X20550)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20552),X20551),X20550) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).

fof(i_0_10218,plain,
    ! [X20553,X20554,X20555] :
      ( ~ class_Lattices_Olattice(X20555)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20555),X20554),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20555),X20554),X20553)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20555),X20554),X20553) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).

fof(i_0_10219,plain,
    ! [X19457,X19458,X19459] :
      ( ~ class_Lattices_Osemilattice__sup(X19459)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19459),X19458),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19459),X19458),X19457)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19459),X19458),X19457) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).

fof(i_0_10220,plain,
    ! [X19451,X19452,X19453] :
      ( ~ class_Lattices_Osemilattice__sup(X19453)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19453),X19452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19453),X19452),X19451)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19453),X19452),X19451) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).

fof(i_0_10221,plain,
    ! [X19454,X19455,X19456] :
      ( ~ class_Lattices_Olattice(X19456)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19456),X19455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19456),X19455),X19454)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19456),X19455),X19454) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).

fof(i_0_10222,plain,
    ! [X18768,X18769,X18770] :
      ( ~ class_Orderings_Olinorder(X18770)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18770),X18769),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18770),X18769),X18768)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18770),X18769),X18768) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).

fof(i_0_10223,plain,
    ! [X18765,X18766,X18767] :
      ( ~ class_Orderings_Olinorder(X18767)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18767),X18766),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18767),X18766),X18765)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18767),X18766),X18765) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).

fof(i_0_10224,plain,
    ! [X18762,X18763,X18764] :
      ( ~ class_Orderings_Olinorder(X18764)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18764),X18763),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18764),X18763),X18762)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18764),X18763),X18762) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).

fof(i_0_10225,plain,
    ! [X18759,X18760,X18761] :
      ( ~ class_Orderings_Olinorder(X18761)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18761),X18760),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18761),X18760),X18759)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18761),X18760),X18759) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).

fof(i_0_10226,plain,
    ! [X18255,X18256,X18257] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18257)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18257),X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18257),X18256),X18255)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18257),X18256),X18255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).

fof(i_0_10227,plain,
    ! [X33938,X33939,X33940] : c_Lazy__Sequence_Oflat(X33940,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X33940),X33939,X33938)) = c_Lazy__Sequence_Oappend(X33940,X33939,c_Lazy__Sequence_Oflat(X33940,X33938)),
    inference(variable_rename,[status(thm)],[fact__03]) ).

fof(i_0_10228,plain,
    ! [X32511,X32512,X32514] :
      ( ( hAPP(c_List_Oset(X32512),esk460_2(X32511,X32512)) = X32511
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32512),X32511))
        | ~ class_Orderings_Olinorder(X32512) )
      & ( c_List_Olinorder__class_Osorted(X32512,esk460_2(X32511,X32512))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32512),X32511))
        | ~ class_Orderings_Olinorder(X32512) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32512),esk460_2(X32511,X32512)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32512),X32511))
        | ~ class_Orderings_Olinorder(X32512) )
      & ( hAPP(c_List_Oset(X32512),X32514) != X32511
        | ~ c_List_Olinorder__class_Osorted(X32512,X32514)
        | ~ hBOOL(hAPP(c_List_Odistinct(X32512),X32514))
        | X32514 = esk460_2(X32511,X32512)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32512),X32511))
        | ~ class_Orderings_Olinorder(X32512) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__sorted__distinct__unique])])])])]) ).

fof(i_0_10229,plain,
    ! [X30731,X30732,X30733] : hAPP(hAPP(c_List_Odrop(X30733),X30732),hAPP(c_List_Otl(X30733),X30731)) = hAPP(c_List_Otl(X30733),hAPP(hAPP(c_List_Odrop(X30733),X30732),X30731)),
    inference(variable_rename,[status(thm)],[fact_drop__tl]) ).

fof(i_0_10230,plain,
    ! [X30734,X30735,X30736] : hAPP(c_List_Otl(X30736),hAPP(hAPP(c_List_Odrop(X30736),X30735),X30734)) = hAPP(hAPP(c_List_Odrop(X30736),X30735),hAPP(c_List_Otl(X30736),X30734)),
    inference(variable_rename,[status(thm)],[fact_tl__drop]) ).

fof(i_0_10231,plain,
    ! [X29855,X29856,X29857] : hAPP(c_List_Oset(X29857),hAPP(hAPP(c_List_Olist_OCons(X29857),X29856),X29855)) = hAPP(hAPP(c_Set_Oinsert(X29857),X29856),hAPP(c_List_Oset(X29857),X29855)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(i_0_10232,plain,
    ! [X24187,X24188] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24188,X24187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24187)),X24188),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(i_0_10233,plain,
    ! [X17060,X17061,X17062] :
      ( X17062 != c_Orderings_Obot__class_Obot(tc_fun(X17061,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X17061),X17060),X17062)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5999])]) ).

fof(i_0_10234,plain,
    ! [X28033] : hAPP(c_Set_Oimage(X28033,X28033,c_Fun_Oid(X28033)),c_Orderings_Otop__class_Otop(tc_fun(X28033,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28033,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_surj__id]) ).

fof(i_0_10235,plain,
    ! [X33851,X33852,X33853] :
      ( ( ~ hBOOL(hAPP(c_Quotient_ORespects(X33853,X33852),X33851))
        | hBOOL(hAPP(hAPP(X33852,X33851),X33851)) )
      & ( ~ hBOOL(hAPP(hAPP(X33852,X33851),X33851))
        | hBOOL(hAPP(c_Quotient_ORespects(X33853,X33852),X33851)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Respects__def])]) ).

fof(i_0_10236,plain,
    ! [X28424,X28425,X28427,X28428,X28429] :
      ( ( ~ hBOOL(hAPP(X28425,c_Hilbert__Choice_OEps(X28424,X28425)))
        | hBOOL(hAPP(X28425,esk329_2(X28424,X28425))) )
      & ( ~ hBOOL(hAPP(X28428,X28429))
        | hBOOL(hAPP(X28428,c_Hilbert__Choice_OEps(X28427,X28428))) ) ),
    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_some__eq__ex])])])])]) ).

fof(i_0_10237,plain,
    ! [X31769,X31770,X31771] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X31771),tc_List_Olist(X31771)),c_List_Opartition(X31771,X31770,X31769)) = hAPP(c_List_Ofilter(X31771,X31770),X31769),
    inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).

fof(i_0_10238,plain,
    ! [X25568] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X25568))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25568)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25568))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25568)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6000])]) ).

fof(i_0_10239,plain,
    ! [X33602] :
      ( X33602 = hAPP(c_Code__Numeral_Oof__nat,esk535_1(X33602))
      & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk535_1(X33602)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6001])])]) ).

fof(i_0_10240,plain,
    ! [X33988] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33988)),
    inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).

fof(i_0_10241,plain,
    ! [X20315,X20316] : hBOOL(hAPP(hAPP(c_member(X20316),X20315),c_Orderings_Otop__class_Otop(tc_fun(X20316,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_10242,plain,
    ! [X19353,X19354] : hBOOL(hAPP(hAPP(c_member(X19354),X19353),c_Orderings_Otop__class_Otop(tc_fun(X19354,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_10243,plain,
    ! [X23706,X23707] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | X23707 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23706)
        | hAPP(c_Int_Onat,X23707) != X23706 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | X23706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Int_Onat,X23707) != X23706 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | hAPP(c_Int_Onat,X23707) = X23706 )
      & ( X23706 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | hAPP(c_Int_Onat,X23707) = X23706 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23707))
        | X23707 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23706)
        | hAPP(c_Int_Onat,X23707) = X23706 )
      & ( X23706 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23707 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23706)
        | hAPP(c_Int_Onat,X23707) = X23706 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6002])])]) ).

fof(i_0_10244,plain,
    ! [X23708,X23709] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | X23708 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23709)
        | X23709 != hAPP(c_Int_Onat,X23708) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | X23709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23709 != hAPP(c_Int_Onat,X23708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | X23709 = hAPP(c_Int_Onat,X23708) )
      & ( X23709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | X23709 = hAPP(c_Int_Onat,X23708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23708))
        | X23708 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23709)
        | X23709 = hAPP(c_Int_Onat,X23708) )
      & ( X23709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23708 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23709)
        | X23709 = hAPP(c_Int_Onat,X23708) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6003])])]) ).

fof(i_0_10245,plain,
    ! [X19202,X19203,X19204] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19204,tc_HOL_Obool)),X19203) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19204,tc_HOL_Obool)),X19202)
        | X19203 = X19202 )
      & ( X19203 != X19202
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19204,tc_HOL_Obool)),X19203) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19204,tc_HOL_Obool)),X19202) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).

fof(i_0_10246,plain,
    ! [X18799,X18800,X18801,X18802] :
      ( ~ class_Groups_Ouminus(X18802)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X18801,X18802)),X18800),X18799) = hAPP(c_Groups_Ouminus__class_Ouminus(X18802),hAPP(X18800,X18799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).

fof(i_0_10247,plain,
    ! [X18789,X18790,X18791,X18792] :
      ( ~ class_Groups_Ouminus(X18792)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X18791,X18792)),X18790),X18789) = hAPP(c_Groups_Ouminus__class_Ouminus(X18792),hAPP(X18790,X18789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_10248,plain,
    ! [X23683] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23683))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23683)) = X23683 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).

fof(i_0_10249,plain,
    ! [X23680] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23680))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23680)) = X23680 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23680))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23680)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6004])]) ).

fof(i_0_10250,plain,
    ! [X23413,X23414] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23414),X23413))
      | c_Nat__Transfer_Otsub(X23413,X23414) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23413),X23414) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).

fof(i_0_10251,plain,
    ! [X23272,X23273] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23273),X23272))
        | c_Nat__Transfer_Otsub(X23272,X23273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23272),X23273) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23273),X23272))
        | c_Nat__Transfer_Otsub(X23272,X23273) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])]) ).

fof(i_0_10252,plain,
    ! [X31320,X31321] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X31321)),hAPP(c_Code__Numeral_Oof__nat,X31320)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31321),X31320)),
    inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(i_0_10253,plain,
    ! [X23681,X23682] :
      ( ( X23682 = hAPP(c_Int_Onat,X23681)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23682) != X23681 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23681))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23682) != X23681 )
      & ( X23682 != hAPP(c_Int_Onat,X23681)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23681))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23682) = X23681 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).

fof(i_0_10254,plain,
    ! [X19176,X19177,X19178,X19179] :
      ( ~ c_Big__Operators_Osemilattice__big(X19179,X19178,X19177)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19179),X19176))
      | hAPP(X19177,X19176) = hAPP(c_Finite__Set_Ofold1(X19179,X19178),X19176) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).

fof(i_0_10255,plain,
    ! [X19090,X19091,X19092,X19093] :
      ( ~ c_Finite__Set_Ofolding__one(X19093,X19092,X19091)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19093),X19090))
      | hAPP(X19091,X19090) = hAPP(c_Finite__Set_Ofold1(X19093,X19092),X19090) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).

fof(i_0_10256,plain,
    ! [X25653,X25654] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25653)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25654),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25653)) = c_Groups_Ozero__class_Ozero(X25654)
        | ~ class_Int_Onumber__ring(X25654) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25653)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25654),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25653)) = hAPP(c_Int_Onumber__class_Onumber__of(X25654),X25653)
        | ~ class_Int_Onumber__ring(X25654) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6006])])]) ).

fof(i_0_10257,plain,
    ! [X25113] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25113,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X25113,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X25113,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).

fof(i_0_10258,plain,
    ! [X25102] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X25102,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25102,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X25102,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__empty]) ).

fof(i_0_10259,plain,
    ! [X21596] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X21596,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X21596,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X21596,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).

fof(i_0_10260,plain,
    ! [X21605] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X21605,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X21605,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X21605,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).

cnf(i_0_10261,plain,
    ( X1 = X2
    | c_List_Oupt(X1,X3) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5718]) ).

fof(i_0_10262,plain,
    ! [X17051,X17052,X17053] : hAPP(hAPP(c_Set_Oinsert(X17053),X17052),hAPP(hAPP(c_Set_Oinsert(X17053),X17052),X17051)) = hAPP(hAPP(c_Set_Oinsert(X17053),X17052),X17051),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

cnf(i_0_10263,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).

fof(i_0_10264,plain,
    ! [X21838,X21839,X21840,X21841] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21841)
      | X21840 = c_Orderings_Obot__class_Obot(tc_fun(X21839,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X21839,X21841),X21840),hAPP(c_COMBK(X21841,X21839),X21838)) = X21838 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).

fof(i_0_10265,plain,
    ! [X21159,X21160,X21161,X21162] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21162)
      | X21161 = c_Orderings_Obot__class_Obot(tc_fun(X21160,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21160,X21162),X21161),hAPP(c_COMBK(X21162,X21160),X21159)) = X21159 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).

cnf(i_0_10266,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6007]) ).

fof(i_0_10267,plain,
    ! [X20992,X20993,X20994] :
      ( ~ class_Lattices_Oboolean__algebra(X20994)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20994),X20993),X20992) != c_Orderings_Obot__class_Obot(X20994)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20994),X20993),X20992) != c_Orderings_Otop__class_Otop(X20994)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20994),X20993) = X20992 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).

fof(i_0_10268,plain,
    ! [X21831,X21832] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21832),hAPP(c_Nat_OSuc,X21831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21832),X21831)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).

cnf(i_0_10269,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6008]) ).

fof(i_0_10270,plain,
    ! [X23228] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23228))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(i_0_10271,plain,
    ! [X31826,X31827] : c_List_Otranspose(X31827,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31827)),c_List_Olist_ONil(X31827)),X31826)) = c_List_Otranspose(X31827,X31826),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(i_0_10272,plain,
    ! [X31780,X31781,X31782,X31783] :
      ( hBOOL(hAPP(X31783,X31782))
      | c_List_Oremove1(X31781,X31782,hAPP(c_List_Ofilter(X31781,X31783),X31780)) = hAPP(c_List_Ofilter(X31781,X31783),X31780) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6009])]) ).

fof(i_0_10273,plain,
    ! [X27246] : hAPP(c_Relation_OField(X27246),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27246,X27246),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27246,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Field__empty]) ).

fof(i_0_10274,plain,
    ! [X24842,X24843] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24843),X24842))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24843,X24842) = X24843 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).

fof(i_0_10275,plain,
    ! [X24324,X24325] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24325),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24324) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X24325,X24324),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(i_0_10276,plain,
    ! [X25160,X25161,X25162] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25162)
      | c_Complete__Lattice_OSup__class_OSup(X25162,hAPP(hAPP(c_Set_Oinsert(X25162),X25161),X25160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25162),X25161),c_Complete__Lattice_OSup__class_OSup(X25162,X25160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).

fof(i_0_10277,plain,
    ! [X21911,X21912,X21913] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21913)
      | c_Complete__Lattice_OInf__class_OInf(X21913,hAPP(hAPP(c_Set_Oinsert(X21913),X21912),X21911)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21913),X21912),c_Complete__Lattice_OInf__class_OInf(X21913,X21911)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).

fof(i_0_10278,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__int]) ).

fof(i_0_10279,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat]) ).

fof(i_0_10280,plain,
    ! [X32410,X32411,X32412] : c_List_Oinsert(X32412,X32411,c_List_Oremdups(X32412,X32410)) = c_List_Oremdups(X32412,c_List_Oinsert(X32412,X32411,X32410)),
    inference(variable_rename,[status(thm)],[fact_insert__remdups]) ).

fof(i_0_10281,plain,
    ! [X32676,X32677,X32678] :
      ( ( ~ c_List_Olist__all(X32678,X32677,hAPP(c_List_Orev(X32678),X32676))
        | c_List_Olist__all(X32678,X32677,X32676) )
      & ( ~ c_List_Olist__all(X32678,X32677,X32676)
        | c_List_Olist__all(X32678,X32677,hAPP(c_List_Orev(X32678),X32676)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])]) ).

fof(i_0_10282,plain,
    ! [X32614,X32615,X32616] :
      ( ( ~ c_List_Olist__ex(X32616,X32615,hAPP(c_List_Orev(X32616),X32614))
        | c_List_Olist__ex(X32616,X32615,X32614) )
      & ( ~ c_List_Olist__ex(X32616,X32615,X32614)
        | c_List_Olist__ex(X32616,X32615,hAPP(c_List_Orev(X32616),X32614)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])]) ).

fof(i_0_10283,plain,
    ! [X30472,X30473,X30474] :
      ( ( X30474 != c_List_Olist_ONil(X30473)
        | c_List_Obutlast(X30473,hAPP(hAPP(c_List_Oappend(X30473),X30472),X30474)) = c_List_Obutlast(X30473,X30472) )
      & ( X30474 = c_List_Olist_ONil(X30473)
        | c_List_Obutlast(X30473,hAPP(hAPP(c_List_Oappend(X30473),X30472),X30474)) = hAPP(hAPP(c_List_Oappend(X30473),X30472),c_List_Obutlast(X30473,X30474)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).

fof(i_0_10284,plain,
    ! [X30188,X30189,X30190] :
      ( ( X30190 != c_List_Olist_ONil(X30189)
        | c_List_Obutlast(X30189,hAPP(hAPP(c_List_Olist_OCons(X30189),X30188),X30190)) = c_List_Olist_ONil(X30189) )
      & ( X30190 = c_List_Olist_ONil(X30189)
        | c_List_Obutlast(X30189,hAPP(hAPP(c_List_Olist_OCons(X30189),X30188),X30190)) = hAPP(hAPP(c_List_Olist_OCons(X30189),X30188),c_List_Obutlast(X30189,X30190)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).

fof(i_0_10285,plain,
    ! [X25529,X25530,X25531] : hAPP(c_Relation_OImage(X25531,X25530,X25529),c_Orderings_Obot__class_Obot(tc_fun(X25531,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X25530,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Image__empty]) ).

fof(i_0_10286,plain,
    ! [X20741,X20742,X20743] : hAPP(c_Set_Ovimage(X20743,X20742,X20741),c_Orderings_Otop__class_Otop(tc_fun(X20742,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X20743,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).

fof(i_0_10287,plain,
    ! [X20719,X20720,X20721] : hAPP(c_Set_Ovimage(X20721,X20720,X20719),c_Orderings_Obot__class_Obot(tc_fun(X20720,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X20721,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).

fof(i_0_10288,plain,
    ! [X17140,X17141,X17142] : hAPP(c_Set_Oimage(X17142,X17141,X17140),c_Orderings_Obot__class_Obot(tc_fun(X17142,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X17141,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_image__empty]) ).

fof(i_0_10289,plain,
    ! [X29736,X29737,X29738] :
      ( ~ c_Relation_Orefl__on(X29738,X29737,X29736)
      | c_Relation_Orefl__on(tc_List_Olist(X29738),c_List_Olists(X29738,X29737),c_List_Olistrel(X29738,X29736)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).

fof(i_0_10290,plain,
    ! [X29733,X29734,X29735] :
      ( ~ c_Equiv__Relations_Oequiv(X29735,X29734,X29733)
      | c_Equiv__Relations_Oequiv(tc_List_Olist(X29735),c_List_Olists(X29735,X29734),c_List_Olistrel(X29735,X29733)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).

fof(i_0_10291,plain,
    ! [X17036,X17037,X17038] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17038),X17037),X17036))
        | hBOOL(hAPP(X17036,X17037)) )
      & ( ~ hBOOL(hAPP(X17036,X17037))
        | hBOOL(hAPP(hAPP(c_member(X17038),X17037),X17036)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

fof(i_0_10292,plain,
    ! [X25650,X25651,X25652] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X25652,X25651,X25650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X25650)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I3_J]) ).

fof(i_0_10293,plain,
    ! [X34061,X34062,X34063,X34064] :
      ( ~ class_Rings_Odvd(X34064)
      | X34063 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X34064),X34062),X34061)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34064),X34062),X34063)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).

cnf(i_0_10294,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6010]) ).

fof(i_0_10295,plain,
    ! [X23450,X23451] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23451),X23450))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23451),X23450) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).

fof(i_0_10296,plain,
    ! [X22510,X22511] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22511),X22510) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22511),X22510)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22511),X22510))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22511),X22510) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).

fof(i_0_10297,plain,
    ! [X22508,X22509] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22509),X22508))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22509),X22508) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H])]) ).

fof(i_0_10298,plain,
    ! [X20776,X20777] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20777,tc_HOL_Obool)),X20776),c_Orderings_Otop__class_Otop(tc_fun(X20777,tc_HOL_Obool))) = X20776,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).

fof(i_0_10299,plain,
    ! [X19581,X19582] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19582,tc_HOL_Obool)),X19581),c_Orderings_Obot__class_Obot(tc_fun(X19582,tc_HOL_Obool))) = X19581,
    inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).

fof(i_0_10300,plain,
    ! [X17330,X17331] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17331,tc_HOL_Obool)),X17330),c_Orderings_Obot__class_Obot(tc_fun(X17331,tc_HOL_Obool))) = X17330,
    inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).

fof(i_0_10301,plain,
    ! [X19205,X19206] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19206,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19206,tc_HOL_Obool)),X19205)) = X19205,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

fof(i_0_10302,plain,
    ! [X29302,X29303] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29303,X29303),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29302) = X29302,
    inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).

fof(i_0_10303,plain,
    ! [X25894] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25894)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25894)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25894)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25894)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25894) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6011])]) ).

fof(i_0_10304,plain,
    ! [X30021,X30022,X30023] : hAPP(hAPP(c_List_Olist__update(X30023,X30022),X30021),hAPP(hAPP(c_List_Onth(X30023),X30022),X30021)) = X30022,
    inference(variable_rename,[status(thm)],[fact_list__update__id]) ).

fof(i_0_10305,plain,
    ! [X18990,X18991,X18992] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18991) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18990),X18990)
        | X18991 = X18990
        | X18991 = hAPP(c_Groups_Ouminus__class_Ouminus(X18992),X18990)
        | ~ class_Rings_Oidom(X18992) )
      & ( X18991 != X18990
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18990),X18990)
        | ~ class_Rings_Oidom(X18992) )
      & ( X18991 != hAPP(c_Groups_Ouminus__class_Ouminus(X18992),X18990)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18990),X18990)
        | ~ class_Rings_Oidom(X18992) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_10306,plain,
    ! [X21571,X21572] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21572)),X21571) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21572),X21571)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_10307,plain,
    ! [X30602,X30603,X30604] : hAPP(hAPP(c_List_Odrop(X30604),X30603),c_List_Obutlast(X30604,X30602)) = c_List_Obutlast(X30604,hAPP(hAPP(c_List_Odrop(X30604),X30603),X30602)),
    inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).

fof(i_0_10308,plain,
    ! [X30599,X30600,X30601] : c_List_Obutlast(X30601,hAPP(hAPP(c_List_Odrop(X30601),X30600),X30599)) = hAPP(hAPP(c_List_Odrop(X30601),X30600),c_List_Obutlast(X30601,X30599)),
    inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).

fof(i_0_10309,plain,
    ! [X31304] :
      ( ( X31304 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X31304)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X31304))
        | X31304 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero])]) ).

fof(i_0_10310,plain,
    ! [X27715,X27716,X27717] :
      ( ( hAPP(c_Relation_ODomain(X27717,X27716),X27715) != c_Orderings_Obot__class_Obot(tc_fun(X27717,tc_HOL_Obool))
        | X27715 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27717,X27716),tc_HOL_Obool)) )
      & ( X27715 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27717,X27716),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(X27717,X27716),X27715) = c_Orderings_Obot__class_Obot(tc_fun(X27717,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).

fof(i_0_10311,plain,
    ! [X27641,X27642,X27643] :
      ( ( hAPP(c_Relation_ORange(X27643,X27642),X27641) != c_Orderings_Obot__class_Obot(tc_fun(X27642,tc_HOL_Obool))
        | X27641 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27643,X27642),tc_HOL_Obool)) )
      & ( X27641 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27643,X27642),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(X27643,X27642),X27641) = c_Orderings_Obot__class_Obot(tc_fun(X27642,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).

fof(i_0_10312,plain,
    ! [X25163] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25163),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25163) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25163) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25163),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25163) = X25163 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6012])]) ).

fof(i_0_10313,plain,
    ! [X25085,X25086] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25086),X25085)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25086) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])]) ).

fof(i_0_10314,plain,
    ! [X23027,X23028] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23028),X23027))
      | X23028 = X23027
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23027),X23028)) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_10315,plain,
    ! [X20076,X20077] :
      ( X20077 = X20076
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20077),X20076))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20076),X20077)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6013])]) ).

fof(i_0_10316,plain,
    ! [X20074,X20075] :
      ( ( X20075 = X20074
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20075),X20074))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20074),X20075)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20075),X20074))
        | X20075 != X20074 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20074),X20075))
        | X20075 != X20074 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_10317,plain,
    ! [X23695,X23696] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23696),X23695)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23695),X23696)),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).

cnf(i_0_10318,plain,
    ( c_Divides_Odivmod__nat(X1,X2) = X3
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6014]) ).

fof(i_0_10319,plain,
    ! [X24969,X24970] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24970)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24970),X24969),hAPP(c_Groups_Oabs__class_Oabs(X24970),X24969))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).

fof(i_0_10320,plain,
    ! [X23400,X23401] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X23401,X23400)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23400),hAPP(c_Nat_OSuc,X23401)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(i_0_10321,plain,
    ! [X33431,X33432,X33433] :
      ( ~ hBOOL(hAPP(hAPP(X33432,X33433),X33433))
      | ~ c_Predicate_Osymp(X33431,X33432)
      | ~ c_Predicate_Otransp(X33431,X33432)
      | c_Equiv__Relations_Opart__equivp(X33431,X33432) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivpI])])]) ).

fof(i_0_10322,plain,
    ! [X23055,X23056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23056),X23055))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23055),X23056)) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_10323,plain,
    ! [X19903,X19904] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19904),X19903))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19903),X19904)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_10324,plain,
    ! [X23295,X23296] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23296)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23295)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23296),X23295),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(i_0_10325,plain,
    ! [X23297,X23298] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23298),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23297)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23298)),X23297),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).

fof(i_0_10326,plain,
    ! [X30777,X30778,X30779] : hAPP(hAPP(c_List_Odrop(X30779),hAPP(c_Nat_OSuc,X30778)),X30777) = hAPP(hAPP(c_List_Odrop(X30779),X30778),hAPP(c_List_Otl(X30779),X30777)),
    inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).

fof(i_0_10327,plain,
    ! [X22452,X22454,X22455] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22452))
        | X22452 = hAPP(c_Nat_OSuc,esk122_1(X22452)) )
      & ( X22454 != hAPP(c_Nat_OSuc,X22455)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22454)) ) ),
    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_gr0__conv__Suc])])])])]) ).

fof(i_0_10328,plain,
    ! [X19219,X19220] :
      ( ~ class_Orderings_Olinorder(X19220)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19220),X19219))
      | c_Big__Operators_Olattice_OInf__fin(X19220,c_Orderings_Oord__class_Omin(X19220),X19219) = hAPP(c_Finite__Set_Ofold1(X19220,c_Orderings_Oord__class_Omin(X19220)),X19219) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).

fof(i_0_10329,plain,
    ! [X19221,X19222] :
      ( ~ class_Orderings_Olinorder(X19222)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19222),X19221))
      | c_Big__Operators_Olattice_OSup__fin(X19222,c_Orderings_Oord__class_Omax(X19222),X19221) = hAPP(c_Finite__Set_Ofold1(X19222,c_Orderings_Oord__class_Omax(X19222)),X19221) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).

fof(i_0_10330,plain,
    ! [X30914] :
      ( ~ class_Orderings_Olinorder(X30914)
      | c_Finite__Set_Ofun__left__comm(X30914,tc_List_Olist(X30914),c_List_Olinorder__class_Oinsort__key(X30914,X30914,c_COMBI(X30914))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).

fof(i_0_10331,plain,
    ! [X24934] :
      ( ( X24934 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24934) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24934))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24934) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X24934 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24934))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24934) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X24934 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6015])])]) ).

fof(i_0_10332,plain,
    ! [X33423,X33424,X33425] :
      ( ~ c_Relation_Orefl__on(X33425,X33424,X33423)
      | ~ c_Relation_Osym(X33425,X33423)
      | ~ c_Relation_Otrans(X33425,X33423)
      | c_Equiv__Relations_Oequiv(X33425,X33424,X33423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivI])]) ).

fof(i_0_10333,plain,
    ! [X33420,X33421,X33422] :
      ( ( c_Relation_Orefl__on(X33422,X33421,X33420)
        | ~ c_Equiv__Relations_Oequiv(X33422,X33421,X33420) )
      & ( c_Relation_Osym(X33422,X33420)
        | ~ c_Equiv__Relations_Oequiv(X33422,X33421,X33420) )
      & ( c_Relation_Otrans(X33422,X33420)
        | ~ c_Equiv__Relations_Oequiv(X33422,X33421,X33420) )
      & ( ~ c_Relation_Orefl__on(X33422,X33421,X33420)
        | ~ c_Relation_Osym(X33422,X33420)
        | ~ c_Relation_Otrans(X33422,X33420)
        | c_Equiv__Relations_Oequiv(X33422,X33421,X33420) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__def])])]) ).

fof(i_0_10334,plain,
    ! [X30740,X30741] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30741),X30740))
      | hBOOL(hAPP(c_List_Odistinct(X30741),hAPP(c_List_Otl(X30741),X30740))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).

fof(i_0_10335,plain,
    ! [X24314,X24315] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24314),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24315,X24314),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(i_0_10336,plain,
    ! [X25569] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25569),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25569),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,X25569)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).

fof(i_0_10337,plain,
    ! [X30141,X30142] :
      ( hAPP(c_Finite__Set_Ocard(X30142),hAPP(c_List_Oset(X30142),X30141)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30142)),X30141)
      | hBOOL(hAPP(c_List_Odistinct(X30142),X30141)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).

fof(i_0_10338,plain,
    ! [X23415,X23416] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23416),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23415)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23416),X23415)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(i_0_10339,plain,
    ! [X32140,X32141,X32142] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X32142),X32141),c_List_Olist_ONil(X32142)) != hAPP(c_List_Orev(X32142),X32140)
        | X32140 = hAPP(hAPP(c_List_Olist_OCons(X32142),X32141),c_List_Olist_ONil(X32142)) )
      & ( X32140 != hAPP(hAPP(c_List_Olist_OCons(X32142),X32141),c_List_Olist_ONil(X32142))
        | hAPP(hAPP(c_List_Olist_OCons(X32142),X32141),c_List_Olist_ONil(X32142)) = hAPP(c_List_Orev(X32142),X32140) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).

fof(i_0_10340,plain,
    ! [X32143,X32144,X32145] :
      ( ( hAPP(c_List_Orev(X32145),X32144) != hAPP(hAPP(c_List_Olist_OCons(X32145),X32143),c_List_Olist_ONil(X32145))
        | X32144 = hAPP(hAPP(c_List_Olist_OCons(X32145),X32143),c_List_Olist_ONil(X32145)) )
      & ( X32144 != hAPP(hAPP(c_List_Olist_OCons(X32145),X32143),c_List_Olist_ONil(X32145))
        | hAPP(c_List_Orev(X32145),X32144) = hAPP(hAPP(c_List_Olist_OCons(X32145),X32143),c_List_Olist_ONil(X32145)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).

fof(i_0_10341,plain,
    ! [X23556,X23557] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X23557,X23556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X23556)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I14_J]) ).

fof(i_0_10342,plain,
    ! [X29617,X29618] : c_List_Olistrel1(X29618,hAPP(c_Relation_Oconverse(X29618,X29618),X29617)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X29618),tc_List_Olist(X29618)),c_List_Olistrel1(X29618,X29617)),
    inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).

fof(i_0_10343,plain,
    ! [X19014,X19015,X19016] :
      ( ~ class_Groups_Oab__group__add(X19016)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X19016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19016),X19015),X19014)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19016),X19014),X19015) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).

cnf(i_0_10344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | c_List_Oupt(X1,X2) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5807]) ).

fof(i_0_10345,plain,
    ! [X32879,X32880,X32881] : hAPP(c_List_Orev(X32881),c_List_Oreplicate(X32881,X32880,X32879)) = c_List_Oreplicate(X32881,X32880,X32879),
    inference(variable_rename,[status(thm)],[fact_rev__replicate]) ).

fof(i_0_10346,plain,
    ! [X27567,X27568,X27569] :
      ( ~ c_Wellfounded_Owf(X27569,X27568)
      | hBOOL(hAPP(hAPP(c_member(X27569),X27567),c_Wellfounded_Oacc(X27569,X27568))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).

fof(i_0_10347,plain,
    ! [X20016,X20017] :
      ( ~ class_Rings_Ocomm__ring__1(X20017)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20017),X20016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20017),hAPP(c_Groups_Ouminus__class_Ouminus(X20017),c_Groups_Oone__class_Oone(X20017))),X20016) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).

fof(i_0_10348,plain,
    ! [X23226,X23227] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23227),X23226))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(i_0_10349,plain,
    ! [X22985,X22986] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22986),X22985))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_10350,plain,
    ! [X33151,X33152,X33153] :
      ( ( ~ c_List_Olist__all(tc_Int_Oint,X33153,c_List_Oupto(X33152,X33151))
        | c_List_Oall__interval__int(X33153,X33152,X33151) )
      & ( ~ c_List_Oall__interval__int(X33153,X33152,X33151)
        | c_List_Olist__all(tc_Int_Oint,X33153,c_List_Oupto(X33152,X33151)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int])]) ).

fof(i_0_10351,plain,
    ! [X32566,X32567,X32568] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32567),X32566))
        | hBOOL(hAPP(X32566,X32568))
        | ~ class_Enum_Oenum(X32567) )
      & ( ~ hBOOL(hAPP(X32566,esk470_2(X32566,X32567)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32567),X32566))
        | ~ class_Enum_Oenum(X32567) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all])])])])]) ).

fof(i_0_10352,plain,
    ! [X32562,X32563,X32565] :
      ( ( ~ hBOOL(hAPP(X32562,esk469_2(X32562,X32563)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32563),X32562))
        | ~ class_Enum_Oenum(X32563) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32563),X32562))
        | hBOOL(hAPP(X32562,X32565))
        | ~ class_Enum_Oenum(X32563) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__code])])])])]) ).

fof(i_0_10353,plain,
    ! [X27103] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X27103)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat_Osize_I4_J]) ).

cnf(i_0_10354,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6016]) ).

fof(i_0_10355,plain,
    ! [X18310,X18311,X18312] :
      ( ~ class_Orderings_Oorder(X18312)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18312),X18311),X18310))
      | X18311 != X18310 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_10356,plain,
    ! [X18301,X18302,X18303] :
      ( ~ class_Orderings_Oorder(X18303)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18303),X18302),X18301))
      | X18302 != X18301 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_10357,plain,
    ! [X18298,X18299,X18300] :
      ( ~ class_Orderings_Oorder(X18300)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18300),X18299),X18298))
      | X18298 != X18299 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

cnf(i_0_10358,plain,
    c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6017]) ).

fof(i_0_10359,plain,
    ! [X32922,X32923,X32924,X32925,X32926] :
      ( ( X32925 = X32923
        | c_List_Oreplicate(X32926,X32925,X32924) != c_List_Oreplicate(X32926,X32923,X32922) )
      & ( X32925 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X32924 = X32922
        | c_List_Oreplicate(X32926,X32925,X32924) != c_List_Oreplicate(X32926,X32923,X32922) )
      & ( X32925 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X32925 != X32923
        | c_List_Oreplicate(X32926,X32925,X32924) = c_List_Oreplicate(X32926,X32923,X32922) )
      & ( X32924 != X32922
        | X32925 != X32923
        | c_List_Oreplicate(X32926,X32925,X32924) = c_List_Oreplicate(X32926,X32923,X32922) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate])])]) ).

fof(i_0_10360,plain,
    ! [X18133,X18134,X18135,X18136,X18137] :
      ( ( X18136 != X18135
        | X18134 = X18133
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18137),X18136),X18135) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18137),X18134),X18133)
        | ~ class_Groups_Oab__group__add(X18137) )
      & ( X18134 != X18133
        | X18136 = X18135
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18137),X18136),X18135) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18137),X18134),X18133)
        | ~ class_Groups_Oab__group__add(X18137) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).

fof(i_0_10361,plain,
    ! [X32155,X32156,X32157] : hAPP(c_List_Orev(X32157),hAPP(c_List_Ofilter(X32157,X32156),X32155)) = hAPP(c_List_Ofilter(X32157,X32156),hAPP(c_List_Orev(X32157),X32155)),
    inference(variable_rename,[status(thm)],[fact_rev__filter]) ).

fof(i_0_10362,plain,
    ! [X24742,X24743] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24743),X24742) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24743,X24742) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero])]) ).

fof(i_0_10363,plain,
    ! [X24744,X24745] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24745,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24744)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24745,X24744) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero])]) ).

fof(i_0_10364,plain,
    ! [X18328,X18329] :
      ( ~ class_Orderings_Opreorder(X18329)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18329),X18328),X18328)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6018])]) ).

fof(i_0_10365,plain,
    ! [X22151] :
      ( ( X22151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22151)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22151))
        | X22151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_10366,plain,
    ! [X31572,X31573] :
      ( ( X31573 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31572,X31573,c_List_Olist_ONil(X31572)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31572)),c_List_Olist_ONil(X31572)),c_List_Olist_ONil(tc_List_Olist(X31572))) )
      & ( X31573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31572,X31573,c_List_Olist_ONil(X31572)) = c_List_Olist_ONil(tc_List_Olist(X31572)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__lists__Nil])]) ).

fof(i_0_10367,plain,
    ! [X18057,X18058,X18059,X18060] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18060),X18059),X18058) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18060),X18057),X18058)
        | X18059 = X18057
        | ~ class_Groups_Ocancel__semigroup__add(X18060) )
      & ( X18059 != X18057
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18060),X18059),X18058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18060),X18057),X18058)
        | ~ class_Groups_Ocancel__semigroup__add(X18060) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_10368,plain,
    ! [X18045,X18046,X18047,X18048] :
      ( ~ class_Groups_Ocancel__semigroup__add(X18048)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18048),X18047),X18046) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18048),X18045),X18046)
      | X18047 = X18045 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_10369,plain,
    ! [X18049,X18050,X18051,X18052] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X18052)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18052),X18051),X18050) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18052),X18051),X18049)
      | X18050 = X18049 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_10370,plain,
    ! [X18061,X18062,X18063,X18064] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18064),X18063),X18062) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18064),X18063),X18061)
        | X18062 = X18061
        | ~ class_Groups_Ocancel__semigroup__add(X18064) )
      & ( X18062 != X18061
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18064),X18063),X18062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18064),X18063),X18061)
        | ~ class_Groups_Ocancel__semigroup__add(X18064) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_10371,plain,
    ! [X18053,X18054,X18055,X18056] :
      ( ~ class_Groups_Ocancel__semigroup__add(X18056)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18056),X18055),X18054) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18056),X18055),X18053)
      | X18054 = X18053 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_10372,plain,
    ! [X33010,X33011,X33012,X33013,X33014] :
      ( ( X33013 = X33011
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33013,X33012) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33011,X33010) )
      & ( X33012 = X33010
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33013,X33012) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33011,X33010) )
      & ( X33013 != X33011
        | X33012 != X33010
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33013,X33012) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33014,X33011,X33010) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])]) ).

fof(i_0_10373,plain,
    ! [X25661,X25662,X25663,X25664,X25665,X25666] :
      ( ( X25666 = X25663
        | c_Com_Ocom_OLocal(X25666,X25665,X25664) != c_Com_Ocom_OLocal(X25663,X25662,X25661) )
      & ( X25665 = X25662
        | c_Com_Ocom_OLocal(X25666,X25665,X25664) != c_Com_Ocom_OLocal(X25663,X25662,X25661) )
      & ( X25664 = X25661
        | c_Com_Ocom_OLocal(X25666,X25665,X25664) != c_Com_Ocom_OLocal(X25663,X25662,X25661) )
      & ( X25666 != X25663
        | X25665 != X25662
        | X25664 != X25661
        | c_Com_Ocom_OLocal(X25666,X25665,X25664) = c_Com_Ocom_OLocal(X25663,X25662,X25661) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])]) ).

fof(i_0_10374,plain,
    ! [X25587,X25588,X25589,X25590,X25591,X25592] :
      ( ( X25592 = X25589
        | c_Com_Ocom_OCond(X25592,X25591,X25590) != c_Com_Ocom_OCond(X25589,X25588,X25587) )
      & ( X25591 = X25588
        | c_Com_Ocom_OCond(X25592,X25591,X25590) != c_Com_Ocom_OCond(X25589,X25588,X25587) )
      & ( X25590 = X25587
        | c_Com_Ocom_OCond(X25592,X25591,X25590) != c_Com_Ocom_OCond(X25589,X25588,X25587) )
      & ( X25592 != X25589
        | X25591 != X25588
        | X25590 != X25587
        | c_Com_Ocom_OCond(X25592,X25591,X25590) = c_Com_Ocom_OCond(X25589,X25588,X25587) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])]) ).

fof(i_0_10375,plain,
    ! [X23673] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,X23673) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__0])]) ).

fof(i_0_10376,plain,
    ! [X23672] :
      ( ( hAPP(c_Int_Onat,X23672) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23672),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23672),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,X23672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__iff])]) ).

fof(i_0_10377,plain,
    ! [X24069] :
      ( ( ~ c_Nat__Transfer_Ois__nat(X24069)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24069)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24069))
        | c_Nat__Transfer_Ois__nat(X24069) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).

fof(i_0_10378,plain,
    ! [X21569,X21570] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21570),hAPP(c_Nat_OSuc,X21569)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21570),X21569)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_10379,plain,
    ! [X25689,X25690,X25691,X25692,X25693,X25694] : c_Com_Ocom_OLocal(X25694,X25693,X25692) != c_Com_Ocom_OCond(X25691,X25690,X25689),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J]) ).

fof(i_0_10380,plain,
    ! [X25683,X25684,X25685,X25686,X25687,X25688] : c_Com_Ocom_OCond(X25688,X25687,X25686) != c_Com_Ocom_OLocal(X25685,X25684,X25683),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I37_J]) ).

fof(i_0_10381,plain,
    ! [X27616,X27617] : hAPP(c_List_Olexn(X27617,X27616),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X27617),tc_List_Olist(X27617)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(i_0_10382,plain,
    ! [X23009] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23009))),
    inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).

fof(i_0_10383,plain,
    ! [X23008] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23008))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(i_0_10384,plain,
    ! [X17328,X17329] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17329,tc_HOL_Obool)),X17328),X17328) = c_Orderings_Obot__class_Obot(tc_fun(X17329,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).

fof(i_0_10385,plain,
    ! [X33350] : c_Relation_Oantisym(X33350,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X33350,X33350),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_antisym__empty]) ).

fof(i_0_10386,plain,
    ! [X27499] : c_Wellfounded_Owf(X27499,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27499,X27499),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_wf__empty]) ).

fof(i_0_10387,plain,
    ! [X24159,X24160,X24161] :
      ( ~ class_Orderings_Oorder(X24161)
      | X24160 != X24159
      | c_SetInterval_Oord__class_OatLeastAtMost(X24161,X24160,X24159) = hAPP(hAPP(c_Set_Oinsert(X24161),X24160),c_Orderings_Obot__class_Obot(tc_fun(X24161,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).

fof(i_0_10388,plain,
    ! [X32104,X32105] :
      ( ( hAPP(c_List_Oset(X32105),c_List_Olinorder__class_Osorted__list__of__set(X32105,X32104)) = X32104
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32105),X32104))
        | ~ class_Orderings_Olinorder(X32105) )
      & ( c_List_Olinorder__class_Osorted(X32105,c_List_Olinorder__class_Osorted__list__of__set(X32105,X32104))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32105),X32104))
        | ~ class_Orderings_Olinorder(X32105) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32105),c_List_Olinorder__class_Osorted__list__of__set(X32105,X32104)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32105),X32104))
        | ~ class_Orderings_Olinorder(X32105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).

fof(i_0_10389,plain,
    ! [X24709,X24710,X24711] :
      ( ~ class_Divides_Osemiring__div(X24711)
      | c_Divides_Odiv__class_Omod(X24711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24711),X24710),X24709),X24710) = c_Groups_Ozero__class_Ozero(X24711) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).

fof(i_0_10390,plain,
    ! [X24712,X24713,X24714] :
      ( ~ class_Divides_Osemiring__div(X24714)
      | c_Divides_Odiv__class_Omod(X24714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24714),X24713),X24712),X24712) = c_Groups_Ozero__class_Ozero(X24714) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).

fof(i_0_10391,plain,
    ! [X30181,X30182] :
      ( X30182 = c_List_Olist_ONil(X30181)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30181),X30182))
      | hBOOL(hAPP(c_List_Odistinct(X30181),c_List_Obutlast(X30181,X30182))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).

fof(i_0_10392,plain,
    ! [X23488,X23489] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23489,X23488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23488),X23489),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(i_0_10393,plain,
    ! [X29564,X29565,X29566,X29567,X29568] :
      ( ( X29567 = X29565
        | hAPP(hAPP(c_List_Olist_OCons(X29568),X29567),X29566) != hAPP(hAPP(c_List_Olist_OCons(X29568),X29565),X29564) )
      & ( X29566 = X29564
        | hAPP(hAPP(c_List_Olist_OCons(X29568),X29567),X29566) != hAPP(hAPP(c_List_Olist_OCons(X29568),X29565),X29564) )
      & ( X29567 != X29565
        | X29566 != X29564
        | hAPP(hAPP(c_List_Olist_OCons(X29568),X29567),X29566) = hAPP(hAPP(c_List_Olist_OCons(X29568),X29565),X29564) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).

fof(i_0_10394,plain,
    ! [X30406,X30407,X30408,X30409] :
      ( ( hAPP(hAPP(c_List_Oappend(X30409),X30408),X30407) != hAPP(hAPP(c_List_Oappend(X30409),X30406),X30407)
        | X30408 = X30406 )
      & ( X30408 != X30406
        | hAPP(hAPP(c_List_Oappend(X30409),X30408),X30407) = hAPP(hAPP(c_List_Oappend(X30409),X30406),X30407) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).

fof(i_0_10395,plain,
    ! [X30410,X30411,X30412,X30413] :
      ( ( hAPP(hAPP(c_List_Oappend(X30413),X30412),X30411) != hAPP(hAPP(c_List_Oappend(X30413),X30412),X30410)
        | X30411 = X30410 )
      & ( X30411 != X30410
        | hAPP(hAPP(c_List_Oappend(X30413),X30412),X30411) = hAPP(hAPP(c_List_Oappend(X30413),X30412),X30410) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).

fof(i_0_10396,plain,
    ! [X24166,X24167] :
      ( ~ class_Orderings_Oorder(X24167)
      | c_SetInterval_Oord__class_OatLeastAtMost(X24167,X24166,X24166) = hAPP(hAPP(c_Set_Oinsert(X24167),X24166),c_Orderings_Obot__class_Obot(tc_fun(X24167,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).

fof(i_0_10397,plain,
    ! [X30201,X30202] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30202),X30201))
      | c_List_Oupto(X30201,X30202) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).

fof(i_0_10398,plain,
    ! [X31574,X31575] : c_Enum_On__lists(X31575,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31574) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31575)),c_List_Olist_ONil(X31575)),c_List_Olist_ONil(tc_List_Olist(X31575))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J]) ).

fof(i_0_10399,plain,
    ! [X24299] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24299)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24299)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24299)),
    inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).

fof(i_0_10400,plain,
    ! [X33611,X33612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33612),X33611))
        | c_Quickcheck_Obeyond(X33612,X33611) = X33611 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33612),X33611))
        | c_Quickcheck_Obeyond(X33612,X33611) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6019])]) ).

fof(i_0_10401,plain,
    ! [X25941] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25941) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25941),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25941),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__0])]) ).

fof(i_0_10402,plain,
    ! [X25886] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25886)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25886) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0])]) ).

fof(i_0_10403,plain,
    ! [X25942] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25942)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25942),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25942),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25942) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

cnf(i_0_10404,plain,
    c_List_Orotate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_6020]) ).

fof(i_0_10405,plain,
    ! [X20662,X20663,X20664] :
      ( ~ class_Lattices_Olattice(X20664)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20664),X20663),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20664),X20663),X20662)) = X20663 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).

fof(i_0_10406,plain,
    ! [X20665,X20666,X20667] :
      ( ~ class_Lattices_Olattice(X20667)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20667),X20666),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20667),X20666),X20665)) = X20666 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).

fof(i_0_10407,plain,
    ! [X18774,X18775,X18776] :
      ( ~ class_Orderings_Olinorder(X18776)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18776),X18775),hAPP(hAPP(c_Orderings_Oord__class_Omin(X18776),X18775),X18774)) = X18775 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).

fof(i_0_10408,plain,
    ! [X18771,X18772,X18773] :
      ( ~ class_Orderings_Olinorder(X18773)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18773),X18772),hAPP(hAPP(c_Orderings_Oord__class_Omax(X18773),X18772),X18771)) = X18772 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).

fof(i_0_10409,plain,
    ! [X32833,X32834,X32835] : c_Predicate_Oconversep(X32835,X32834,c_Predicate_Oconversep(X32834,X32835,X32833)) = X32833,
    inference(variable_rename,[status(thm)],[fact_conversep__conversep]) ).

fof(i_0_10410,plain,
    ! [X22163] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X22163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).

fof(i_0_10411,plain,
    ! [X30582,X30583,X30584] : hAPP(hAPP(c_List_Odrop(X30584),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X30584),X30583),X30582)) = X30582,
    inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).

fof(i_0_10412,plain,
    ! [X21591,X21592] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21592)),hAPP(c_Nat_OSuc,X21591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21592),X21591),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(i_0_10413,plain,
    ! [X21573,X21574] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21574)),X21573) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21574),hAPP(c_Nat_OSuc,X21573)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_10414,plain,
    ! [X19108,X19109,X19110] : hAPP(c_Finite__Set_Ofold1(X19110,X19109),X19108) = c_HOL_OThe(X19110,c_Finite__Set_Ofold1Set(X19110,X19109,X19108)),
    inference(variable_rename,[status(thm)],[fact_fold1__def]) ).

fof(i_0_10415,plain,
    ! [X24736,X24737,X24739,X24740,X24741] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X24737,X24736) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X24737 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24736),esk214_2(X24736,X24737)) )
      & ( X24740 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24739),X24741)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X24740,X24739) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    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_zmod__eq__0__iff])])])])]) ).

fof(i_0_10416,plain,
    ! [X24867,X24868,X24870,X24871,X24872] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24868,X24867) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X24868 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24867),esk215_2(X24867,X24868)) )
      & ( X24871 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24870),X24872)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24871,X24870) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    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_mod__eq__0__iff])])])])]) ).

fof(i_0_10417,plain,
    ! [X24080,X24081] :
      ( ~ c_Nat__Transfer_Onat__set(X24081)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24080),X24081))
      | c_Nat__Transfer_Ois__nat(X24080) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).

fof(i_0_10418,plain,
    ! [X33410,X33411] :
      ( ( ~ c_Relation_Osym(X33411,hAPP(c_Relation_Oconverse(X33411,X33411),X33410))
        | c_Relation_Osym(X33411,X33410) )
      & ( ~ c_Relation_Osym(X33411,X33410)
        | c_Relation_Osym(X33411,hAPP(c_Relation_Oconverse(X33411,X33411),X33410)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__converse])]) ).

fof(i_0_10419,plain,
    ! [X33348,X33349] :
      ( ( ~ c_Relation_Oantisym(X33349,hAPP(c_Relation_Oconverse(X33349,X33349),X33348))
        | c_Relation_Oantisym(X33349,X33348) )
      & ( ~ c_Relation_Oantisym(X33349,X33348)
        | c_Relation_Oantisym(X33349,hAPP(c_Relation_Oconverse(X33349,X33349),X33348)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__converse])]) ).

fof(i_0_10420,plain,
    ! [X33248,X33249] :
      ( ( ~ c_Relation_Otrans(X33249,hAPP(c_Relation_Oconverse(X33249,X33249),X33248))
        | c_Relation_Otrans(X33249,X33248) )
      & ( ~ c_Relation_Otrans(X33249,X33248)
        | c_Relation_Otrans(X33249,hAPP(c_Relation_Oconverse(X33249,X33249),X33248)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__converse])]) ).

fof(i_0_10421,plain,
    ! [X29083,X29084] :
      ( ( ~ c_Wellfounded_Oacyclic(X29084,hAPP(c_Relation_Oconverse(X29084,X29084),X29083))
        | c_Wellfounded_Oacyclic(X29084,X29083) )
      & ( ~ c_Wellfounded_Oacyclic(X29084,X29083)
        | c_Wellfounded_Oacyclic(X29084,hAPP(c_Relation_Oconverse(X29084,X29084),X29083)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).

fof(i_0_10422,plain,
    ! [X22152] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22152),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6021]) ).

fof(i_0_10423,plain,
    ! [X22150] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22150),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6022]) ).

fof(i_0_10424,plain,
    ! [X22030] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22030),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6023]) ).

fof(i_0_10425,plain,
    ! [X30143,X30144] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30144),X30143))
      | hAPP(c_Finite__Set_Ocard(X30144),hAPP(c_List_Oset(X30144),X30143)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30144)),X30143) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).

fof(i_0_10426,plain,
    ! [X31617,X31618] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31618)),c_List_Oremdups(X31618,X31617)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31618)),X31617)
        | c_List_Oremdups(X31618,X31617) = X31617 )
      & ( c_List_Oremdups(X31618,X31617) != X31617
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31618)),c_List_Oremdups(X31618,X31617)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31618)),X31617) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])]) ).

fof(i_0_10427,plain,
    ! [X29152,X29153,X29154] : hAPP(c_Relation_ODomain(X29154,X29153),hAPP(c_Relation_Oconverse(X29153,X29154),X29152)) = hAPP(c_Relation_ORange(X29153,X29154),X29152),
    inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).

fof(i_0_10428,plain,
    ! [X29149,X29150,X29151] : hAPP(c_Relation_ORange(X29151,X29150),hAPP(c_Relation_Oconverse(X29150,X29151),X29149)) = hAPP(c_Relation_ODomain(X29150,X29151),X29149),
    inference(variable_rename,[status(thm)],[fact_Range__converse]) ).

fof(i_0_10429,plain,
    ! [X31814,X31815,X31816] : c_List_Oremdups(X31816,hAPP(c_List_Ofilter(X31816,X31815),X31814)) = hAPP(c_List_Ofilter(X31816,X31815),c_List_Oremdups(X31816,X31814)),
    inference(variable_rename,[status(thm)],[fact_remdups__filter]) ).

fof(i_0_10430,plain,
    ! [X29142,X29143] : c_Transitive__Closure_Ortrancl(X29143,hAPP(c_Relation_Oconverse(X29143,X29143),X29142)) = hAPP(c_Relation_Oconverse(X29143,X29143),c_Transitive__Closure_Ortrancl(X29143,X29142)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).

fof(i_0_10431,plain,
    ! [X29155,X29156,X29157] : hAPP(c_Relation_ORange(X29157,X29156),X29155) = hAPP(c_Relation_ODomain(X29156,X29157),hAPP(c_Relation_Oconverse(X29157,X29156),X29155)),
    inference(variable_rename,[status(thm)],[fact_Range__def]) ).

fof(i_0_10432,plain,
    ! [X32487,X32488,X32489] :
      ( ( ~ hBOOL(hAPP(X32487,X32489))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32488),X32487))
        | ~ class_Enum_Oenum(X32488) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32488),X32487))
        | hBOOL(hAPP(X32487,esk457_2(X32487,X32488)))
        | ~ class_Enum_Oenum(X32488) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exists__code])])])])]) ).

fof(i_0_10433,plain,
    ! [X32483,X32484,X32486] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32484),X32483))
        | hBOOL(hAPP(X32483,esk456_2(X32483,X32484)))
        | ~ class_Enum_Oenum(X32484) )
      & ( ~ hBOOL(hAPP(X32483,X32486))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32484),X32483))
        | ~ class_Enum_Oenum(X32484) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex])])])])]) ).

fof(i_0_10434,plain,
    ! [X30245,X30246,X30247,X30248] :
      ( ( hAPP(hAPP(c_List_Olist__update(X30248,X30247),X30246),X30245) != c_List_Olist_ONil(X30248)
        | X30247 = c_List_Olist_ONil(X30248) )
      & ( X30247 != c_List_Olist_ONil(X30248)
        | hAPP(hAPP(c_List_Olist__update(X30248,X30247),X30246),X30245) = c_List_Olist_ONil(X30248) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).

fof(i_0_10435,plain,
    ! [X31073,X31074,X31075,X31076] :
      ( ( hAPP(hAPP(c_List_Omap(X31076,X31075),X31074),X31073) != c_List_Olist_ONil(X31075)
        | X31073 = c_List_Olist_ONil(X31076) )
      & ( X31073 != c_List_Olist_ONil(X31076)
        | hAPP(hAPP(c_List_Omap(X31076,X31075),X31074),X31073) = c_List_Olist_ONil(X31075) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).

fof(i_0_10436,plain,
    ! [X31080,X31081,X31082,X31083] :
      ( ( c_List_Olist_ONil(X31083) != hAPP(hAPP(c_List_Omap(X31082,X31083),X31081),X31080)
        | X31080 = c_List_Olist_ONil(X31082) )
      & ( X31080 != c_List_Olist_ONil(X31082)
        | c_List_Olist_ONil(X31083) = hAPP(hAPP(c_List_Omap(X31082,X31083),X31081),X31080) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).

fof(i_0_10437,plain,
    ! [X22167,X22168] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22168),X22167) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22167),X22168) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X22168 = X22167 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).

fof(i_0_10438,plain,
    ! [X20023,X20024,X20025] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20025)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20024,X20025),X20023),c_Orderings_Obot__class_Obot(tc_fun(X20024,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X20025) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).

fof(i_0_10439,plain,
    ! [X20020,X20021,X20022] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20022)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20021,X20022),X20020),c_Orderings_Obot__class_Obot(tc_fun(X20021,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X20022) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).

fof(i_0_10440,plain,
    ! [X22428,X22429,X22430] :
      ( ~ class_Groups_Ocomm__monoid__add(X22430)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22429,X22430),X22428),c_Orderings_Obot__class_Obot(tc_fun(X22429,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X22430) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).

fof(i_0_10441,plain,
    ! [X22425,X22426,X22427] :
      ( ~ class_Groups_Ocomm__monoid__add(X22427)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22426,X22427),X22425),c_Orderings_Obot__class_Obot(tc_fun(X22426,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X22427) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).

fof(i_0_10442,plain,
    ! [X22153,X22154] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22154),X22153))
      | X22153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).

fof(i_0_10443,plain,
    ! [X19640] :
      ( ~ class_Finite__Set_Ofinite(X19640)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X19640),c_Orderings_Otop__class_Otop(tc_fun(X19640,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_10444,plain,
    ! [X23837,X23838,X23839,X23840] :
      ( ( X23838 = c_Groups_Ozero__class_Ozero(X23840)
        | X23839 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23840),X23837),X23838)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) != X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) )
      & ( X23838 != c_Groups_Ozero__class_Ozero(X23840)
        | X23837 = c_Groups_Ozero__class_Ozero(X23840)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) != X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) )
      & ( X23838 = c_Groups_Ozero__class_Ozero(X23840)
        | X23838 != c_Groups_Ozero__class_Ozero(X23840)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) = X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) )
      & ( X23837 != c_Groups_Ozero__class_Ozero(X23840)
        | X23838 != c_Groups_Ozero__class_Ozero(X23840)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) = X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) )
      & ( X23838 = c_Groups_Ozero__class_Ozero(X23840)
        | X23839 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23840),X23837),X23838)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) = X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) )
      & ( X23837 != c_Groups_Ozero__class_Ozero(X23840)
        | X23839 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23840),X23837),X23838)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23840),X23839),X23838) = X23837
        | ~ class_Fields_Ofield__inverse__zero(X23840) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_10445,plain,
    ! [X23841,X23842,X23843,X23844] :
      ( ( X23841 = c_Groups_Ozero__class_Ozero(X23844)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23844),X23843),X23841) = X23842
        | X23843 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) )
      & ( X23841 != c_Groups_Ozero__class_Ozero(X23844)
        | X23843 = c_Groups_Ozero__class_Ozero(X23844)
        | X23843 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) )
      & ( X23841 = c_Groups_Ozero__class_Ozero(X23844)
        | X23841 != c_Groups_Ozero__class_Ozero(X23844)
        | X23843 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) )
      & ( X23843 != c_Groups_Ozero__class_Ozero(X23844)
        | X23841 != c_Groups_Ozero__class_Ozero(X23844)
        | X23843 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) )
      & ( X23841 = c_Groups_Ozero__class_Ozero(X23844)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23844),X23843),X23841) != X23842
        | X23843 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) )
      & ( X23843 != c_Groups_Ozero__class_Ozero(X23844)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23844),X23843),X23841) != X23842
        | X23843 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23844),X23842),X23841)
        | ~ class_Fields_Ofield__inverse__zero(X23844) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_10446,plain,
    ! [X22952,X22953] :
      ( ~ class_Rings_Osemiring__1(X22953)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22953),hAPP(c_Nat_OSuc,X22952)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22953),c_Groups_Oone__class_Oone(X22953)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22953),X22952)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).

fof(i_0_10447,plain,
    ! [X22032] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X22032))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_10448,plain,
    ! [X20081,X20082] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20082),X20081))
      | X20082 != X20081 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_10449,plain,
    ! [X20079,X20080] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20080),X20079))
      | X20079 != X20080 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

cnf(i_0_10450,plain,
    c_Divides_Odivmod__nat(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(split_conjunct,[status(thm)],[i_0_6024]) ).

fof(i_0_10451,plain,
    ! [X23164] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23164),hAPP(c_Nat_OSuc,X23164)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X23164),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).

cnf(i_0_10452,plain,
    ( c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5531]) ).

fof(i_0_10453,plain,
    ! [X32241,X32242,X32243] :
      ( ~ class_Orderings_Olinorder(X32243)
      | ~ c_List_Olinorder__class_Osorted(X32243,X32242)
      | c_List_Olinorder__class_Osorted(X32243,c_List_OtakeWhile(X32243,X32241,X32242)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile])]) ).

fof(i_0_10454,plain,
    ! [X32025,X32026,X32027] :
      ( ~ class_Orderings_Olinorder(X32027)
      | ~ c_List_Olinorder__class_Osorted(X32027,X32026)
      | c_List_Olinorder__class_Osorted(X32027,c_List_Oremove1(X32027,X32025,X32026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).

fof(i_0_10455,plain,
    ! [X22179,X22180,X22181] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22181),X22180) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22179),X22180)
        | X22181 = X22179
        | X22180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22181 != X22179
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22181),X22180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22179),X22180) )
      & ( X22180 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22181),X22180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22179),X22180) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).

fof(i_0_10456,plain,
    ! [X22176,X22177,X22178] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22177) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22176)
        | X22177 = X22176
        | X22178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22177 != X22176
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22177) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22176) )
      & ( X22178 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22177) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22178),X22176) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).

fof(i_0_10457,plain,
    ! [X22169,X22170,X22171] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22170) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22169)
        | X22171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22170 = X22169 )
      & ( X22171 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22169) )
      & ( X22170 != X22169
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22171),X22169) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_10458,plain,
    ! [X30719,X30720,X30721] :
      ( ( X30721 != c_List_Olist_ONil(X30720)
        | hAPP(c_List_Ohd(X30720),hAPP(hAPP(c_List_Oappend(X30720),X30721),X30719)) = hAPP(c_List_Ohd(X30720),X30719) )
      & ( X30721 = c_List_Olist_ONil(X30720)
        | hAPP(c_List_Ohd(X30720),hAPP(hAPP(c_List_Oappend(X30720),X30721),X30719)) = hAPP(c_List_Ohd(X30720),X30721) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).

fof(i_0_10459,plain,
    ! [X25098,X25099] :
      ( ~ class_Rings_Olinordered__idom(X25099)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25099),c_Groups_Osgn__class_Osgn(X25099,X25098)),hAPP(c_Groups_Oabs__class_Oabs(X25099),X25098)) = X25098 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).

fof(i_0_10460,plain,
    ! [X22383] :
      ( ~ class_Rings_Olinordered__semidom(X22383)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22383),c_Groups_Ozero__class_Ozero(X22383)),c_Groups_Oone__class_Oone(X22383))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_10461,plain,
    ! [X22381] :
      ( ~ class_Rings_Olinordered__semidom(X22381)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22381),c_Groups_Ozero__class_Ozero(X22381)),c_Groups_Oone__class_Oone(X22381))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_10462,plain,
    ! [X26498] :
      ( ~ class_Rings_Osemiring__1(X26498)
      | hBOOL(hAPP(hAPP(c_member(X26498),c_Groups_Ozero__class_Ozero(X26498)),c_Nat_Osemiring__1__class_ONats(X26498))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).

fof(i_0_10463,plain,
    ! [X22932] :
      ( ~ class_Rings_Oring__1(X22932)
      | hBOOL(hAPP(hAPP(c_member(X22932),c_Groups_Ozero__class_Ozero(X22932)),c_Int_Oring__1__class_OInts(X22932))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_10464,plain,
    ! [X26507] :
      ( ~ class_Rings_Osemiring__1(X26507)
      | hBOOL(hAPP(hAPP(c_member(X26507),c_Groups_Oone__class_Oone(X26507)),c_Nat_Osemiring__1__class_ONats(X26507))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).

fof(i_0_10465,plain,
    ! [X22942] :
      ( ~ class_Rings_Oring__1(X22942)
      | hBOOL(hAPP(hAPP(c_member(X22942),c_Groups_Oone__class_Oone(X22942)),c_Int_Oring__1__class_OInts(X22942))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_10466,plain,
    ! [X23611,X23612,X23613,X23614] :
      ( ~ class_Rings_Odivision__ring(X23614)
      | X23613 = c_Groups_Ozero__class_Ozero(X23614)
      | X23612 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23614),X23611),X23613)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23614),X23612),X23613) = X23611 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_10467,plain,
    ! [X23615,X23616,X23617,X23618] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23618),X23616),X23617) != X23615
        | X23616 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23618),X23615),X23617)
        | X23617 = c_Groups_Ozero__class_Ozero(X23618)
        | ~ class_Rings_Odivision__ring(X23618) )
      & ( X23616 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23618),X23615),X23617)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23618),X23616),X23617) = X23615
        | X23617 = c_Groups_Ozero__class_Ozero(X23618)
        | ~ class_Rings_Odivision__ring(X23618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_10468,plain,
    ! [X23619,X23620,X23621,X23622] :
      ( ( X23620 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23622),X23619),X23621)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23622),X23620),X23621) = X23619
        | X23621 = c_Groups_Ozero__class_Ozero(X23622)
        | ~ class_Rings_Odivision__ring(X23622) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23622),X23620),X23621) != X23619
        | X23620 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23622),X23619),X23621)
        | X23621 = c_Groups_Ozero__class_Ozero(X23622)
        | ~ class_Rings_Odivision__ring(X23622) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).

fof(i_0_10469,plain,
    ! [X23607,X23608,X23609,X23610] :
      ( ~ class_Rings_Odivision__ring(X23610)
      | X23609 = c_Groups_Ozero__class_Ozero(X23610)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23610),X23608),X23609) != X23607
      | X23608 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23610),X23607),X23609) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_10470,plain,
    ! [X19070,X19071,X19072] :
      ( ~ class_Groups_Ogroup__add(X19072)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19072),X19071),hAPP(c_Groups_Ouminus__class_Ouminus(X19072),X19070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19072),X19071),X19070) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).

fof(i_0_10471,plain,
    ! [X20845,X20846,X20847] :
      ( ~ class_Lattices_Oboolean__algebra(X20847)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20847),X20846),X20845) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20847),X20846),hAPP(c_Groups_Ouminus__class_Ouminus(X20847),X20845)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).

fof(i_0_10472,plain,
    ! [X19073,X19074,X19075] :
      ( ~ class_Rings_Ocomm__ring__1(X19075)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19075),X19074),X19073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19075),X19074),hAPP(c_Groups_Ouminus__class_Ouminus(X19075),X19073)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).

fof(i_0_10473,plain,
    ! [X19064,X19065,X19066] :
      ( ~ class_Groups_Ogroup__add(X19066)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19066),X19065),X19064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19066),X19065),hAPP(c_Groups_Ouminus__class_Ouminus(X19066),X19064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).

fof(i_0_10474,plain,
    ! [X19067,X19068,X19069] :
      ( ~ class_Groups_Oab__group__add(X19069)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19069),X19068),X19067) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19069),X19068),hAPP(c_Groups_Ouminus__class_Ouminus(X19069),X19067)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).

fof(i_0_10475,plain,
    ! [X26351,X26352] :
      ( ~ class_Int_Onumber__ring(X26352)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26352),hAPP(c_Int_Onumber__class_Onumber__of(X26352),c_Int_OMin)),X26351) = hAPP(c_Groups_Ouminus__class_Ouminus(X26352),X26351) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).

fof(i_0_10476,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).

fof(i_0_10477,plain,
    ! [X20078] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20078),X20078)),
    inference(variable_rename,[status(thm)],[i_0_6025]) ).

fof(i_0_10478,plain,
    ! [X20073] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20073),X20073)),
    inference(variable_rename,[status(thm)],[i_0_6026]) ).

fof(i_0_10479,plain,
    ! [X30716,X30717,X30718] :
      ( X30718 = c_List_Olist_ONil(X30717)
      | hAPP(c_List_Ohd(X30717),hAPP(hAPP(c_List_Oappend(X30717),X30718),X30716)) = hAPP(c_List_Ohd(X30717),X30718) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).

cnf(i_0_10480,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6027]) ).

fof(i_0_10481,plain,
    ! [X19943,X19944,X19945] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19945),X19944) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19943),X19944)
        | X19945 = X19943 )
      & ( X19945 != X19943
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19945),X19944) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19943),X19944) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_10482,plain,
    ! [X19946,X19947,X19948] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19948),X19947) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19948),X19946)
        | X19947 = X19946 )
      & ( X19947 != X19946
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19948),X19947) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19948),X19946) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_10483,plain,
    ! [X25336,X25337] : hAPP(c_Set_OCollect(X25337),hAPP(c_fequal,X25336)) = hAPP(hAPP(c_Set_Oinsert(X25337),X25336),c_Orderings_Obot__class_Obot(tc_fun(X25337,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).

fof(i_0_10484,plain,
    ! [X32017,X32018,X32019] :
      ( ~ class_Orderings_Olinorder(X32019)
      | ~ c_List_Olinorder__class_Osorted(X32019,X32018)
      | c_List_Olinorder__class_Osorted(X32019,hAPP(hAPP(c_List_Odrop(X32019),X32017),X32018)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).

fof(i_0_10485,plain,
    ! [X32022,X32023,X32024] :
      ( ~ class_Orderings_Olinorder(X32024)
      | ~ c_List_Olinorder__class_Osorted(X32024,X32023)
      | c_List_Olinorder__class_Osorted(X32024,hAPP(hAPP(c_List_Otake(X32024),X32022),X32023)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).

fof(i_0_10486,plain,
    ! [X17118] : hBOOL(hAPP(c_Finite__Set_Ofinite(X17118),c_Orderings_Obot__class_Obot(tc_fun(X17118,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(i_0_10487,plain,
    ! [X16983] : hBOOL(hAPP(c_Finite__Set_Ofinite(X16983),c_Orderings_Obot__class_Obot(tc_fun(X16983,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).

fof(i_0_10488,plain,
    ! [X24511,X24512] : hAPP(c_Set_OPow(X24512),X24511) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24512,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).

fof(i_0_10489,plain,
    ! [X20030,X20031,X20032,X20033] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20033)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20032),X20031))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20032,X20033),X20030),X20031) = c_Groups_Oone__class_Oone(X20033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6028])]) ).

fof(i_0_10490,plain,
    ! [X20026,X20027,X20028,X20029] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20029)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20028),X20027))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20028,X20029),X20026),X20027) = c_Groups_Oone__class_Oone(X20029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6029])]) ).

fof(i_0_10491,plain,
    ! [X22435,X22436,X22437,X22438] :
      ( ~ class_Groups_Ocomm__monoid__add(X22438)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22437),X22436))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22437,X22438),X22435),X22436) = c_Groups_Ozero__class_Ozero(X22438) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6030])]) ).

fof(i_0_10492,plain,
    ! [X22431,X22432,X22433,X22434] :
      ( ~ class_Groups_Ocomm__monoid__add(X22434)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22433),X22432))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X22433,X22434),X22431),X22432) = c_Groups_Ozero__class_Ozero(X22434) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6031])]) ).

fof(i_0_10493,plain,
    ! [X19741] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19741,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19741,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X19741,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(i_0_10494,plain,
    ! [X19740] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19740,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X19740,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19740,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

fof(i_0_10495,plain,
    ! [X24538] : hAPP(c_Set_OPow(X24538),c_Orderings_Otop__class_Otop(tc_fun(X24538,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X24538,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).

fof(i_0_10496,plain,
    ! [X27261] : c_Relation_OId__on(X27261,c_Orderings_Obot__class_Obot(tc_fun(X27261,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27261,X27261),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).

fof(i_0_10497,plain,
    ! [X20498,X20499] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20499,tc_HOL_Obool)),X20498),X20498) = X20498,
    inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).

fof(i_0_10498,plain,
    ! [X19374,X19375] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19375,tc_HOL_Obool)),X19374),X19374) = X19374,
    inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).

fof(i_0_10499,plain,
    ! [X28215,X28216] :
      ( ~ c_Wellfounded_Owf(X28216,X28215)
      | c_Wellfounded_OwfP(X28216,c_FunDef_Oin__rel(X28216,X28216,X28215)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).

fof(i_0_10500,plain,
    ! [X27540,X27541,X27542] :
      ( ~ c_Wellfounded_Owf(X27542,X27541)
      | c_Wellfounded_Owf(X27542,c_Wellfounded_Omlex__prod(X27542,X27540,X27541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).

fof(i_0_10501,plain,
    ! [X25564] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25564))),
    inference(variable_rename,[status(thm)],[i_0_6032]) ).

fof(i_0_10502,plain,
    ! [X33426,X33427,X33428] :
      ( ( c_Relation_Orefl__on(X33428,X33427,X33426)
        | ~ c_Equiv__Relations_Oequiv(X33428,X33427,X33426) )
      & ( c_Relation_Osym(X33428,X33426)
        | ~ c_Equiv__Relations_Oequiv(X33428,X33427,X33426) )
      & ( c_Relation_Otrans(X33428,X33426)
        | ~ c_Equiv__Relations_Oequiv(X33428,X33427,X33426) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6033])])]) ).

fof(i_0_10503,plain,
    ! [X21959,X21960] :
      ( ~ class_Lattices_Olattice(X21960)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21960),X21959))
      | c_Big__Operators_Olattice__class_OInf__fin(X21960,X21959) = hAPP(c_Finite__Set_Ofold1(X21960,c_Lattices_Osemilattice__inf__class_Oinf(X21960)),X21959) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).

fof(i_0_10504,plain,
    ! [X20340,X20341] :
      ( ~ class_Lattices_Olattice(X20341)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20341),X20340))
      | c_Big__Operators_Olattice__class_OSup__fin(X20341,X20340) = hAPP(c_Finite__Set_Ofold1(X20341,c_Lattices_Osemilattice__sup__class_Osup(X20341)),X20340) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).

fof(i_0_10505,plain,
    ! [X19008,X19009] :
      ( ~ class_Orderings_Olinorder(X19009)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19009),X19008))
      | c_Big__Operators_Olinorder__class_OMin(X19009,X19008) = hAPP(c_Finite__Set_Ofold1(X19009,c_Orderings_Oord__class_Omin(X19009)),X19008) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).

fof(i_0_10506,plain,
    ! [X19006,X19007] :
      ( ~ class_Orderings_Olinorder(X19007)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19007),X19006))
      | c_Big__Operators_Olinorder__class_OMax(X19007,X19006) = hAPP(c_Finite__Set_Ofold1(X19007,c_Orderings_Oord__class_Omax(X19007)),X19006) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).

fof(i_0_10507,plain,
    ! [X21519] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21519),hAPP(c_Nat_OSuc,X21519))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_10508,plain,
    ! [X32865,X32866,X32867] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32867)),c_List_Oreplicate(X32867,X32866,X32865)) = X32866,
    inference(variable_rename,[status(thm)],[fact_length__replicate]) ).

fof(i_0_10509,plain,
    ! [X20843,X20844] :
      ( ~ class_Lattices_Oboolean__algebra(X20844)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20844),hAPP(c_Groups_Ouminus__class_Ouminus(X20844),X20843)),X20843) = c_Orderings_Obot__class_Obot(X20844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).

fof(i_0_10510,plain,
    ! [X19499,X19500] :
      ( ~ class_Lattices_Oboolean__algebra(X19500)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19500),hAPP(c_Groups_Ouminus__class_Ouminus(X19500),X19499)),X19499) = c_Orderings_Otop__class_Otop(X19500) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).

fof(i_0_10511,plain,
    ! [X22406,X22407] :
      ( ~ class_Groups_Ogroup__add(X22407)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22407),hAPP(c_Groups_Ouminus__class_Ouminus(X22407),X22406)),X22406) = c_Groups_Ozero__class_Ozero(X22407) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_10512,plain,
    ! [X22404,X22405] :
      ( ~ class_Groups_Oab__group__add(X22405)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22405),hAPP(c_Groups_Ouminus__class_Ouminus(X22405),X22404)),X22404) = c_Groups_Ozero__class_Ozero(X22405) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_10513,plain,
    ! [X30983,X30984,X30985] :
      ( X30985 != c_List_Olist_ONil(X30984)
      | c_List_Olast(X30984,hAPP(hAPP(c_List_Oappend(X30984),X30983),X30985)) = c_List_Olast(X30984,X30983) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).

fof(i_0_10514,plain,
    ! [X30977,X30978,X30979] :
      ( ( X30979 != c_List_Olist_ONil(X30978)
        | c_List_Olast(X30978,hAPP(hAPP(c_List_Oappend(X30978),X30977),X30979)) = c_List_Olast(X30978,X30977) )
      & ( X30979 = c_List_Olist_ONil(X30978)
        | c_List_Olast(X30978,hAPP(hAPP(c_List_Oappend(X30978),X30977),X30979)) = c_List_Olast(X30978,X30979) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).

fof(i_0_10515,plain,
    ! [X22504,X22505] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22505),X22504)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).

fof(i_0_10516,plain,
    ! [X29858,X29859,X29860] : c_List_Osublist(X29860,X29859,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X29858)) = hAPP(hAPP(c_List_Otake(X29860),X29858),X29859),
    inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(i_0_10517,plain,
    ! [X17794,X17795] :
      ( ~ class_Orderings_Obot(X17795)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17795),c_Orderings_Obot__class_Obot(X17795)),X17794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).

fof(i_0_10518,plain,
    ! [X26392,X26393] :
      ( X26393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26392,X26393),c_Divides_Odivmod__int(X26392,X26393))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).

fof(i_0_10519,plain,
    ! [X26829,X26830] :
      ( ( X26830 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X26829,X26830) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26829)) )
      & ( X26830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X26829,X26830) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26829),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26830)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).

fof(i_0_10520,plain,
    ! [X32008,X32009] :
      ( ~ class_Orderings_Olinorder(X32009)
      | c_List_Olinorder__class_Osorted(X32009,hAPP(hAPP(c_List_Olist_OCons(X32009),X32008),c_List_Olist_ONil(X32009))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).

fof(i_0_10521,plain,
    ! [X30980,X30981,X30982] :
      ( X30982 = c_List_Olist_ONil(X30981)
      | c_List_Olast(X30981,hAPP(hAPP(c_List_Oappend(X30981),X30980),X30982)) = c_List_Olast(X30981,X30982) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).

fof(i_0_10522,plain,
    ! [X30971,X30972,X30973] :
      ( X30973 = c_List_Olist_ONil(X30972)
      | c_List_Olast(X30972,hAPP(hAPP(c_List_Olist_OCons(X30972),X30971),X30973)) = c_List_Olast(X30972,X30973) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).

fof(i_0_10523,plain,
    ! [X30968,X30969,X30970] :
      ( ( X30970 != c_List_Olist_ONil(X30969)
        | c_List_Olast(X30969,hAPP(hAPP(c_List_Olist_OCons(X30969),X30968),X30970)) = X30968 )
      & ( X30970 = c_List_Olist_ONil(X30969)
        | c_List_Olast(X30969,hAPP(hAPP(c_List_Olist_OCons(X30969),X30968),X30970)) = c_List_Olast(X30969,X30970) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).

fof(i_0_10524,plain,
    ! [X25232,X25233] :
      ( ( X25233 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X25232,X25233) = X25232 )
      & ( X25233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X25232,X25233) = c_Nitpick_Onat__gcd(X25233,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25232,X25233)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).

fof(i_0_10525,plain,
    ! [X23367,X23368] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23368)),X23367) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X23368,X23367),
    inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_10526,plain,
    ! [X23105,X23106] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23106),X23105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23105),X23106),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(i_0_10527,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_simplification,[status(thm)],[fact_rel__simps_I7_J]) ).

fof(i_0_10528,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_simplification,[status(thm)],[fact_rel__simps_I3_J]) ).

fof(i_0_10529,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J]) ).

fof(i_0_10530,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J]) ).

fof(i_0_10531,hypothesis,
    ~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
    inference(fof_simplification,[status(thm)],[conj_2]) ).

fof(i_0_10532,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__number__of__Pls]) ).

fof(i_0_10533,plain,
    ! [X30222,X30223,X30224] : hAPP(hAPP(c_List_Ozip(X30224,X30223),c_List_Olist_ONil(X30224)),X30222) = c_List_Olist_ONil(tc_prod(X30224,X30223)),
    inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).

fof(i_0_10534,plain,
    ! [X19343,X19344] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X19344,tc_HOL_Obool)),X19343)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_10535,plain,
    ! [X28023,X28024] : hAPP(c_Set_Ovimage(X28024,X28024,c_Fun_Oid(X28024)),X28023) = X28023,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

fof(i_0_10536,plain,
    ! [X20588,X20589] : hAPP(c_Set_Ovimage(X20589,X20589,c_COMBI(X20589)),X20588) = X20588,
    inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).

fof(i_0_10537,plain,
    ! [X28019,X28020] : hAPP(c_Set_Oimage(X28020,X28020,c_Fun_Oid(X28020)),X28019) = X28019,
    inference(variable_rename,[status(thm)],[fact_image__id]) ).

fof(i_0_10538,plain,
    ! [X17293,X17294] : hAPP(c_Set_Oimage(X17294,X17294,c_COMBI(X17294)),X17293) = X17293,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_10539,plain,
    ! [X29008,X29009] : c_Relation_Orefl__on(X29009,c_Orderings_Otop__class_Otop(tc_fun(X29009,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X29009,X29008)),
    inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).

fof(i_0_10540,plain,
    ! [X32886,X32887,X32888] :
      ( X32888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Ohd(X32887),c_List_Oreplicate(X32887,X32888,X32886)) = X32886 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])]) ).

cnf(i_0_10541,plain,
    c_Code__Numeral_OSuc__code__numeral(X1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[i_0_6034]) ).

cnf(i_0_10542,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X1),
    inference(split_conjunct,[status(thm)],[i_0_6035]) ).

fof(i_0_10543,plain,
    ! [X34274,X34275] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X34275),X34274))
      | ~ hBOOL(X34275)
      | hBOOL(X34274) ),
    inference(variable_rename,[status(thm)],[i_0_6036]) ).

fof(i_0_10544,plain,
    ! [X24322,X24323] :
      ( ~ class_Orderings_Olinorder(X24323)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24323,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24323),X24322)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24323),X24322) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).

fof(i_0_10545,plain,
    ! [X24316,X24317] :
      ( ~ class_Orderings_Olinorder(X24317)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24317,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24317),X24316)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24317),X24316) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).

fof(i_0_10546,plain,
    ! [X24320,X24321] :
      ( ~ class_Orderings_Olinorder(X24321)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24321,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24321),X24320)) = hAPP(c_SetInterval_Oord__class_OatMost(X24321),X24320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).

fof(i_0_10547,plain,
    ! [X24318,X24319] :
      ( ~ class_Orderings_Olinorder(X24319)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24319,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24319),X24318)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24319),X24318) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).

fof(i_0_10548,plain,
    ! [X22615,X22616] :
      ( ( hAPP(c_Finite__Set_Ocard(X22616),X22615) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22615 = c_Orderings_Obot__class_Obot(tc_fun(X22616,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22616),X22615)) )
      & ( X22615 != c_Orderings_Obot__class_Obot(tc_fun(X22616,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X22616),X22615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22616),X22615))
        | hAPP(c_Finite__Set_Ocard(X22616),X22615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6037])])]) ).

fof(i_0_10549,plain,
    ! [X16955,X16956] : c_Hoare__Mirabelle_Ohoare__derivs(X16956,X16955,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16956),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(i_0_10550,plain,
    ! [X16953,X16954] : c_Hoare__Mirabelle_Ohoare__derivs(X16954,X16953,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16954),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_empty]) ).

fof(i_0_10551,plain,
    ! [X25196,X25197] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25197)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25197),X25196))
      | X25196 = c_Orderings_Obot__class_Obot(tc_fun(X25197,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X25197,X25196) = c_Complete__Lattice_OSup__class_OSup(X25197,X25196) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).

fof(i_0_10552,plain,
    ! [X21597,X21598] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21598)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21598),X21597))
      | X21597 = c_Orderings_Obot__class_Obot(tc_fun(X21598,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X21598,X21597) = c_Complete__Lattice_OInf__class_OInf(X21598,X21597) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).

fof(i_0_10553,plain,
    ! [X25927,X25928] :
      ( ~ class_Int_Onumber__ring(X25928)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25928),hAPP(c_Int_Onumber__class_Onumber__of(X25928),c_Int_OPls)),X25927) = X25927 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_10554,plain,
    ! [X22465,X22466] :
      ( ( X22466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22466 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22465 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22466 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22465 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22466 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22465 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22466 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22465 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22466),X22465) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).

fof(i_0_10555,plain,
    ! [X22463,X22464] :
      ( ( X22464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22464 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) )
      & ( X22463 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22464 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) )
      & ( X22464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) )
      & ( X22463 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) )
      & ( X22464 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) )
      & ( X22464 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22463 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22464),X22463) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_10556,plain,
    ! [X28421,X28422,X28423] :
      ( ~ hBOOL(hAPP(X28422,X28423))
      | hBOOL(hAPP(X28422,c_Hilbert__Choice_OEps(X28421,X28422))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).

fof(i_0_10557,plain,
    ! [X28395,X28396,X28397] :
      ( ~ hBOOL(hAPP(X28397,X28396))
      | hBOOL(hAPP(X28397,c_Hilbert__Choice_OEps(X28395,X28397))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).

fof(i_0_10558,plain,
    ! [X28392,X28393,X28394] :
      ( ~ hBOOL(hAPP(X28393,X28394))
      | hBOOL(hAPP(X28393,c_Hilbert__Choice_OEps(X28392,X28393))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).

fof(i_0_10559,plain,
    ! [X34268,X34269] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X34269),X34268))
      | hBOOL(X34269)
      | hBOOL(X34268) ),
    inference(variable_rename,[status(thm)],[i_0_6038]) ).

fof(i_0_10560,plain,
    ! [X24182,X24183] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24183),X24182) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X24183,X24182),
    inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_10561,plain,
    ! [X20018,X20019] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20019),X20018),X20018) != c_Groups_Oone__class_Oone(X20019)
        | X20018 = c_Groups_Oone__class_Oone(X20019)
        | X20018 = hAPP(c_Groups_Ouminus__class_Ouminus(X20019),c_Groups_Oone__class_Oone(X20019))
        | ~ class_Rings_Oring__1__no__zero__divisors(X20019) )
      & ( X20018 != c_Groups_Oone__class_Oone(X20019)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20019),X20018),X20018) = c_Groups_Oone__class_Oone(X20019)
        | ~ class_Rings_Oring__1__no__zero__divisors(X20019) )
      & ( X20018 != hAPP(c_Groups_Ouminus__class_Ouminus(X20019),c_Groups_Oone__class_Oone(X20019))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20019),X20018),X20018) = c_Groups_Oone__class_Oone(X20019)
        | ~ class_Rings_Oring__1__no__zero__divisors(X20019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).

fof(i_0_10562,plain,
    ! [X16950,X16951] :
      ( hAPP(X16951,esk1_2(X16950,X16951)) != hAPP(X16950,esk1_2(X16950,X16951))
      | X16951 = X16950 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_10563,plain,
    ! [X30225,X30226,X30227] : hAPP(hAPP(c_List_Ozip(X30227,X30226),X30225),c_List_Olist_ONil(X30226)) = c_List_Olist_ONil(tc_prod(X30227,X30226)),
    inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(i_0_10564,plain,
    ! [X17205,X17206,X17207,X17208] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17208,X17207,X17206)
      | hAPP(hAPP(X17207,X17205),X17205) = X17205 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).

fof(i_0_10565,plain,
    ! [X31558] : c_Enum_Osublists(X31558,c_List_Olist_ONil(X31558)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31558)),c_List_Olist_ONil(X31558)),c_List_Olist_ONil(tc_List_Olist(X31558))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(i_0_10566,plain,
    ! [X33986,X33987] :
      ( ~ class_Rings_Ocomm__semiring__1(X33987)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33987),X33986),c_Groups_Ozero__class_Ozero(X33987))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).

fof(i_0_10567,plain,
    ! [X19672,X19673] :
      ( ~ class_Orderings_Otop(X19673)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19673),X19672),c_Orderings_Otop__class_Otop(X19673))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_10568,plain,
    ! [X30974,X30975,X30976] :
      ( X30976 != c_List_Olist_ONil(X30975)
      | c_List_Olast(X30975,hAPP(hAPP(c_List_Olist_OCons(X30975),X30974),X30976)) = X30974 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).

fof(i_0_10569,plain,
    ! [X32893,X32894,X32895] :
      ( X32895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_List_Olast(X32894,c_List_Oreplicate(X32894,X32895,X32893)) = X32893 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])]) ).

fof(i_0_10570,plain,
    ! [X26025,X26026,X26027] : hAPP(c_Nat_Onat_Onat__rec(X26027,X26026,X26025),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26026,
    inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).

fof(i_0_10571,plain,
    ! [X17127,X17128,X17129] : hAPP(hAPP(c_Set_Oinsert(X17129),X17128),X17127) != c_Orderings_Obot__class_Obot(tc_fun(X17129,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).

fof(i_0_10572,plain,
    ! [X17130,X17131,X17132] : c_Orderings_Obot__class_Obot(tc_fun(X17132,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X17132),X17131),X17130),
    inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).

fof(i_0_10573,plain,
    ! [X34260,X34261] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34261),X34260))
      | hBOOL(X34261) ),
    inference(variable_rename,[status(thm)],[i_0_6039]) ).

fof(i_0_10574,plain,
    ! [X34262,X34263] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34263),X34262))
      | hBOOL(X34262) ),
    inference(variable_rename,[status(thm)],[i_0_6040]) ).

fof(i_0_10575,plain,
    ! [X22866] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X22866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22866)),
    inference(variable_rename,[status(thm)],[fact_int__Suc]) ).

fof(i_0_10576,plain,
    ! [X23040,X23041] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23041),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23040)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23041),X23040),
    inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(i_0_10577,plain,
    ! [X23038,X23039] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23039),X23038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23038)),
    inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).

fof(i_0_10578,plain,
    ! [X30737,X30738,X30739] : hAPP(c_List_Otl(X30739),hAPP(hAPP(c_List_Olist_OCons(X30739),X30738),X30737)) = X30737,
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(i_0_10579,plain,
    ! [X30713,X30714,X30715] : hAPP(c_List_Ohd(X30715),hAPP(hAPP(c_List_Olist_OCons(X30715),X30714),X30713)) = X30714,
    inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).

fof(i_0_10580,plain,
    ! [X22073,X22074,X22075] :
      ( ( X22074 = c_Groups_Ozero__class_Ozero(X22075)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22075),X22074),X22073) != c_Groups_Ozero__class_Ozero(X22075)
        | ~ class_Power_Opower(X22075)
        | ~ class_Rings_Omult__zero(X22075)
        | ~ class_Rings_Ono__zero__divisors(X22075)
        | ~ class_Rings_Ozero__neq__one(X22075) )
      & ( X22073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22075),X22074),X22073) != c_Groups_Ozero__class_Ozero(X22075)
        | ~ class_Power_Opower(X22075)
        | ~ class_Rings_Omult__zero(X22075)
        | ~ class_Rings_Ono__zero__divisors(X22075)
        | ~ class_Rings_Ozero__neq__one(X22075) )
      & ( X22074 != c_Groups_Ozero__class_Ozero(X22075)
        | X22073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22075),X22074),X22073) = c_Groups_Ozero__class_Ozero(X22075)
        | ~ class_Power_Opower(X22075)
        | ~ class_Rings_Omult__zero(X22075)
        | ~ class_Rings_Ono__zero__divisors(X22075)
        | ~ class_Rings_Ozero__neq__one(X22075) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).

fof(i_0_10581,plain,
    ! [X24707,X24708] :
      ( ~ c_Nat__Transfer_Ois__nat(X24708)
      | ~ c_Nat__Transfer_Ois__nat(X24707)
      | c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X24708,X24707)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10582,plain,
    ! [X25293,X25294,X25295,X25296,X25298] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25294,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X25294),X25293)
        | ~ hBOOL(hAPP(X25293,X25295)) )
      & ( hBOOL(hAPP(X25296,esk237_1(X25296)))
        | c_Orderings_Obot__class_Obot(tc_fun(X25298,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X25298),X25296) ) ),
    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_6041])])])])]) ).

fof(i_0_10583,plain,
    ! [X25299,X25300,X25301,X25302,X25304] :
      ( ( hAPP(c_Set_OCollect(X25300),X25299) != c_Orderings_Obot__class_Obot(tc_fun(X25300,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X25299,X25301)) )
      & ( hBOOL(hAPP(X25302,esk238_1(X25302)))
        | hAPP(c_Set_OCollect(X25304),X25302) = c_Orderings_Obot__class_Obot(tc_fun(X25304,tc_HOL_Obool)) ) ),
    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_6042])])])])]) ).

fof(i_0_10584,plain,
    ! [X34252,X34253] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X34253),X34252))
      | X34253 = X34252 ),
    inference(variable_rename,[status(thm)],[i_0_6043]) ).

fof(i_0_10585,plain,
    ! [X26356,X26357] :
      ( ~ class_Fields_Ofield__inverse__zero(X26357)
      | ~ class_Int_Onumber__ring(X26357)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26357),X26356),hAPP(c_Int_Onumber__class_Onumber__of(X26357),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X26357),X26356) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).

fof(i_0_10586,plain,
    ! [X27611,X27612,X27613] :
      ( ~ c_Wellfounded_Owf(X27613,X27612)
      | c_Wellfounded_Owf(tc_List_Olist(X27613),hAPP(c_List_Olexn(X27613,X27612),X27611)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).

fof(i_0_10587,plain,
    ! [X30242,X30243,X30244] : hAPP(hAPP(c_List_Olist__update(X30244,c_List_Olist_ONil(X30244)),X30243),X30242) = c_List_Olist_ONil(X30244),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(i_0_10588,plain,
    ! [X30239,X30240,X30241] : hAPP(hAPP(c_List_Olist__update(X30241,c_List_Olist_ONil(X30241)),X30240),X30239) = c_List_Olist_ONil(X30241),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(i_0_10589,plain,
    ! [X22139] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22139) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).

fof(i_0_10590,plain,
    ! [X32422,X32423] : c_List_Oinsert(X32423,X32422,c_List_Olist_ONil(X32423)) = hAPP(hAPP(c_List_Olist_OCons(X32423),X32422),c_List_Olist_ONil(X32423)),
    inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).

fof(i_0_10591,plain,
    ! [X29806,X29807] : hBOOL(hAPP(c_Finite__Set_Ofinite(X29807),hAPP(c_List_Oset(X29807),X29806))),
    inference(variable_rename,[status(thm)],[fact_finite__set]) ).

fof(i_0_10592,plain,
    ! [X29109,X29110,X29111] : hAPP(c_Relation_Oconverse(X29111,X29110),hAPP(c_Relation_Oconverse(X29110,X29111),X29109)) = X29109,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

fof(i_0_10593,plain,
    ! [X22763] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22763)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X22763),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22763)),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).

fof(i_0_10594,plain,
    ! [X29115,X29116] : hAPP(c_Relation_OField(X29116),hAPP(c_Relation_Oconverse(X29116,X29116),X29115)) = hAPP(c_Relation_OField(X29116),X29115),
    inference(variable_rename,[status(thm)],[fact_Field__converse]) ).

fof(i_0_10595,plain,
    ! [X25767,X25768] :
      ( ~ class_Int_Onumber__ring(X25768)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25768),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25767)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25768),hAPP(c_Int_Onumber__class_Onumber__of(X25768),X25767)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_10596,plain,
    ! [X24062,X24063] :
      ( ~ class_Rings_Oring__1(X24063)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24063),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24062)) = hAPP(c_Groups_Ouminus__class_Ouminus(X24063),hAPP(c_Int_Oring__1__class_Oof__int(X24063),X24062)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).

fof(i_0_10597,plain,
    ! [X25765,X25766] :
      ( ~ class_Int_Onumber__ring(X25766)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25766),hAPP(c_Int_Onumber__class_Onumber__of(X25766),X25765)) = hAPP(c_Int_Onumber__class_Onumber__of(X25766),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25765)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_10598,plain,
    ! [X22140,X22141] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22141),X22140) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22141 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22140 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22141),X22140) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22141 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22141),X22140) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).

fof(i_0_10599,plain,
    ! [X17624,X17625,X17626] :
      ( ~ class_Orderings_Opreorder(X17626)
      | X17625 != X17624
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17626),X17625),X17624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_10600,plain,
    ! [X23421,X23422] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X23422,X23421)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X23421)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I6_J]) ).

fof(i_0_10601,plain,
    ! [X22401,X22402,X22403] :
      ( ~ class_Groups_Ogroup__add(X22403)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22403),X22402),X22401) != c_Groups_Ozero__class_Ozero(X22403)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22403),X22402) = X22401 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_10602,plain,
    ! [X22408,X22409,X22410] :
      ( ( X22409 != hAPP(c_Groups_Ouminus__class_Ouminus(X22410),X22408)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22410),X22409),X22408) = c_Groups_Ozero__class_Ozero(X22410)
        | ~ class_Groups_Ogroup__add(X22410) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22410),X22409),X22408) != c_Groups_Ozero__class_Ozero(X22410)
        | X22409 = hAPP(c_Groups_Ouminus__class_Ouminus(X22410),X22408)
        | ~ class_Groups_Ogroup__add(X22410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_10603,plain,
    ! [X31652,X31653] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31653)),c_List_Oremdups(X31653,X31652)) = hAPP(c_Finite__Set_Ocard(X31653),hAPP(c_List_Oset(X31653),X31652)),
    inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(i_0_10604,plain,
    ! [X25307] : c_Orderings_Otop__class_Otop(tc_fun(X25307,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X25307),hAPP(c_COMBK(tc_HOL_Obool,X25307),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(i_0_10605,plain,
    ! [X25292] : c_Orderings_Obot__class_Obot(tc_fun(X25292,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X25292),hAPP(c_COMBK(tc_HOL_Obool,X25292),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(i_0_10606,plain,
    ! [X24294,X24295] :
      ( ~ c_Nat__Transfer_Ois__nat(X24295)
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24295,X24294)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).

fof(i_0_10607,plain,
    ! [X26349,X26350] :
      ( ~ class_Int_Onumber__ring(X26350)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26350),X26349),hAPP(c_Int_Onumber__class_Onumber__of(X26350),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X26350),X26349) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).

fof(i_0_10608,plain,
    ! [X22478,X22479] :
      ( ( X22479 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22479),X22478) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22478 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22479),X22478) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22479 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22478 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22479),X22478) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])]) ).

fof(i_0_10609,plain,
    ! [X26969] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X26969)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X26969)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J]) ).

fof(i_0_10610,plain,
    ! [X34162,X34163] :
      ( ~ class_Rings_Ocomm__semiring__1(X34163)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X34163),X34162),X34162)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).

fof(i_0_10611,plain,
    ! [X17560,X17561] :
      ( ~ class_Orderings_Opreorder(X17561)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17561),X17560),X17560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_10612,plain,
    ! [X23694] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23694)) = hAPP(c_Int_Onat,X23694),
    inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(i_0_10613,plain,
    ! [X23053] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23053)),X23053) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_10614,plain,
    ! [X24143,X24144] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24144),hAPP(c_Nat_OSuc,X24143)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24144,X24143),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_10615,plain,
    ! [X26908,X26909] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X26909,X26908) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X26909,X26908)),
    inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).

fof(i_0_10616,plain,
    ! [X20547,X20548,X20549] :
      ( ~ class_Lattices_Osemilattice__inf(X20549)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20549),X20548),X20547) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20549),X20547),X20548) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).

fof(i_0_10617,plain,
    ! [X20541,X20542,X20543] :
      ( ~ class_Lattices_Osemilattice__inf(X20543)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20543),X20542),X20541) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20543),X20541),X20542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).

fof(i_0_10618,plain,
    ! [X20544,X20545,X20546] :
      ( ~ class_Lattices_Olattice(X20546)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20546),X20545),X20544) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20546),X20544),X20545) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).

fof(i_0_10619,plain,
    ! [X19448,X19449,X19450] :
      ( ~ class_Lattices_Osemilattice__sup(X19450)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19450),X19449),X19448) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19450),X19448),X19449) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).

fof(i_0_10620,plain,
    ! [X19442,X19443,X19444] :
      ( ~ class_Lattices_Osemilattice__sup(X19444)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19444),X19443),X19442) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19444),X19442),X19443) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).

fof(i_0_10621,plain,
    ! [X19445,X19446,X19447] :
      ( ~ class_Lattices_Olattice(X19447)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19447),X19446),X19445) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19447),X19445),X19446) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).

fof(i_0_10622,plain,
    ! [X18786,X18787,X18788] :
      ( ~ class_Orderings_Olinorder(X18788)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18788),X18787),X18786) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18788),X18786),X18787) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).

fof(i_0_10623,plain,
    ! [X18783,X18784,X18785] :
      ( ~ class_Orderings_Olinorder(X18785)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18785),X18784),X18783) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X18785),X18783),X18784) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).

fof(i_0_10624,plain,
    ! [X18780,X18781,X18782] :
      ( ~ class_Orderings_Olinorder(X18782)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18782),X18781),X18780) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18782),X18780),X18781) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).

fof(i_0_10625,plain,
    ! [X18777,X18778,X18779] :
      ( ~ class_Orderings_Olinorder(X18779)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18779),X18778),X18777) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X18779),X18777),X18778) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).

fof(i_0_10626,plain,
    ! [X18626,X18627,X18628] :
      ( ~ class_Rings_Ocomm__semiring__1(X18628)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18628),X18627),X18626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18628),X18626),X18627) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(i_0_10627,plain,
    ! [X18592,X18593,X18594] :
      ( ~ class_Rings_Ocomm__semiring__1(X18594)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18594),X18593),X18592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18594),X18592),X18593) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_10628,plain,
    ! [X23690] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23690))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).

fof(i_0_10629,plain,
    ! [X22155] :
      ( X22155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_10630,plain,
    ! [X24033,X24034] :
      ( ~ c_Nat__Transfer_Ois__nat(X24034)
      | ~ c_Nat__Transfer_Ois__nat(X24033)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24034),X24033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10631,plain,
    ! [X24031,X24032] :
      ( ~ c_Nat__Transfer_Ois__nat(X24032)
      | ~ c_Nat__Transfer_Ois__nat(X24031)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24032),X24031)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10632,plain,
    ! [X24028,X24029] :
      ( ~ c_Nat__Transfer_Ois__nat(X24029)
      | ~ c_Nat__Transfer_Ois__nat(X24028)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24029),X24028)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10633,plain,
    ! [X22858,X22859] :
      ( ( X22859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22859)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22858) )
      & ( X22858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22859)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22858) )
      & ( X22859 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22858 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22859)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22858) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).

fof(i_0_10634,plain,
    ! [X25678,X25679,X25680,X25681,X25682] : c_Com_Ocom_OLocal(X25682,X25681,X25680) != c_Com_Ocom_OWhile(X25679,X25678),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I38_J]) ).

fof(i_0_10635,plain,
    ! [X25695,X25696,X25697,X25698,X25699] : c_Com_Ocom_OLocal(X25699,X25698,X25697) != c_Com_Ocom_OSemi(X25696,X25695),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J]) ).

fof(i_0_10636,plain,
    ! [X25593,X25594,X25595,X25596,X25597] : c_Com_Ocom_OCond(X25597,X25596,X25595) != c_Com_Ocom_OWhile(X25594,X25593),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I52_J]) ).

fof(i_0_10637,plain,
    ! [X25603,X25604,X25605,X25606,X25607] : c_Com_Ocom_OCond(X25607,X25606,X25605) != c_Com_Ocom_OSemi(X25604,X25603),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J]) ).

fof(i_0_10638,plain,
    ! [X25673,X25674,X25675,X25676,X25677] : c_Com_Ocom_OWhile(X25677,X25676) != c_Com_Ocom_OLocal(X25675,X25674,X25673),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J]) ).

fof(i_0_10639,plain,
    ! [X25598,X25599,X25600,X25601,X25602] : c_Com_Ocom_OWhile(X25602,X25601) != c_Com_Ocom_OCond(X25600,X25599,X25598),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I53_J]) ).

fof(i_0_10640,plain,
    ! [X25700,X25701,X25702,X25703,X25704] : c_Com_Ocom_OSemi(X25704,X25703) != c_Com_Ocom_OLocal(X25702,X25701,X25700),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I35_J]) ).

fof(i_0_10641,plain,
    ! [X25608,X25609,X25610,X25611,X25612] : c_Com_Ocom_OSemi(X25612,X25611) != c_Com_Ocom_OCond(X25610,X25609,X25608),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I44_J]) ).

cnf(i_0_10642,plain,
    hAPP(c_Code__Numeral_Onat__of,X1) = c_Code__Numeral_Onat__of__aux(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_6044]) ).

fof(i_0_10643,plain,
    ! [X22162] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22162)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_10644,plain,
    ! [X22031] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22031)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_10645,plain,
    ! [X29328,X29329] : c_Relation_Ototal__on(X29329,c_Orderings_Obot__class_Obot(tc_fun(X29329,tc_HOL_Obool)),X29328),
    inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).

fof(i_0_10646,plain,
    ! [X22103,X22104,X22105] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22105),X22104),X22103) != c_Groups_Ozero__class_Ozero(X22105)
        | X22104 = c_Groups_Ozero__class_Ozero(X22105)
        | X22103 = c_Groups_Ozero__class_Ozero(X22105)
        | ~ class_Rings_Oring__no__zero__divisors(X22105) )
      & ( X22104 != c_Groups_Ozero__class_Ozero(X22105)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22105),X22104),X22103) = c_Groups_Ozero__class_Ozero(X22105)
        | ~ class_Rings_Oring__no__zero__divisors(X22105) )
      & ( X22103 != c_Groups_Ozero__class_Ozero(X22105)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22105),X22104),X22103) = c_Groups_Ozero__class_Ozero(X22105)
        | ~ class_Rings_Oring__no__zero__divisors(X22105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_10647,plain,
    ! [X22109,X22110,X22111] :
      ( ~ class_Rings_Ono__zero__divisors(X22111)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22111),X22110),X22109) != c_Groups_Ozero__class_Ozero(X22111)
      | X22110 = c_Groups_Ozero__class_Ozero(X22111)
      | X22109 = c_Groups_Ozero__class_Ozero(X22111) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_10648,plain,
    ! [X22106,X22107,X22108] :
      ( ~ class_Rings_Ono__zero__divisors(X22108)
      | X22107 = c_Groups_Ozero__class_Ozero(X22108)
      | X22106 = c_Groups_Ozero__class_Ozero(X22108)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22108),X22107),X22106) != c_Groups_Ozero__class_Ozero(X22108) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_10649,plain,
    ! [X26794] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26794) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_posDivAlg__0]) ).

fof(i_0_10650,plain,
    ! [X27019,X27020] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X27020),X27019) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X27020,X27019)),
    inference(variable_rename,[status(thm)],[fact_div__int__def]) ).

fof(i_0_10651,plain,
    ! [X22439,X22440] :
      ( ~ class_Power_Opower(X22440)
      | ~ class_Rings_Osemiring__0(X22440)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22440),c_Groups_Ozero__class_Ozero(X22440)),hAPP(c_Nat_OSuc,X22439)) = c_Groups_Ozero__class_Ozero(X22440) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).

fof(i_0_10652,plain,
    ! [X25939,X25940] :
      ( ~ class_Fields_Ofield__inverse__zero(X25940)
      | ~ class_Int_Onumber__ring(X25940)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25940),X25939),hAPP(c_Int_Onumber__class_Onumber__of(X25940),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X25940) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_10653,plain,
    ! [X25100,X25101] :
      ( ~ class_Rings_Olinordered__idom(X25101)
      | hAPP(c_Groups_Oabs__class_Oabs(X25101),X25100) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25101),X25100),c_Groups_Osgn__class_Osgn(X25101,X25100)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).

fof(i_0_10654,plain,
    ! [X29729] : c_List_Olists(X29729,c_Orderings_Otop__class_Otop(tc_fun(X29729,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X29729),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).

fof(i_0_10655,plain,
    ! [X31146,X31147] : hAPP(hAPP(c_List_Omap(X31147,X31147),c_COMBI(X31147)),X31146) = X31146,
    inference(variable_rename,[status(thm)],[fact_map__ident]) ).

fof(i_0_10656,plain,
    ! [X28184,X28185,X28186] :
      ( ~ c_Wellfounded_OwfP(X28186,X28185)
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X28186,X28185),X28184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).

fof(i_0_10657,plain,
    ! [X28230,X28231,X28232] :
      ( ~ c_Predicate_Oreflp(X28232,X28231)
      | hBOOL(hAPP(hAPP(X28231,X28230),X28230)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).

fof(i_0_10658,plain,
    ! [X27168,X27169,X27170] :
      ( ~ c_Equiv__Relations_Oequivp(X27170,X27169)
      | hBOOL(hAPP(hAPP(X27169,X27168),X27168)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).

fof(i_0_10659,plain,
    ! [X30260,X30261] : c_List_Osublist(X30261,X30260,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X30261),
    inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).

fof(i_0_10660,plain,
    ! [X23623,X23624,X23625] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23625),X23623),X23624) != c_Groups_Oone__class_Oone(X23625)
        | X23623 = X23624
        | X23624 = c_Groups_Ozero__class_Ozero(X23625)
        | ~ class_Rings_Odivision__ring(X23625) )
      & ( X23623 != X23624
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23625),X23623),X23624) = c_Groups_Oone__class_Oone(X23625)
        | X23624 = c_Groups_Ozero__class_Ozero(X23625)
        | ~ class_Rings_Odivision__ring(X23625) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_10661,plain,
    ! [X32184,X32185] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32185)),hAPP(c_List_Orev(X32185),X32184)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32185)),X32184),
    inference(variable_rename,[status(thm)],[fact_length__rev]) ).

fof(i_0_10662,plain,
    ! [X30627,X30628] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30628)),hAPP(c_List_Orotate1(X30628),X30627)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30628)),X30627),
    inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).

fof(i_0_10663,plain,
    ! [X28446,X28447,X28448,X28449] :
      ( ~ hBOOL(hAPP(X28448,X28449))
      | X28447 != c_Hilbert__Choice_OEps(X28446,X28448)
      | hBOOL(hAPP(X28448,X28447)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).

fof(i_0_10664,plain,
    ! [X29359,X29360] : hAPP(hAPP(c_Nat_Ocompow(X29360,X29360),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29359) = c_Fun_Oid(X29360),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(i_0_10665,plain,
    ! [X31077,X31078,X31079] : hAPP(hAPP(c_List_Omap(X31079,X31078),X31077),c_List_Olist_ONil(X31079)) = c_List_Olist_ONil(X31078),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(i_0_10666,plain,
    ! [X20841,X20842] :
      ( ~ class_Lattices_Oboolean__algebra(X20842)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20842),X20841),hAPP(c_Groups_Ouminus__class_Ouminus(X20842),X20841)) = c_Orderings_Obot__class_Obot(X20842) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).

fof(i_0_10667,plain,
    ! [X19497,X19498] :
      ( ~ class_Lattices_Oboolean__algebra(X19498)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19498),X19497),hAPP(c_Groups_Ouminus__class_Ouminus(X19498),X19497)) = c_Orderings_Otop__class_Otop(X19498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).

fof(i_0_10668,plain,
    ! [X22411,X22412] :
      ( ~ class_Groups_Ogroup__add(X22412)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22412),X22411),hAPP(c_Groups_Ouminus__class_Ouminus(X22412),X22411)) = c_Groups_Ozero__class_Ozero(X22412) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_10669,plain,
    ! [X24035,X24036] :
      ( ~ c_Nat__Transfer_Ois__nat(X24036)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24036),X24035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).

fof(i_0_10670,plain,
    ! [X26362,X26363] :
      ( ( X26363 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X26363 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X26362 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X26363 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X26363 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X26362 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X26362 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X26362 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X26363 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X26362 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X26363 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X26362 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26363),X26362) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])]) ).

fof(i_0_10671,plain,
    ! [X20688,X20689,X20690] :
      ( ( X20689 = c_Orderings_Otop__class_Otop(X20690)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20690),X20689),X20688) != c_Orderings_Otop__class_Otop(X20690)
        | ~ class_Lattices_Obounded__lattice__top(X20690) )
      & ( X20688 = c_Orderings_Otop__class_Otop(X20690)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20690),X20689),X20688) != c_Orderings_Otop__class_Otop(X20690)
        | ~ class_Lattices_Obounded__lattice__top(X20690) )
      & ( X20689 != c_Orderings_Otop__class_Otop(X20690)
        | X20688 != c_Orderings_Otop__class_Otop(X20690)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20690),X20689),X20688) = c_Orderings_Otop__class_Otop(X20690)
        | ~ class_Lattices_Obounded__lattice__top(X20690) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).

fof(i_0_10672,plain,
    ! [X19563,X19564,X19565] :
      ( ( X19564 = c_Orderings_Obot__class_Obot(X19565)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19565),X19564),X19563) != c_Orderings_Obot__class_Obot(X19565)
        | ~ class_Lattices_Obounded__lattice__bot(X19565) )
      & ( X19563 = c_Orderings_Obot__class_Obot(X19565)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19565),X19564),X19563) != c_Orderings_Obot__class_Obot(X19565)
        | ~ class_Lattices_Obounded__lattice__bot(X19565) )
      & ( X19564 != c_Orderings_Obot__class_Obot(X19565)
        | X19563 != c_Orderings_Obot__class_Obot(X19565)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19565),X19564),X19563) = c_Orderings_Obot__class_Obot(X19565)
        | ~ class_Lattices_Obounded__lattice__bot(X19565) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).

fof(i_0_10673,plain,
    ! [X22142,X22143,X22144] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X22144)
      | X22143 = c_Groups_Ozero__class_Ozero(X22144)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22144),X22143),X22142) != c_Groups_Ozero__class_Ozero(X22144) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).

fof(i_0_10674,plain,
    ! [X22785,X22786] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22786),X22785),X22785) != c_Groups_Ozero__class_Ozero(X22786)
        | X22785 = c_Groups_Ozero__class_Ozero(X22786)
        | ~ class_Groups_Olinordered__ab__group__add(X22786) )
      & ( X22785 != c_Groups_Ozero__class_Ozero(X22786)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22786),X22785),X22785) = c_Groups_Ozero__class_Ozero(X22786)
        | ~ class_Groups_Olinordered__ab__group__add(X22786) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_10675,plain,
    ! [X22082,X22083] :
      ( ( c_Groups_Ozero__class_Ozero(X22083) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22083),X22082),X22082)
        | X22082 = c_Groups_Ozero__class_Ozero(X22083)
        | ~ class_Groups_Olinordered__ab__group__add(X22083) )
      & ( X22082 != c_Groups_Ozero__class_Ozero(X22083)
        | c_Groups_Ozero__class_Ozero(X22083) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22083),X22082),X22082)
        | ~ class_Groups_Olinordered__ab__group__add(X22083) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_10676,plain,
    ! [X24280] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24280))),
    inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).

fof(i_0_10677,plain,
    ! [X22758] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22758))),
    inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).

cnf(i_0_10678,plain,
    ( c_Code__Numeral_Onat__of__aux(X1,X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_5819]) ).

fof(i_0_10679,plain,
    ! [X25865] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25865)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25865)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_10680,plain,
    ! [X22119,X22120,X22121] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22121),X22120),X22119) != c_Groups_Ozero__class_Ozero(X22121)
        | X22120 = X22119
        | ~ class_Groups_Ogroup__add(X22121) )
      & ( X22120 != X22119
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22121),X22120),X22119) = c_Groups_Ozero__class_Ozero(X22121)
        | ~ class_Groups_Ogroup__add(X22121) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).

fof(i_0_10681,plain,
    ! [X22116,X22117,X22118] :
      ( ( X22117 != X22116
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22118),X22117),X22116) = c_Groups_Ozero__class_Ozero(X22118)
        | ~ class_Groups_Oab__group__add(X22118) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22118),X22117),X22116) != c_Groups_Ozero__class_Ozero(X22118)
        | X22117 = X22116
        | ~ class_Groups_Oab__group__add(X22118) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).

fof(i_0_10682,plain,
    ! [X19908,X19909] :
      ( X19909 != X19908
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19909),X19908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_10683,plain,
    ! [X30203,X30204,X30205] :
      ( ( hAPP(hAPP(c_List_Otake(X30205),X30204),X30203) != c_List_Olist_ONil(X30205)
        | X30204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30203 = c_List_Olist_ONil(X30205) )
      & ( X30204 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X30205),X30204),X30203) = c_List_Olist_ONil(X30205) )
      & ( X30203 != c_List_Olist_ONil(X30205)
        | hAPP(hAPP(c_List_Otake(X30205),X30204),X30203) = c_List_Olist_ONil(X30205) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).

fof(i_0_10684,plain,
    ! [X26364,X26365] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26365),X26364) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X26365 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X26365 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma])]) ).

fof(i_0_10685,plain,
    ! [X22092,X22093,X22094] :
      ( ( X22093 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22094),X22093),X22092)
        | X22092 = c_Groups_Ozero__class_Ozero(X22094)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22094) )
      & ( X22092 != c_Groups_Ozero__class_Ozero(X22094)
        | X22093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22094),X22093),X22092)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22094) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_10686,plain,
    ! [X32950,X32951,X32952] :
      ( ( c_List_Oreplicate(X32952,X32951,X32950) != c_List_Olist_ONil(X32952)
        | X32951 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X32951 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(X32952,X32951,X32950) = c_List_Olist_ONil(X32952) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])]) ).

fof(i_0_10687,plain,
    ! [X32947,X32948,X32949] :
      ( ( c_List_Olist_ONil(X32949) != c_List_Oreplicate(X32949,X32948,X32947)
        | X32948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X32948 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(X32949) = c_List_Oreplicate(X32949,X32948,X32947) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__replicate])]) ).

fof(i_0_10688,plain,
    ! [X21874] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21874)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21874,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(i_0_10689,plain,
    ! [X29985,X29986] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29986,X29985)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29986,X29985),
    inference(variable_rename,[status(thm)],[fact_set__upto]) ).

fof(i_0_10690,plain,
    ! [X29983,X29984] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29984,X29983) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29984,X29983)),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(i_0_10691,plain,
    ! [X32703,X32704] : ~ c_List_Olist__ex1(X32704,X32703,c_List_Olist_ONil(X32704)),
    inference(variable_rename,[status(thm)],[i_0_6045]) ).

fof(i_0_10692,plain,
    ! [X32600,X32601] : ~ c_List_Olist__ex(X32601,X32600,c_List_Olist_ONil(X32601)),
    inference(variable_rename,[status(thm)],[i_0_6046]) ).

fof(i_0_10693,plain,
    ! [X25929,X25930] :
      ( ~ class_Int_Onumber__ring(X25930)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25930),X25929),hAPP(c_Int_Onumber__class_Onumber__of(X25930),c_Int_OPls)) = X25929 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

fof(i_0_10694,plain,
    ! [X33985] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33985),X33985)),
    inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).

fof(i_0_10695,plain,
    ! [X23054] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23054),X23054)),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_10696,plain,
    ! [X19890] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19890),X19890)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_10697,plain,
    ! [X31372,X31373] : hBOOL(hAPP(c_List_Olistsp(X31373,X31372),c_List_Olist_ONil(X31373))),
    inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(i_0_10698,plain,
    ! [X31370,X31371] : hBOOL(hAPP(c_List_Olistsp(X31371,X31370),c_List_Olist_ONil(X31371))),
    inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).

fof(i_0_10699,plain,
    ! [X31604,X31605] : hBOOL(hAPP(c_List_Odistinct(X31605),c_List_Oremdups(X31605,X31604))),
    inference(variable_rename,[status(thm)],[fact_distinct__remdups]) ).

fof(i_0_10700,plain,
    ! [X30460,X30461,X30462] :
      ( ( X30461 = c_List_Olist_ONil(X30462)
        | hAPP(hAPP(c_List_Oappend(X30462),X30461),X30460) != c_List_Olist_ONil(X30462) )
      & ( X30460 = c_List_Olist_ONil(X30462)
        | hAPP(hAPP(c_List_Oappend(X30462),X30461),X30460) != c_List_Olist_ONil(X30462) )
      & ( X30461 != c_List_Olist_ONil(X30462)
        | X30460 != c_List_Olist_ONil(X30462)
        | hAPP(hAPP(c_List_Oappend(X30462),X30461),X30460) = c_List_Olist_ONil(X30462) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).

fof(i_0_10701,plain,
    ! [X30449,X30450,X30451] :
      ( ( X30450 = c_List_Olist_ONil(X30451)
        | c_List_Olist_ONil(X30451) != hAPP(hAPP(c_List_Oappend(X30451),X30450),X30449) )
      & ( X30449 = c_List_Olist_ONil(X30451)
        | c_List_Olist_ONil(X30451) != hAPP(hAPP(c_List_Oappend(X30451),X30450),X30449) )
      & ( X30450 != c_List_Olist_ONil(X30451)
        | X30449 != c_List_Olist_ONil(X30451)
        | c_List_Olist_ONil(X30451) = hAPP(hAPP(c_List_Oappend(X30451),X30450),X30449) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).

cnf(i_0_10702,plain,
    c_Int_Opred(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[i_0_6047]) ).

cnf(i_0_10703,plain,
    c_Int_Osucc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[i_0_6048]) ).

cnf(i_0_10704,plain,
    c_List_Oupt(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_6049]) ).

fof(i_0_10705,plain,
    ! [X28961,X28962] : hAPP(c_Relation_ODomain(X28962,X28962),c_Transitive__Closure_Ortrancl(X28962,X28961)) = c_Orderings_Otop__class_Otop(tc_fun(X28962,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).

fof(i_0_10706,plain,
    ! [X28963,X28964] : hAPP(c_Relation_ORange(X28964,X28964),c_Transitive__Closure_Ortrancl(X28964,X28963)) = c_Orderings_Otop__class_Otop(tc_fun(X28964,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).

fof(i_0_10707,plain,
    ! [X34230,X34231,X34232,X34233] : hAPP(hAPP(c_COMBK(X34233,X34232),X34231),X34230) = X34231,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(i_0_10708,plain,
    ( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5981]) ).

fof(i_0_10709,plain,
    ! [X33140,X33141,X33142] : c_Lazy__Sequence_Olazy__sequence_OInsert(X33142,X33141,X33140) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X33142),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I3_J]) ).

fof(i_0_10710,plain,
    ! [X33137,X33138,X33139] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X33139) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33139,X33138,X33137),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I2_J]) ).

fof(i_0_10711,plain,
    ! [X26369] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26369),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26369),
    inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(i_0_10712,plain,
    ! [X22835,X22836] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22836),X22835) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22835),X22836),
    inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).

fof(i_0_10713,plain,
    ! [X20248,X20249] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20249),X20248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20248),X20249),
    inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).

fof(i_0_10714,plain,
    ! [X23030,X23031] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23031),X23030) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23030),X23031),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_10715,plain,
    ! [X19955,X19956] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19956),X19955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19955),X19956),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_10716,plain,
    ! [X27697,X27698,X27699] : hAPP(hAPP(c_Nitpick_Ofrac(X27699),X27698),X27697) = c_Nitpick_OAbs__Frac(X27699,c_Nitpick_Onorm__frac(X27698,X27697)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(i_0_10717,plain,
    ! [X22423,X22424] :
      ( ~ class_Groups_Ogroup__add(X22424)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22424),c_Groups_Ozero__class_Ozero(X22424)),X22423) = hAPP(c_Groups_Ouminus__class_Ouminus(X22424),X22423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).

fof(i_0_10718,plain,
    ! [X34258,X34259] :
      ( ~ hBOOL(X34259)
      | ~ hBOOL(X34258)
      | hBOOL(hAPP(hAPP(c_fconj,X34259),X34258)) ),
    inference(variable_rename,[status(thm)],[i_0_6050]) ).

fof(i_0_10719,plain,
    ! [X30466,X30467,X30468] :
      ( ( hAPP(hAPP(c_List_Oappend(X30468),X30467),X30466) != X30466
        | X30467 = c_List_Olist_ONil(X30468) )
      & ( X30467 != c_List_Olist_ONil(X30468)
        | hAPP(hAPP(c_List_Oappend(X30468),X30467),X30466) = X30466 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).

fof(i_0_10720,plain,
    ! [X30463,X30464,X30465] :
      ( ( hAPP(hAPP(c_List_Oappend(X30465),X30464),X30463) != X30464
        | X30463 = c_List_Olist_ONil(X30465) )
      & ( X30463 != c_List_Olist_ONil(X30465)
        | hAPP(hAPP(c_List_Oappend(X30465),X30464),X30463) = X30464 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).

fof(i_0_10721,plain,
    ! [X30454,X30455,X30456] :
      ( ( X30456 != hAPP(hAPP(c_List_Oappend(X30455),X30456),X30454)
        | X30454 = c_List_Olist_ONil(X30455) )
      & ( X30454 != c_List_Olist_ONil(X30455)
        | X30456 = hAPP(hAPP(c_List_Oappend(X30455),X30456),X30454) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).

fof(i_0_10722,plain,
    ! [X30457,X30458,X30459] :
      ( ( X30459 != hAPP(hAPP(c_List_Oappend(X30458),X30457),X30459)
        | X30457 = c_List_Olist_ONil(X30458) )
      & ( X30457 != c_List_Olist_ONil(X30458)
        | X30459 = hAPP(hAPP(c_List_Oappend(X30458),X30457),X30459) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).

fof(i_0_10723,plain,
    ! [X22076,X22077] :
      ( ( X22076 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22077),c_Groups_Ozero__class_Ozero(X22077)),X22076) = c_Groups_Oone__class_Oone(X22077)
        | ~ class_Power_Opower(X22077)
        | ~ class_Rings_Osemiring__0(X22077) )
      & ( X22076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22077),c_Groups_Ozero__class_Ozero(X22077)),X22076) = c_Groups_Ozero__class_Ozero(X22077)
        | ~ class_Power_Opower(X22077)
        | ~ class_Rings_Osemiring__0(X22077) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).

fof(i_0_10724,plain,
    ! [X30194,X30195,X30196] : hAPP(hAPP(c_List_Olist_OCons(X30196),X30195),X30194) != c_List_Olist_ONil(X30196),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(i_0_10725,plain,
    ! [X30191,X30192,X30193] : c_List_Olist_ONil(X30193) != hAPP(hAPP(c_List_Olist_OCons(X30193),X30192),X30191),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(i_0_10726,plain,
    ! [X30122,X30123] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X30123,X30122))),
    inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).

cnf(i_0_10727,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = c_Int_Opred(X1),
    inference(split_conjunct,[status(thm)],[i_0_6051]) ).

fof(i_0_10728,plain,
    ! [X25705,X25706,X25707] : c_Com_Ocom_OLocal(X25707,X25706,X25705) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I11_J]) ).

fof(i_0_10729,plain,
    ! [X25613,X25614,X25615] : c_Com_Ocom_OCond(X25615,X25614,X25613) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I15_J]) ).

fof(i_0_10730,plain,
    ! [X25708,X25709,X25710] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X25710,X25709,X25708),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J]) ).

fof(i_0_10731,plain,
    ! [X25616,X25617,X25618] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X25618,X25617,X25616),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I14_J]) ).

fof(i_0_10732,plain,
    ! [X29677,X29678] : c_List_Olistrel(X29678,c_Transitive__Closure_Ortrancl(X29678,X29677)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X29678),c_List_Olistrel1(X29678,X29677)),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(i_0_10733,plain,
    ! [X27543,X27544] :
      ( ~ c_Wellfounded_Owf(X27544,X27543)
      | c_Wellfounded_Owf(tc_fun(X27544,tc_HOL_Obool),c_Wellfounded_Omax__ext(X27544,X27543)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).

fof(i_0_10734,plain,
    ! [X27515,X27516] :
      ( ~ c_Wellfounded_Owf(X27516,X27515)
      | c_Wellfounded_Owf(tc_fun(X27516,tc_HOL_Obool),c_Wellfounded_Omin__ext(X27516,X27515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).

fof(i_0_10735,plain,
    ! [X32182,X32183] :
      ( ~ class_Groups_Ocomm__monoid__add(X32183)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X32183),hAPP(c_List_Orev(X32183),X32182)) = hAPP(c_List_Omonoid__add__class_Olistsum(X32183),X32182) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).

fof(i_0_10736,plain,
    ! [X24979,X24980] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24980)
      | hAPP(c_Groups_Oabs__class_Oabs(X24980),hAPP(c_Groups_Oabs__class_Oabs(X24980),X24979)) = hAPP(c_Groups_Oabs__class_Oabs(X24980),X24979) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).

fof(i_0_10737,plain,
    ! [X24974,X24975] :
      ( ~ class_Rings_Olinordered__idom(X24975)
      | hAPP(c_Groups_Oabs__class_Oabs(X24975),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24975),X24974)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24975),X24974) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).

fof(i_0_10738,plain,
    ! [X24972,X24973] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24973)
      | hAPP(c_Groups_Oabs__class_Oabs(X24973),hAPP(c_Groups_Ouminus__class_Ouminus(X24973),X24972)) = hAPP(c_Groups_Oabs__class_Oabs(X24973),X24972) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).

fof(i_0_10739,plain,
    ! [X26347] :
      ( ~ class_Int_Onumber__ring(X26347)
      | ~ c_Int_Oiszero(X26347,hAPP(c_Int_Onumber__class_Onumber__of(X26347),c_Int_OMin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6052])]) ).

fof(i_0_10740,plain,
    ! [X19639] : c_Orderings_Otop__class_Otop(tc_fun(X19639,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X19639,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).

fof(i_0_10741,plain,
    ! [X26360] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X26360,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__minus1__right]) ).

fof(i_0_10742,plain,
    ! [X24864] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24864,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mod__1]) ).

fof(i_0_10743,plain,
    ! [X22174,X22175] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22175),X22174) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22175 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22175),X22174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22174 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22175),X22174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).

fof(i_0_10744,plain,
    ! [X29561,X29562,X29563] : hAPP(hAPP(c_List_Olist_OCons(X29563),X29562),X29561) != X29561,
    inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).

fof(i_0_10745,plain,
    ! [X29558,X29559,X29560] : X29560 != hAPP(hAPP(c_List_Olist_OCons(X29559),X29558),X29560),
    inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).

fof(i_0_10746,plain,
    ! [X17493] : c_Finite__Set_Ofun__left__comm__idem(X17493,tc_fun(X17493,tc_HOL_Obool),c_Set_Oinsert(X17493)),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(i_0_10747,plain,
    ! [X34272,X34273] :
      ( ~ hBOOL(X34273)
      | hBOOL(hAPP(hAPP(c_fimplies,X34272),X34273)) ),
    inference(variable_rename,[status(thm)],[i_0_6053]) ).

fof(i_0_10748,plain,
    ! [X34264,X34265] :
      ( ~ hBOOL(X34265)
      | hBOOL(hAPP(hAPP(c_fdisj,X34265),X34264)) ),
    inference(variable_rename,[status(thm)],[i_0_6054]) ).

fof(i_0_10749,plain,
    ! [X34266,X34267] :
      ( ~ hBOOL(X34267)
      | hBOOL(hAPP(hAPP(c_fdisj,X34266),X34267)) ),
    inference(variable_rename,[status(thm)],[i_0_6055]) ).

fof(i_0_10750,plain,
    ! [X19418,X19419,X19420] :
      ( ~ class_Orderings_Otop(X19420)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X19419,X19420)),X19418) = c_Orderings_Otop__class_Otop(X19420) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_10751,plain,
    ! [X17176,X17177,X17178] :
      ( ~ class_Orderings_Obot(X17178)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17177,X17178)),X17176) = c_Orderings_Obot__class_Obot(X17178) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).

fof(i_0_10752,plain,
    ! [X17154,X17155,X17156] :
      ( ~ class_Orderings_Obot(X17156)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17155,X17156)),X17154) = c_Orderings_Obot__class_Obot(X17156) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).

fof(i_0_10753,plain,
    ! [X31348,X31349] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X31349),X31348) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X31349),X31348),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(i_0_10754,plain,
    ! [X33332,X33333] :
      ( ( c_Predicate_Oreflp(X33333,X33332)
        | ~ c_Equiv__Relations_Oequivp(X33333,X33332) )
      & ( c_Predicate_Osymp(X33333,X33332)
        | ~ c_Equiv__Relations_Oequivp(X33333,X33332) )
      & ( c_Predicate_Otransp(X33333,X33332)
        | ~ c_Equiv__Relations_Oequivp(X33333,X33332) )
      & ( ~ c_Predicate_Oreflp(X33333,X33332)
        | ~ c_Predicate_Osymp(X33333,X33332)
        | ~ c_Predicate_Otransp(X33333,X33332)
        | c_Equiv__Relations_Oequivp(X33333,X33332) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp__symp__transp])])]) ).

fof(i_0_10755,plain,
    ! [X33326,X33327] :
      ( ~ c_Predicate_Oreflp(X33327,X33326)
      | ~ c_Predicate_Osymp(X33327,X33326)
      | ~ c_Predicate_Otransp(X33327,X33326)
      | c_Equiv__Relations_Oequivp(X33327,X33326) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivpI])]) ).

fof(i_0_10756,plain,
    ! [X32028,X32029] :
      ( ~ class_Orderings_Olinorder(X32029)
      | ~ c_List_Olinorder__class_Osorted(X32029,X32028)
      | c_List_Olinorder__class_Osorted(X32029,hAPP(c_List_Otl(X32029),X32028)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).

fof(i_0_10757,plain,
    ! [X31613,X31614] :
      ( ( c_List_Oremdups(X31614,X31613) != X31613
        | hBOOL(hAPP(c_List_Odistinct(X31614),X31613)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31614),X31613))
        | c_List_Oremdups(X31614,X31613) = X31613 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])]) ).

fof(i_0_10758,plain,
    ! [X31608,X31609] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31609),X31608))
      | c_List_Oremdups(X31609,X31608) = X31608 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id])]) ).

cnf(i_0_10759,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__list__functions_I2_J]) ).

fof(i_0_10760,plain,
    ! [X22512,X22513] :
      ( X22513 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22513),X22512)
      | X22512 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X22513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).

fof(i_0_10761,plain,
    ! [X30724,X30725] :
      ( X30725 = c_List_Olist_ONil(X30724)
      | hAPP(c_List_Ohd(X30724),X30725) = hAPP(hAPP(c_List_Onth(X30724),X30725),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__conv__nth])]) ).

fof(i_0_10762,plain,
    ! [X34270,X34271] :
      ( hBOOL(X34271)
      | hBOOL(hAPP(hAPP(c_fimplies,X34271),X34270)) ),
    inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).

fof(i_0_10763,plain,
    ! [X29221,X29222] : c_Relation_Osingle__valued(X29222,X29222,c_Relation_OId__on(X29222,X29221)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).

fof(i_0_10764,plain,
    ! [X28176,X28177] : c_Relation_Orefl__on(X28177,X28176,c_Relation_OId__on(X28177,X28176)),
    inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).

fof(i_0_10765,plain,
    ! [X22158,X22159] :
      ( ( X22159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22159),X22158) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22159),X22158) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22159 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22158 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22159),X22158) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).

fof(i_0_10766,plain,
    ! [X19959,X19960] :
      ( ( X19960 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19960),X19959) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19959 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19960),X19959) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19960 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19959 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19960),X19959) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).

fof(i_0_10767,plain,
    ! [X19962,X19963] :
      ( ( X19963 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19963),X19962) )
      & ( X19962 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19963),X19962) )
      & ( X19963 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19962 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19963),X19962) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).

fof(i_0_10768,plain,
    ! [X25670,X25671,X25672] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X25672),X25671) != hAPP(c_Int_Onumber__class_Onumber__of(X25672),X25670)
        | X25671 = X25670
        | ~ class_Int_Onumber__ring(X25672)
        | ~ class_Int_Oring__char__0(X25672) )
      & ( X25671 != X25670
        | hAPP(c_Int_Onumber__class_Onumber__of(X25672),X25671) = hAPP(c_Int_Onumber__class_Onumber__of(X25672),X25670)
        | ~ class_Int_Onumber__ring(X25672)
        | ~ class_Int_Oring__char__0(X25672) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_10769,plain,
    ! [X29099,X29100] : hAPP(c_Relation_Oconverse(X29100,X29100),c_Relation_OId__on(X29100,X29099)) = c_Relation_OId__on(X29100,X29099),
    inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).

fof(i_0_10770,plain,
    ! [X34254,X34255] :
      ( X34255 != X34254
      | hBOOL(hAPP(hAPP(c_fequal,X34255),X34254)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_10771,plain,
    ! [X25659,X25660] :
      ( ~ class_Int_Onumber__ring(X25660)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25660),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25659)) = hAPP(c_Int_Onumber__class_Onumber__of(X25660),X25659) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).

fof(i_0_10772,plain,
    ! [X24060,X24061] :
      ( ~ class_Rings_Oring__1(X24061)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24061),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24060)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24061),X24060) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).

fof(i_0_10773,plain,
    ! [X30234,X30235] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X30235,tc_HOL_Obool)) != hAPP(c_List_Oset(X30235),X30234)
        | X30234 = c_List_Olist_ONil(X30235) )
      & ( X30234 != c_List_Olist_ONil(X30235)
        | c_Orderings_Obot__class_Obot(tc_fun(X30235,tc_HOL_Obool)) = hAPP(c_List_Oset(X30235),X30234) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).

fof(i_0_10774,plain,
    ! [X30232,X30233] :
      ( ( hAPP(c_List_Oset(X30233),X30232) != c_Orderings_Obot__class_Obot(tc_fun(X30233,tc_HOL_Obool))
        | X30232 = c_List_Olist_ONil(X30233) )
      & ( X30232 != c_List_Olist_ONil(X30233)
        | hAPP(c_List_Oset(X30233),X30232) = c_Orderings_Obot__class_Obot(tc_fun(X30233,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).

fof(i_0_10775,plain,
    ! [X33408,X33409] :
      ( ( ~ c_Relation_Osym(X33409,X33408)
        | hAPP(c_Relation_Oconverse(X33409,X33409),X33408) = X33408 )
      & ( hAPP(c_Relation_Oconverse(X33409,X33409),X33408) != X33408
        | c_Relation_Osym(X33409,X33408) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__conv__converse__eq])]) ).

fof(i_0_10776,plain,
    ! [X32162,X32163] : hAPP(c_List_Oset(X32163),hAPP(c_List_Orev(X32163),X32162)) = hAPP(c_List_Oset(X32163),X32162),
    inference(variable_rename,[status(thm)],[fact_set__rev]) ).

fof(i_0_10777,plain,
    ! [X30629,X30630] : hAPP(c_List_Oset(X30630),hAPP(c_List_Orotate1(X30630),X30629)) = hAPP(c_List_Oset(X30630),X30629),
    inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).

fof(i_0_10778,plain,
    ! [X20422] :
      ( ~ class_Power_Opower(X20422)
      | c_Power_Opower__class_Opower(X20422) = c_Power_Opower_Opower(X20422,c_Groups_Oone__class_Oone(X20422),c_Groups_Otimes__class_Otimes(X20422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).

fof(i_0_10779,plain,
    ! [X22156,X22157] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22157),X22156) != X22157
      | X22156 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).

fof(i_0_10780,plain,
    ! [X32203,X32204] :
      ( X32204 = c_List_Olist_ONil(X32203)
      | hAPP(c_List_Ohd(X32203),hAPP(c_List_Orev(X32203),X32204)) = c_List_Olast(X32203,X32204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).

fof(i_0_10781,plain,
    ! [X32205,X32206] :
      ( X32206 = c_List_Olist_ONil(X32205)
      | c_List_Olast(X32205,hAPP(c_List_Orev(X32205),X32206)) = hAPP(c_List_Ohd(X32205),X32206) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).

fof(i_0_10782,plain,
    ! [X30347] :
      ( ~ class_Orderings_Olinorder(X30347)
      | c_List_Olinorder__class_Osorted__list__of__set(X30347,c_Orderings_Obot__class_Obot(tc_fun(X30347,tc_HOL_Obool))) = c_List_Olist_ONil(X30347) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).

fof(i_0_10783,plain,
    ! [X25164] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25164)
      | c_Complete__Lattice_OSup__class_OSup(X25164,c_Orderings_Otop__class_Otop(tc_fun(X25164,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X25164) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).

fof(i_0_10784,plain,
    ! [X25156] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25156)
      | c_Complete__Lattice_OSup__class_OSup(X25156,c_Orderings_Obot__class_Obot(tc_fun(X25156,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X25156) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).

fof(i_0_10785,plain,
    ! [X21910] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21910)
      | c_Complete__Lattice_OInf__class_OInf(X21910,c_Orderings_Otop__class_Otop(tc_fun(X21910,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X21910) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).

fof(i_0_10786,plain,
    ! [X21909] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X21909)
      | c_Complete__Lattice_OInf__class_OInf(X21909,c_Orderings_Obot__class_Obot(tc_fun(X21909,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X21909) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).

fof(i_0_10787,plain,
    ! [X23449] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23449),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X23449,
    inference(variable_rename,[status(thm)],[fact_div__1]) ).

fof(i_0_10788,plain,
    ! [X24961,X24962] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X24962,tc_HOL_Obool),hAPP(c_Set_OPow(X24962),X24961)) = X24961,
    inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).

fof(i_0_10789,plain,
    ! [X23581,X23582] :
      ( ~ class_Rings_Odivision__ring(X23582)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23582),c_Groups_Ozero__class_Ozero(X23582)),X23581) = c_Groups_Ozero__class_Ozero(X23582) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_10790,plain,
    ! [X23301,X23302] :
      ( ~ class_Divides_Osemiring__div(X23302)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23302),c_Groups_Ozero__class_Ozero(X23302)),X23301) = c_Groups_Ozero__class_Ozero(X23302) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).

fof(i_0_10791,plain,
    ! [X20658,X20659] :
      ( ~ class_Lattices_Obounded__lattice__bot(X20659)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20659),c_Orderings_Obot__class_Obot(X20659)),X20658) = c_Orderings_Obot__class_Obot(X20659) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).

fof(i_0_10792,plain,
    ! [X20400,X20401] :
      ( ~ class_Groups_Omonoid__mult(X20401)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20401),c_Groups_Oone__class_Oone(X20401)),X20400) = c_Groups_Oone__class_Oone(X20401) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).

fof(i_0_10793,plain,
    ! [X19429,X19430] :
      ( ~ class_Lattices_Obounded__lattice__top(X19430)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19430),c_Orderings_Otop__class_Otop(X19430)),X19429) = c_Orderings_Otop__class_Otop(X19430) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).

fof(i_0_10794,plain,
    ! [X22095,X22096] :
      ( ~ class_Rings_Omult__zero(X22096)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22096),c_Groups_Ozero__class_Ozero(X22096)),X22095) = c_Groups_Ozero__class_Ozero(X22096) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).

fof(i_0_10795,plain,
    ! [X22097,X22098] :
      ( ~ class_Rings_Ocomm__semiring__1(X22098)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22098),c_Groups_Ozero__class_Ozero(X22098)),X22097) = c_Groups_Ozero__class_Ozero(X22098) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

fof(i_0_10796,plain,
    ! [X32033,X32034] :
      ( ~ class_Orderings_Olinorder(X32034)
      | X32033 = c_List_Olist_ONil(X32034)
      | ~ c_List_Olinorder__class_Osorted(X32034,X32033)
      | c_List_Olinorder__class_Osorted(X32034,c_List_Obutlast(X32034,X32033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).

fof(i_0_10797,plain,
    ! [X26368] :
      ( ~ class_Int_Onumber__ring(X26368)
      | hAPP(c_Int_Oring__1__class_Oof__int(X26368),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X26368),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).

fof(i_0_10798,plain,
    ! [X22475] : hAPP(c_Finite__Set_Ocard(X22475),c_Orderings_Obot__class_Obot(tc_fun(X22475,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).

cnf(i_0_10799,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6056]) ).

cnf(i_0_10800,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6057]) ).

fof(i_0_10801,plain,
    ! [X26355] :
      ( ~ class_Int_Onumber__ring(X26355)
      | ~ class_Rings_Olinordered__idom(X26355)
      | hAPP(c_Groups_Oabs__class_Oabs(X26355),hAPP(c_Int_Onumber__class_Onumber__of(X26355),c_Int_OMin)) = c_Groups_Oone__class_Oone(X26355) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).

fof(i_0_10802,plain,
    ! [X24296] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24296) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24296),
    inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).

cnf(i_0_10803,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[i_0_6058]) ).

cnf(i_0_10804,plain,
    c_Int_OMin != c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_6059]) ).

fof(i_0_10805,plain,
    ! [X24281,X24282,X24283] :
      ( ( hAPP(c_SetInterval_Oord__class_OatMost(X24283),X24282) != hAPP(c_SetInterval_Oord__class_OatMost(X24283),X24281)
        | X24282 = X24281
        | ~ class_Orderings_Olinorder(X24283) )
      & ( X24282 != X24281
        | hAPP(c_SetInterval_Oord__class_OatMost(X24283),X24282) = hAPP(c_SetInterval_Oord__class_OatMost(X24283),X24281)
        | ~ class_Orderings_Olinorder(X24283) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).

fof(i_0_10806,plain,
    ! [X24284,X24285,X24286] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeast(X24286),X24285) != hAPP(c_SetInterval_Oord__class_OatLeast(X24286),X24284)
        | X24285 = X24284
        | ~ class_Orderings_Olinorder(X24286) )
      & ( X24285 != X24284
        | hAPP(c_SetInterval_Oord__class_OatLeast(X24286),X24285) = hAPP(c_SetInterval_Oord__class_OatLeast(X24286),X24284)
        | ~ class_Orderings_Olinorder(X24286) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).

fof(i_0_10807,plain,
    ! [X24021,X24022,X24023] :
      ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X24023),X24022) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X24023),X24021)
        | X24022 = X24021
        | ~ class_Orderings_Olinorder(X24023) )
      & ( X24022 != X24021
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(X24023),X24022) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24023),X24021)
        | ~ class_Orderings_Olinorder(X24023) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).

fof(i_0_10808,plain,
    ! [X24024,X24025,X24026] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X24026),X24025) != hAPP(c_Int_Oring__1__class_Oof__int(X24026),X24024)
        | X24025 = X24024
        | ~ class_Int_Oring__char__0(X24026) )
      & ( X24025 != X24024
        | hAPP(c_Int_Oring__1__class_Oof__int(X24026),X24025) = hAPP(c_Int_Oring__1__class_Oof__int(X24026),X24024)
        | ~ class_Int_Oring__char__0(X24026) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).

fof(i_0_10809,plain,
    ! [X22851,X22852,X22853] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22853),X22852) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22853),X22851)
        | X22852 = X22851
        | ~ class_Nat_Osemiring__char__0(X22853) )
      & ( X22852 != X22851
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22853),X22852) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22853),X22851)
        | ~ class_Nat_Osemiring__char__0(X22853) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).

fof(i_0_10810,plain,
    ! [X22759,X22760,X22761] :
      ( ( hAPP(c_SetInterval_Oord__class_OlessThan(X22761),X22760) != hAPP(c_SetInterval_Oord__class_OlessThan(X22761),X22759)
        | X22760 = X22759
        | ~ class_Orderings_Olinorder(X22761) )
      & ( X22760 != X22759
        | hAPP(c_SetInterval_Oord__class_OlessThan(X22761),X22760) = hAPP(c_SetInterval_Oord__class_OlessThan(X22761),X22759)
        | ~ class_Orderings_Olinorder(X22761) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).

fof(i_0_10811,plain,
    ! [X18732,X18733,X18734] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18733) != hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18732)
        | X18733 = X18732
        | ~ class_Lattices_Oboolean__algebra(X18734) )
      & ( X18733 != X18732
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18733) = hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18732)
        | ~ class_Lattices_Oboolean__algebra(X18734) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_10812,plain,
    ! [X18683,X18684,X18685] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18684) != hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18683)
        | X18684 = X18683
        | ~ class_Groups_Ogroup__add(X18685) )
      & ( X18684 != X18683
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18684) = hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18683)
        | ~ class_Groups_Ogroup__add(X18685) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_10813,plain,
    ! [X20684,X20685] :
      ( ~ class_Lattices_Obounded__lattice__top(X20685)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20685),c_Orderings_Otop__class_Otop(X20685)),X20684) = X20684 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).

fof(i_0_10814,plain,
    ! [X19559,X19560] :
      ( ~ class_Lattices_Obounded__lattice__bot(X19560)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19560),c_Orderings_Obot__class_Obot(X19560)),X19559) = X19559 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).

fof(i_0_10815,plain,
    ! [X19989,X19990] :
      ( ~ class_Groups_Omonoid__mult(X19990)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19990),c_Groups_Oone__class_Oone(X19990)),X19989) = X19989 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_10816,plain,
    ! [X19987,X19988] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19988)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19988),c_Groups_Oone__class_Oone(X19988)),X19987) = X19987 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_10817,plain,
    ! [X19991,X19992] :
      ( ~ class_Rings_Ocomm__semiring__1(X19992)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19992),c_Groups_Oone__class_Oone(X19992)),X19991) = X19991 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_10818,plain,
    ! [X22078,X22079] :
      ( ~ class_Groups_Omonoid__add(X22079)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22079),c_Groups_Ozero__class_Ozero(X22079)),X22078) = X22078 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_10819,plain,
    ! [X22088,X22089] :
      ( ~ class_Rings_Ocomm__semiring__1(X22089)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22089),c_Groups_Ozero__class_Ozero(X22089)),X22088) = X22088 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_10820,plain,
    ! [X22080,X22081] :
      ( ~ class_Groups_Ocomm__monoid__add(X22081)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22081),c_Groups_Ozero__class_Ozero(X22081)),X22080) = X22080 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_10821,plain,
    ! [X23628,X23629] :
      ( ( X23628 != c_Groups_Ozero__class_Ozero(X23629)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23629),X23628),X23628) = c_Groups_Ozero__class_Ozero(X23629)
        | ~ class_Rings_Odivision__ring__inverse__zero(X23629) )
      & ( X23628 = c_Groups_Ozero__class_Ozero(X23629)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23629),X23628),X23628) = c_Groups_Oone__class_Oone(X23629)
        | ~ class_Rings_Odivision__ring__inverse__zero(X23629) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_10822,plain,
    ! [X24666,X24667] :
      ( ~ class_Divides_Osemiring__div(X24667)
      | c_Divides_Odiv__class_Omod(X24667,c_Groups_Ozero__class_Ozero(X24667),X24666) = c_Groups_Ozero__class_Ozero(X24667) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).

fof(i_0_10823,plain,
    ! [X24723,X24724] :
      ( ~ class_Divides_Osemiring__div(X24724)
      | c_Divides_Odiv__class_Omod(X24724,X24723,c_Groups_Oone__class_Oone(X24724)) = c_Groups_Ozero__class_Ozero(X24724) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).

fof(i_0_10824,plain,
    ! [X32044,X32045] :
      ( ~ class_Orderings_Olinorder(X32045)
      | ~ c_List_Olinorder__class_Osorted(X32045,X32044)
      | c_List_Olinorder__class_Osorted(X32045,c_List_Oremdups(X32045,X32044)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remdups])]) ).

fof(i_0_10825,plain,
    ! [X23583,X23584] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X23584)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23584),X23583),c_Groups_Ozero__class_Ozero(X23584)) = c_Groups_Ozero__class_Ozero(X23584) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_10826,plain,
    ! [X23299,X23300] :
      ( ~ class_Divides_Osemiring__div(X23300)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23300),X23299),c_Groups_Ozero__class_Ozero(X23300)) = c_Groups_Ozero__class_Ozero(X23300) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).

fof(i_0_10827,plain,
    ! [X20660,X20661] :
      ( ~ class_Lattices_Obounded__lattice__bot(X20661)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20661),X20660),c_Orderings_Obot__class_Obot(X20661)) = c_Orderings_Obot__class_Obot(X20661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).

fof(i_0_10828,plain,
    ! [X19431,X19432] :
      ( ~ class_Lattices_Obounded__lattice__top(X19432)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19432),X19431),c_Orderings_Otop__class_Otop(X19432)) = c_Orderings_Otop__class_Otop(X19432) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).

fof(i_0_10829,plain,
    ! [X22099,X22100] :
      ( ~ class_Rings_Omult__zero(X22100)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22100),X22099),c_Groups_Ozero__class_Ozero(X22100)) = c_Groups_Ozero__class_Ozero(X22100) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).

fof(i_0_10830,plain,
    ! [X22101,X22102] :
      ( ~ class_Rings_Ocomm__semiring__1(X22102)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22102),X22101),c_Groups_Ozero__class_Ozero(X22102)) = c_Groups_Ozero__class_Ozero(X22102) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_10831,plain,
    ! [X33406,X33407] :
      ( ~ c_Relation_Osym(X33407,X33406)
      | c_Relation_Osym(tc_List_Olist(X33407),c_List_Olistrel(X33407,X33406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__sym])]) ).

fof(i_0_10832,plain,
    ! [X33246,X33247] :
      ( ~ c_Relation_Otrans(X33247,X33246)
      | c_Relation_Otrans(tc_List_Olist(X33247),c_List_Olistrel(X33247,X33246)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).

fof(i_0_10833,plain,
    ! [X33241,X33242] :
      ( ~ c_Relation_Otrans(X33242,X33241)
      | c_Relation_Otrans(tc_List_Olist(X33242),c_List_Olexord(X33242,X33241)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).

fof(i_0_10834,plain,
    ! [X27609,X27610] :
      ( ~ c_Wellfounded_Owf(X27610,X27609)
      | c_Wellfounded_Owf(tc_List_Olist(X27610),c_List_Olex(X27610,X27609)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).

fof(i_0_10835,plain,
    ! [X27596,X27597] :
      ( ~ c_Wellfounded_Owf(X27597,X27596)
      | c_Wellfounded_Owf(tc_List_Olist(X27597),c_List_Olenlex(X27597,X27596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).

fof(i_0_10836,plain,
    ! [X30469,X30470,X30471] :
      ( X30471 != X30470
      | X30471 = hAPP(hAPP(c_List_Oappend(X30469),c_List_Olist_ONil(X30469)),X30470) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).

fof(i_0_10837,plain,
    ! [X23626,X23627] :
      ( ~ class_Rings_Odivision__ring(X23627)
      | X23626 = c_Groups_Ozero__class_Ozero(X23627)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23627),X23626),X23626) = c_Groups_Oone__class_Oone(X23627) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_10838,plain,
    ! [X23332,X23333] :
      ( ~ class_Divides_Osemiring__div(X23333)
      | X23332 = c_Groups_Ozero__class_Ozero(X23333)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23333),X23332),X23332) = c_Groups_Oone__class_Oone(X23333) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).

fof(i_0_10839,plain,
    ! [X24664,X24665] :
      ( ~ class_Divides_Osemiring__div(X24665)
      | c_Divides_Odiv__class_Omod(X24665,X24664,c_Groups_Ozero__class_Ozero(X24665)) = X24664 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).

fof(i_0_10840,plain,
    ! [X25571] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X25571))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X25571)) = X25571 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6060])]) ).

fof(i_0_10841,plain,
    ! [X18462] :
      ( ~ class_Groups_Oab__semigroup__mult(X18462)
      | c_Finite__Set_Ofun__left__comm(X18462,X18462,c_Groups_Otimes__class_Otimes(X18462)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).

fof(i_0_10842,plain,
    ! [X20828] :
      ( ~ class_Lattices_Osemilattice__inf(X20828)
      | c_Finite__Set_Ofun__left__comm__idem(X20828,X20828,c_Lattices_Osemilattice__inf__class_Oinf(X20828)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).

fof(i_0_10843,plain,
    ! [X19658] :
      ( ~ class_Lattices_Osemilattice__sup(X19658)
      | c_Finite__Set_Ofun__left__comm__idem(X19658,X19658,c_Lattices_Osemilattice__sup__class_Osup(X19658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).

fof(i_0_10844,plain,
    ! [X19032] :
      ( ~ class_Orderings_Olinorder(X19032)
      | c_Finite__Set_Ofun__left__comm__idem(X19032,X19032,c_Orderings_Oord__class_Omax(X19032)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).

fof(i_0_10845,plain,
    ! [X19033] :
      ( ~ class_Orderings_Olinorder(X19033)
      | c_Finite__Set_Ofun__left__comm__idem(X19033,X19033,c_Orderings_Oord__class_Omin(X19033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).

fof(i_0_10846,plain,
    ! [X18463] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18463)
      | c_Finite__Set_Ofun__left__comm__idem(X18463,X18463,c_Groups_Otimes__class_Otimes(X18463)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).

fof(i_0_10847,plain,
    ! [X27713,X27714] : hAPP(c_Relation_ODomain(X27714,X27714),c_Relation_OId__on(X27714,X27713)) = X27713,
    inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).

fof(i_0_10848,plain,
    ! [X27632,X27633] : hAPP(c_Relation_ORange(X27633,X27633),c_Relation_OId__on(X27633,X27632)) = X27632,
    inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).

fof(i_0_10849,plain,
    ! [X22471,X22472] :
      ( ~ class_Power_Opower(X22472)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22472),X22471),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X22472) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).

fof(i_0_10850,plain,
    ! [X22473,X22474] :
      ( ~ class_Rings_Ocomm__semiring__1(X22474)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22474),X22473),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X22474) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).

fof(i_0_10851,plain,
    ! [X23588,X23589] :
      ( ~ class_Rings_Odivision__ring(X23589)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23589),X23588),c_Groups_Oone__class_Oone(X23589)) = X23588 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_10852,plain,
    ! [X23303,X23304] :
      ( ~ class_Divides_Osemiring__div(X23304)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23304),X23303),c_Groups_Oone__class_Oone(X23304)) = X23303 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).

fof(i_0_10853,plain,
    ! [X20686,X20687] :
      ( ~ class_Lattices_Obounded__lattice__top(X20687)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20687),X20686),c_Orderings_Otop__class_Otop(X20687)) = X20686 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).

fof(i_0_10854,plain,
    ! [X19561,X19562] :
      ( ~ class_Lattices_Obounded__lattice__bot(X19562)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19562),X19561),c_Orderings_Obot__class_Obot(X19562)) = X19561 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).

fof(i_0_10855,plain,
    ! [X19985,X19986] :
      ( ~ class_Groups_Omonoid__mult(X19986)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19986),X19985),c_Groups_Oone__class_Oone(X19986)) = X19985 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_10856,plain,
    ! [X19983,X19984] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19984)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19984),X19983),c_Groups_Oone__class_Oone(X19984)) = X19983 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_10857,plain,
    ! [X19993,X19994] :
      ( ~ class_Rings_Ocomm__semiring__1(X19994)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19994),X19993),c_Groups_Oone__class_Oone(X19994)) = X19993 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_10858,plain,
    ! [X22084,X22085] :
      ( ~ class_Groups_Omonoid__add(X22085)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22085),X22084),c_Groups_Ozero__class_Ozero(X22085)) = X22084 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_10859,plain,
    ! [X22090,X22091] :
      ( ~ class_Rings_Ocomm__semiring__1(X22091)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22091),X22090),c_Groups_Ozero__class_Ozero(X22091)) = X22090 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_10860,plain,
    ! [X22086,X22087] :
      ( ~ class_Groups_Ocomm__monoid__add(X22087)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22087),X22086),c_Groups_Ozero__class_Ozero(X22087)) = X22086 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_10861,plain,
    ! [X22112,X22113] :
      ( ~ class_Groups_Ogroup__add(X22113)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22113),X22112),c_Groups_Ozero__class_Ozero(X22113)) = X22112 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).

fof(i_0_10862,plain,
    ! [X18797,X18798] :
      ( ~ class_Lattices_Oboolean__algebra(X18798)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18798),hAPP(c_Groups_Ouminus__class_Ouminus(X18798),X18797)) = X18797 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_10863,plain,
    ! [X18698,X18699] :
      ( ~ class_Groups_Ogroup__add(X18699)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18699),hAPP(c_Groups_Ouminus__class_Ouminus(X18699),X18698)) = X18698 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_10864,plain,
    ! [X24992] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24992)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24992),
    inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).

fof(i_0_10865,plain,
    ! [X24027] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24027)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24027),
    inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).

fof(i_0_10866,plain,
    ! [X31615,X31616] : hAPP(c_List_Oset(X31616),c_List_Oremdups(X31616,X31615)) = hAPP(c_List_Oset(X31616),X31615),
    inference(variable_rename,[status(thm)],[fact_set__remdups]) ).

fof(i_0_10867,plain,
    ! [X24662,X24663] :
      ( ~ class_Divides_Osemiring__div(X24663)
      | c_Divides_Odiv__class_Omod(X24663,X24662,X24662) = c_Groups_Ozero__class_Ozero(X24663) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).

fof(i_0_10868,plain,
    ! [X32179,X32180,X32181] :
      ( ( hAPP(c_List_Orev(X32181),X32180) != hAPP(c_List_Orev(X32181),X32179)
        | X32180 = X32179 )
      & ( X32180 != X32179
        | hAPP(c_List_Orev(X32181),X32180) = hAPP(c_List_Orev(X32181),X32179) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).

fof(i_0_10869,plain,
    ! [X22476,X22477] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22477),X22476))
      | hAPP(c_Finite__Set_Ocard(X22477),X22476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6061])]) ).

fof(i_0_10870,plain,
    ! [X29070,X29071] :
      ( ( X29071 != X29070
        | c_Random_Oinc__shift(X29071,X29070) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X29071 = X29070
        | c_Random_Oinc__shift(X29071,X29070) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X29070),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inc__shift__def])]) ).

fof(i_0_10871,plain,
    ! [X30447,X30448] : hAPP(hAPP(c_List_Oappend(X30448),c_List_Olist_ONil(X30448)),X30447) = X30447,
    inference(variable_rename,[status(thm)],[fact_append__Nil]) ).

fof(i_0_10872,plain,
    ! [X22017] : hAPP(c_Nat_OSuc,X22017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X22017),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_10873,plain,
    ! [X30210,X30211] : c_List_Osublist(X30211,c_List_Olist_ONil(X30211),X30210) = c_List_Olist_ONil(X30211),
    inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).

fof(i_0_10874,plain,
    ! [X32283,X32284] : c_List_OtakeWhile(X32284,X32283,c_List_Olist_ONil(X32284)) = c_List_Olist_ONil(X32284),
    inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(i_0_10875,plain,
    ! [X30216,X30217] : c_List_Oremove1(X30217,X30216,c_List_Olist_ONil(X30217)) = c_List_Olist_ONil(X30217),
    inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(i_0_10876,plain,
    ! [X23101] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23101),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan0]) ).

fof(i_0_10877,plain,
    ! [X20406,X20407] :
      ( ~ class_Groups_Omonoid__mult(X20407)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20407),X20406),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20406 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).

fof(i_0_10878,plain,
    ! [X20325,X20326] :
      ( ~ class_Rings_Ocomm__semiring__1(X20326)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20326),X20325),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20325 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).

fof(i_0_10879,plain,
    ! [X22114,X22115] :
      ( ~ class_Groups_Ogroup__add(X22115)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22115),X22114),X22114) = c_Groups_Ozero__class_Ozero(X22115) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).

fof(i_0_10880,plain,
    ! [X30237,X30238] : c_List_Olist_Olist__size(X30238,X30237,c_List_Olist_ONil(X30238)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(i_0_10881,plain,
    ! [X33396,X33397] :
      ( ~ c_Relation_Osym(X33397,X33396)
      | c_Relation_Osym(X33397,c_Transitive__Closure_Ortrancl(X33397,X33396)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__rtrancl])]) ).

fof(i_0_10882,plain,
    ! [X33371,X33372] :
      ( ~ c_Wellfounded_Oacyclic(X33372,X33371)
      | c_Relation_Oantisym(X33372,c_Transitive__Closure_Ortrancl(X33372,X33371)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])]) ).

fof(i_0_10883,plain,
    ! [X30206,X30207] : hAPP(hAPP(c_List_Otake(X30207),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30206) = c_List_Olist_ONil(X30207),
    inference(variable_rename,[status(thm)],[fact_take__0]) ).

fof(i_0_10884,plain,
    ! [X30638,X30639] : hAPP(hAPP(c_List_Odrop(X30639),X30638),c_List_Olist_ONil(X30639)) = c_List_Olist_ONil(X30639),
    inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).

fof(i_0_10885,plain,
    ! [X30208,X30209] : hAPP(hAPP(c_List_Otake(X30209),X30208),c_List_Olist_ONil(X30209)) = c_List_Olist_ONil(X30209),
    inference(variable_rename,[status(thm)],[fact_take__Nil]) ).

fof(i_0_10886,plain,
    ! [X18686,X18687,X18688] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18688),X18687) != X18686
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18688),X18686) = X18687
        | ~ class_Groups_Ogroup__add(X18688) )
      & ( hAPP(c_Groups_Ouminus__class_Ouminus(X18688),X18686) != X18687
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18688),X18687) = X18686
        | ~ class_Groups_Ogroup__add(X18688) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_10887,plain,
    ! [X18689,X18690,X18691] :
      ( ( X18690 != hAPP(c_Groups_Ouminus__class_Ouminus(X18691),X18689)
        | X18689 = hAPP(c_Groups_Ouminus__class_Ouminus(X18691),X18690)
        | ~ class_Groups_Ogroup__add(X18691) )
      & ( X18689 != hAPP(c_Groups_Ouminus__class_Ouminus(X18691),X18690)
        | X18690 = hAPP(c_Groups_Ouminus__class_Ouminus(X18691),X18689)
        | ~ class_Groups_Ogroup__add(X18691) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_10888,plain,
    ! [X30000] :
      ( ( ~ c_List_Onat__list(X30000)
        | c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X30000)) )
      & ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X30000))
        | c_List_Onat__list(X30000) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).

fof(i_0_10889,plain,
    ! [X24298] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24298)) = hAPP(c_Nat_OSuc,X24298),
    inference(variable_rename,[status(thm)],[fact_card__atMost]) ).

fof(i_0_10890,plain,
    ! [X31334] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X31334)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31334),
    inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).

fof(i_0_10891,plain,
    ! [X25875] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25875)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25875),
    inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).

fof(i_0_10892,plain,
    ! [X25874] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25874) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25874)),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).

fof(i_0_10893,plain,
    ! [X22018] : hAPP(c_Nat_OSuc,X22018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22018),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_10894,plain,
    ! [X32945,X32946] : c_List_Oreplicate(X32946,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32945) = c_List_Olist_ONil(X32946),
    inference(variable_rename,[status(thm)],[fact_replicate__0]) ).

fof(i_0_10895,plain,
    ! [X33143,X33144] : c_Lazy__Sequence_Oappend(X33144,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33144),X33143) = X33143,
    inference(variable_rename,[status(thm)],[fact__02]) ).

fof(i_0_10896,plain,
    ! [X32798,X32799] : c_List_Osplice(X32799,c_List_Olist_ONil(X32799),X32798) = X32798,
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(i_0_10897,plain,
    ! [X32800,X32801] : c_List_Osplice(X32801,X32800,c_List_Olist_ONil(X32801)) = X32800,
    inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).

fof(i_0_10898,plain,
    ! [X24854,X24855] :
      ( ~ class_Rings_Olinordered__idom(X24855)
      | c_Groups_Osgn__class_Osgn(X24855,c_Groups_Osgn__class_Osgn(X24855,X24854)) = c_Groups_Osgn__class_Osgn(X24855,X24854) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_10899,plain,
    ! [X32649,X32650] : c_List_Olist__all(X32650,X32649,c_List_Olist_ONil(X32650)),
    inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(i_0_10900,plain,
    ! [X20534,X20535] :
      ( ~ class_Lattices_Osemilattice__inf(X20535)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20535),X20534),X20534) = X20534 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).

fof(i_0_10901,plain,
    ! [X20532,X20533] :
      ( ~ class_Lattices_Osemilattice__inf(X20533)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20533),X20532),X20532) = X20532 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).

fof(i_0_10902,plain,
    ! [X20496,X20497] :
      ( ~ class_Lattices_Olattice(X20497)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20497),X20496),X20496) = X20496 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).

fof(i_0_10903,plain,
    ! [X19435,X19436] :
      ( ~ class_Lattices_Osemilattice__sup(X19436)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19436),X19435),X19435) = X19435 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).

fof(i_0_10904,plain,
    ! [X19433,X19434] :
      ( ~ class_Lattices_Osemilattice__sup(X19434)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19434),X19433),X19433) = X19433 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).

fof(i_0_10905,plain,
    ! [X19368,X19369] :
      ( ~ class_Lattices_Olattice(X19369)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19369),X19368),X19368) = X19368 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).

fof(i_0_10906,plain,
    ! [X18805,X18806] :
      ( ~ class_Orderings_Olinorder(X18806)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18806),X18805),X18805) = X18805 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).

fof(i_0_10907,plain,
    ! [X18795,X18796] :
      ( ~ class_Orderings_Olinorder(X18796)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X18796),X18795),X18795) = X18795 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).

fof(i_0_10908,plain,
    ! [X18803,X18804] :
      ( ~ class_Orderings_Olinorder(X18804)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18804),X18803),X18803) = X18803 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).

fof(i_0_10909,plain,
    ! [X18793,X18794] :
      ( ~ class_Orderings_Olinorder(X18794)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X18794),X18793),X18793) = X18793 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).

fof(i_0_10910,plain,
    ! [X18260,X18261] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18261)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18261),X18260),X18260) = X18260 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).

fof(i_0_10911,plain,
    ! [X18258,X18259] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18259)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18259),X18258),X18258) = X18258 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).

fof(i_0_10912,plain,
    ! [X30229,X30230] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30230)),X30229) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30229 = c_List_Olist_ONil(X30230) )
      & ( X30229 != c_List_Olist_ONil(X30230)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30230)),X30229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__0__conv])]) ).

fof(i_0_10913,plain,
    ! [X26344] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X26344) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26344),
    inference(variable_rename,[status(thm)],[fact_mult__Min]) ).

fof(i_0_10914,plain,
    ! [X23102] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23102) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23102),
    inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).

fof(i_0_10915,plain,
    ! [X32805,X32806,X32807] : hAPP(c_New__DSequence_Opos__single(X32807,X32806),X32805) = hAPP(c_Lazy__Sequence_Osingle(X32807),X32806),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(i_0_10916,plain,
    ! [X30613,X30614] : hAPP(hAPP(c_List_Odrop(X30614),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30613) = X30613,
    inference(variable_rename,[status(thm)],[fact_drop__0]) ).

fof(i_0_10917,plain,
    ! [X30452,X30453] : hAPP(hAPP(c_List_Oappend(X30453),X30452),c_List_Olist_ONil(X30453)) = X30452,
    inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).

fof(i_0_10918,plain,
    ! [X32174,X32175] : hAPP(c_List_Orev(X32175),hAPP(c_List_Orev(X32175),X32174)) = X32174,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

fof(i_0_10919,plain,
    ! [X33000] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X33000) = c_Lazy__Sequence_Osmall__lazy_H(X33000,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33000)),
    inference(variable_rename,[status(thm)],[fact_small__lazy__int__def]) ).

fof(i_0_10920,plain,
    ! [X24622] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24622) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).

fof(i_0_10921,plain,
    ! [X25570] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25570))
      | hAPP(c_Int_Onat,X25570) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).

fof(i_0_10922,plain,
    ! [X24326] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24326)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X24326),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(i_0_10923,plain,
    ! [X24297] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24297)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24297),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(i_0_10924,plain,
    ! [X21898] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21898) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21898)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_10925,plain,
    ! [X24748] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24748),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X24748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X24748 ),
    inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(i_0_10926,plain,
    ! [X26084] :
      ( ~ class_Int_Onumber__ring(X26084)
      | c_Int_Oiszero(X26084,hAPP(c_Int_Onumber__class_Onumber__of(X26084),c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).

fof(i_0_10927,plain,
    ! [X31203] : hAPP(c_List_Omap(X31203,X31203),c_Fun_Oid(X31203)) = c_Fun_Oid(tc_List_Olist(X31203)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).

fof(i_0_10928,plain,
    ! [X31202] : hAPP(c_List_Omap(X31202,X31202),c_COMBI(X31202)) = c_Fun_Oid(tc_List_Olist(X31202)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(i_0_10929,plain,
    ! [X23015,X23016] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23016) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23015)
        | X23016 = X23015 )
      & ( X23016 != X23015
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23016) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23015) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).

fof(i_0_10930,plain,
    ! [X23011,X23012] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23012) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23011)
        | X23012 = X23011 )
      & ( X23012 != X23011
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23012) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23011) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).

fof(i_0_10931,plain,
    ! [X24621] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X24621,X24621) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__self]) ).

fof(i_0_10932,plain,
    ! [X32176,X32177,X32178] :
      ( ( hAPP(c_List_Orev(X32178),X32177) != X32176
        | X32177 = hAPP(c_List_Orev(X32178),X32176) )
      & ( X32177 != hAPP(c_List_Orev(X32178),X32176)
        | hAPP(c_List_Orev(X32178),X32177) = X32176 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).

fof(i_0_10933,plain,
    ! [X23294] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23294) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).

fof(i_0_10934,plain,
    ! [X22185] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_min__0L]) ).

fof(i_0_10935,plain,
    ! [X22172] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22172) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0]) ).

fof(i_0_10936,plain,
    ! [X22164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22164) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).

fof(i_0_10937,plain,
    ! [X30186] : hBOOL(hAPP(c_List_Odistinct(X30186),c_List_Olist_ONil(X30186))),
    inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(i_0_10938,plain,
    ! [X32778,X32779,X32780] : hAPP(c_New__DSequence_Oneg__single(X32780,X32779),X32778) = c_Lazy__Sequence_Ohb__single(X32780,X32779),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(i_0_10939,plain,
    ! [X31619,X31620] : c_List_Oremdups(X31620,c_List_Oremdups(X31620,X31619)) = c_List_Oremdups(X31620,X31619),
    inference(variable_rename,[status(thm)],[fact_remdups__remdups]) ).

fof(i_0_10940,plain,
    ! [X28991,X28992] : c_Transitive__Closure_Ortrancl(X28992,c_Transitive__Closure_Ortrancl(X28992,X28991)) = c_Transitive__Closure_Ortrancl(X28992,X28991),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).

fof(i_0_10941,plain,
    ! [X30236] : hAPP(c_List_Oset(X30236),c_List_Olist_ONil(X30236)) = c_Orderings_Obot__class_Obot(tc_fun(X30236,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(i_0_10942,plain,
    ! [X22187] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22187) = X22187,
    inference(variable_rename,[status(thm)],[fact_max__0L]) ).

fof(i_0_10943,plain,
    ! [X22849] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X22849) = X22849,
    inference(variable_rename,[status(thm)],[fact_zmult__1]) ).

fof(i_0_10944,plain,
    ! [X19964] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19964) = X19964,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

fof(i_0_10945,plain,
    ! [X23068] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23068) = X23068,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_10946,plain,
    ! [X22161] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22161) = X22161,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_10947,plain,
    ! [X32836] : c_Predicate_Oconversep(X32836,X32836,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[fact_conversep__eq]) ).

fof(i_0_10948,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__0]) ).

fof(i_0_10949,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__1]) ).

fof(i_0_10950,plain,
    ! [X23313] :
      ( X23313 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23313),X23313) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).

fof(i_0_10951,plain,
    ! [X26353] :
      ( ~ class_Int_Onumber__ring(X26353)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26353),c_Groups_Oone__class_Oone(X26353)) = hAPP(c_Int_Onumber__class_Onumber__of(X26353),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).

fof(i_0_10952,plain,
    ! [X26354] :
      ( ~ class_Int_Onumber__ring(X26354)
      | hAPP(c_Int_Onumber__class_Onumber__of(X26354),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X26354),c_Groups_Oone__class_Oone(X26354)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).

fof(i_0_10953,plain,
    ! [X22186] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22186),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_min__0R]) ).

fof(i_0_10954,plain,
    ! [X22173] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22173),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).

fof(i_0_10955,plain,
    ! [X22130,X22131] :
      ( ( c_Groups_Ozero__class_Ozero(X22131) != hAPP(c_Groups_Ouminus__class_Ouminus(X22131),X22130)
        | c_Groups_Ozero__class_Ozero(X22131) = X22130
        | ~ class_Groups_Ogroup__add(X22131) )
      & ( c_Groups_Ozero__class_Ozero(X22131) != X22130
        | c_Groups_Ozero__class_Ozero(X22131) = hAPP(c_Groups_Ouminus__class_Ouminus(X22131),X22130)
        | ~ class_Groups_Ogroup__add(X22131) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_10956,plain,
    ! [X24989,X24990] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(X24990),X24989) != c_Groups_Ozero__class_Ozero(X24990)
        | X24989 = c_Groups_Ozero__class_Ozero(X24990)
        | ~ class_Groups_Oordered__ab__group__add__abs(X24990) )
      & ( X24989 != c_Groups_Ozero__class_Ozero(X24990)
        | hAPP(c_Groups_Oabs__class_Oabs(X24990),X24989) = c_Groups_Ozero__class_Ozero(X24990)
        | ~ class_Groups_Oordered__ab__group__add__abs(X24990) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).

fof(i_0_10957,plain,
    ! [X22126,X22127] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X22127),X22126) != c_Groups_Ozero__class_Ozero(X22127)
        | X22126 = c_Groups_Ozero__class_Ozero(X22127)
        | ~ class_Groups_Ogroup__add(X22127) )
      & ( X22126 != c_Groups_Ozero__class_Ozero(X22127)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X22127),X22126) = c_Groups_Ozero__class_Ozero(X22127)
        | ~ class_Groups_Ogroup__add(X22127) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_10958,plain,
    ! [X34256] :
      ( ~ hBOOL(hAPP(c_fNot,X34256))
      | ~ hBOOL(X34256) ),
    inference(variable_rename,[status(thm)],[i_0_6062]) ).

fof(i_0_10959,plain,
    ! [X22188] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22188),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22188,
    inference(variable_rename,[status(thm)],[fact_max__0R]) ).

fof(i_0_10960,plain,
    ! [X22850] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22850),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X22850,
    inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).

fof(i_0_10961,plain,
    ! [X19961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19961),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19961,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).

fof(i_0_10962,plain,
    ! [X23067] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23067),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X23067,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_10963,plain,
    ! [X22160] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22160),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22160,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_10964,plain,
    ! [X22165] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22165),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22165,
    inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(i_0_10965,plain,
    ! [X22762] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X22762)) = X22762,
    inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).

fof(i_0_10966,plain,
    ! [X23029] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23029)) = X23029,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_10967,plain,
    ! [X31795,X31796] : hAPP(c_List_Ofilter(X31796,X31795),c_List_Olist_ONil(X31796)) = c_List_Olist_ONil(X31796),
    inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(i_0_10968,plain,
    ! [X17041,X17042] :
      ( ~ class_Finite__Set_Ofinite(X17042)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17042),X17041)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_10969,plain,
    ! [X17039,X17040] :
      ( ~ class_Finite__Set_Ofinite(X17040)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17040),X17039)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_10970,plain,
    ! [X24042,X24043] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X24043),X24042) != c_Groups_Ozero__class_Ozero(X24043)
        | X24042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X24043) )
      & ( X24042 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X24043),X24042) = c_Groups_Ozero__class_Ozero(X24043)
        | ~ class_Int_Oring__char__0(X24043) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).

fof(i_0_10971,plain,
    ! [X24040,X24041] :
      ( ( c_Groups_Ozero__class_Ozero(X24041) != hAPP(c_Int_Oring__1__class_Oof__int(X24041),X24040)
        | X24040 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X24041) )
      & ( X24040 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(X24041) = hAPP(c_Int_Oring__1__class_Oof__int(X24041),X24040)
        | ~ class_Int_Oring__char__0(X24041) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).

cnf(i_0_10972,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6057]) ).

cnf(i_0_10973,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_6056]) ).

fof(i_0_10974,plain,
    ! [X22166] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22166),X22166) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).

fof(i_0_10975,plain,
    ! [X33149,X33150] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33150,X33149),c_Lazy__Sequence_Olazy__sequence_OEmpty(X33150)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I1_J]) ).

fof(i_0_10976,plain,
    ! [X25657,X25658] :
      ( ~ class_Int_Onumber__ring(X25658)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25658),X25657) = hAPP(c_Int_Oring__1__class_Oof__int(X25658),X25657) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).

fof(i_0_10977,plain,
    ! [X17494,X17495,X17496,X17497] :
      ( ( X17497 = X17495
        | c_Com_Ocom_OWhile(X17497,X17496) != c_Com_Ocom_OWhile(X17495,X17494) )
      & ( X17496 = X17494
        | c_Com_Ocom_OWhile(X17497,X17496) != c_Com_Ocom_OWhile(X17495,X17494) )
      & ( X17497 != X17495
        | X17496 != X17494
        | c_Com_Ocom_OWhile(X17497,X17496) = c_Com_Ocom_OWhile(X17495,X17494) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])]) ).

fof(i_0_10978,plain,
    ! [X17498,X17499,X17500,X17501] :
      ( ( X17501 = X17499
        | c_Com_Ocom_OSemi(X17501,X17500) != c_Com_Ocom_OSemi(X17499,X17498) )
      & ( X17500 = X17498
        | c_Com_Ocom_OSemi(X17501,X17500) != c_Com_Ocom_OSemi(X17499,X17498) )
      & ( X17501 != X17499
        | X17500 != X17498
        | c_Com_Ocom_OSemi(X17501,X17500) = c_Com_Ocom_OSemi(X17499,X17498) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])]) ).

fof(i_0_10979,plain,
    ! [X22124,X22125] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X22125),X22124) != X22124
        | X22124 = c_Groups_Ozero__class_Ozero(X22125)
        | ~ class_Groups_Olinordered__ab__group__add(X22125) )
      & ( X22124 != c_Groups_Ozero__class_Ozero(X22125)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X22125),X22124) = X22124
        | ~ class_Groups_Olinordered__ab__group__add(X22125) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_10980,plain,
    ! [X22128,X22129] :
      ( ( X22128 != hAPP(c_Groups_Ouminus__class_Ouminus(X22129),X22128)
        | X22128 = c_Groups_Ozero__class_Ozero(X22129)
        | ~ class_Groups_Olinordered__ab__group__add(X22129) )
      & ( X22128 != c_Groups_Ozero__class_Ozero(X22129)
        | X22128 = hAPP(c_Groups_Ouminus__class_Ouminus(X22129),X22128)
        | ~ class_Groups_Olinordered__ab__group__add(X22129) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_10981,plain,
    ! [X25921] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25921),c_Int_OPls) = X25921,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

fof(i_0_10982,plain,
    ! [X25920] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25920),c_Int_OPls) = X25920,
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(i_0_10983,plain,
    ! [X23580] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23580)) = X23580,
    inference(variable_rename,[status(thm)],[fact_nat__int]) ).

fof(i_0_10984,plain,
    ! [X34218,X34219] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34219)
      | ~ class_Lazy__Sequence_Osmall__lazy(X34218)
      | class_Lazy__Sequence_Osmall__lazy(tc_prod(X34219,X34218)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_10985,plain,
    ! [X34222,X34223] :
      ( ~ class_Enum_Oenum(X34223)
      | ~ class_Enum_Oenum(X34222)
      | class_Enum_Oenum(tc_prod(X34223,X34222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum])]) ).

fof(i_0_10986,plain,
    ! [X34209,X34210] :
      ( ~ class_Enum_Oenum(X34210)
      | ~ class_Enum_Oenum(X34209)
      | class_Enum_Oenum(tc_sum(X34210,X34209)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum])]) ).

fof(i_0_10987,plain,
    ! [X34203,X34204] :
      ( ~ class_Enum_Oenum(X34204)
      | ~ class_Enum_Oenum(X34203)
      | class_Enum_Oenum(tc_fun(X34204,X34203)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])]) ).

fof(i_0_10988,plain,
    ! [X24037,X24038] :
      ( ~ c_Nat__Transfer_Ois__nat(X24038)
      | ~ c_Nat__Transfer_Ois__nat(X24037)
      | c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X24038,X24037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).

fof(i_0_10989,plain,
    ! [X34220,X34221] :
      ( ~ class_Finite__Set_Ofinite(X34221)
      | ~ class_Finite__Set_Ofinite(X34220)
      | class_Finite__Set_Ofinite(tc_prod(X34221,X34220)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_10990,plain,
    ! [X34207,X34208] :
      ( ~ class_Finite__Set_Ofinite(X34208)
      | ~ class_Finite__Set_Ofinite(X34207)
      | class_Finite__Set_Ofinite(tc_sum(X34208,X34207)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_10991,plain,
    ! [X34187,X34188] :
      ( ~ class_Finite__Set_Ofinite(X34188)
      | ~ class_Finite__Set_Ofinite(X34187)
      | class_Finite__Set_Ofinite(tc_fun(X34188,X34187)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_10992,plain,
    ! [X17410,X17411,X17412,X17413] : c_Com_Ocom_OWhile(X17413,X17412) != c_Com_Ocom_OSemi(X17411,X17410),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J]) ).

fof(i_0_10993,plain,
    ! [X17406,X17407,X17408,X17409] : c_Com_Ocom_OSemi(X17409,X17408) != c_Com_Ocom_OWhile(X17407,X17406),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I46_J]) ).

fof(i_0_10994,plain,
    ! [X25922] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X25922) = X25922,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_10995,plain,
    ! [X32135,X32136] :
      ( ( hAPP(c_List_Orev(X32136),X32135) != c_List_Olist_ONil(X32136)
        | X32135 = c_List_Olist_ONil(X32136) )
      & ( X32135 != c_List_Olist_ONil(X32136)
        | hAPP(c_List_Orev(X32136),X32135) = c_List_Olist_ONil(X32136) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).

fof(i_0_10996,plain,
    ! [X30640,X30641] :
      ( ( hAPP(c_List_Orotate1(X30641),X30640) != c_List_Olist_ONil(X30641)
        | X30640 = c_List_Olist_ONil(X30641) )
      & ( X30640 != c_List_Olist_ONil(X30641)
        | hAPP(c_List_Orotate1(X30641),X30640) = c_List_Olist_ONil(X30641) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).

fof(i_0_10997,plain,
    ! [X32137,X32138] :
      ( ( c_List_Olist_ONil(X32138) != hAPP(c_List_Orev(X32138),X32137)
        | X32137 = c_List_Olist_ONil(X32138) )
      & ( X32137 != c_List_Olist_ONil(X32138)
        | c_List_Olist_ONil(X32138) = hAPP(c_List_Orev(X32138),X32137) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).

fof(i_0_10998,plain,
    ! [X25923] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X25923) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).

fof(i_0_10999,plain,
    ! [X33234] : c_Relation_Otrans(tc_fun(X33234,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X33234)),
    inference(variable_rename,[status(thm)],[fact_trans__finite__psubset]) ).

fof(i_0_11000,plain,
    ! [X27517] : c_Wellfounded_Owf(tc_fun(X27517,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X27517)),
    inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).

fof(i_0_11001,plain,
    ! [X31797] : c_List_Otranspose(X31797,c_List_Olist_ONil(tc_List_Olist(X31797))) = c_List_Olist_ONil(tc_List_Olist(X31797)),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

cnf(i_0_11002,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).

cnf(i_0_11003,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

cnf(i_0_11004,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).

fof(i_0_11005,plain,
    ! [X31329,X31330] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X31330) != hAPP(c_Code__Numeral_Onat__of,X31329)
        | X31330 = X31329 )
      & ( X31330 != X31329
        | hAPP(c_Code__Numeral_Onat__of,X31330) = hAPP(c_Code__Numeral_Onat__of,X31329) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).

fof(i_0_11006,plain,
    ! [X31327,X31328] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X31328) != hAPP(c_Code__Numeral_Onat__of,X31327)
        | X31328 = X31327 )
      & ( X31328 != X31327
        | hAPP(c_Code__Numeral_Onat__of,X31328) = hAPP(c_Code__Numeral_Onat__of,X31327) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).

fof(i_0_11007,plain,
    ! [X31272,X31273] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X31273) != hAPP(c_Code__Numeral_Oof__nat,X31272)
        | X31273 = X31272 )
      & ( X31273 != X31272
        | hAPP(c_Code__Numeral_Oof__nat,X31273) = hAPP(c_Code__Numeral_Oof__nat,X31272) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).

fof(i_0_11008,plain,
    ! [X26989,X26990] :
      ( ( hAPP(c_Int_ORep__Integ,X26990) != hAPP(c_Int_ORep__Integ,X26989)
        | X26990 = X26989 )
      & ( X26990 != X26989
        | hAPP(c_Int_ORep__Integ,X26990) = hAPP(c_Int_ORep__Integ,X26989) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).

fof(i_0_11009,plain,
    ! [X21538,X21539] :
      ( hAPP(c_Nat_OSuc,X21539) != hAPP(c_Nat_OSuc,X21538)
      | X21539 = X21538 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_11010,plain,
    ! [X21536,X21537] :
      ( ( hAPP(c_Nat_OSuc,X21537) != hAPP(c_Nat_OSuc,X21536)
        | X21537 = X21536 )
      & ( X21537 != X21536
        | hAPP(c_Nat_OSuc,X21537) = hAPP(c_Nat_OSuc,X21536) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_11011,plain,
    ! [X24856,X24857] :
      ( ( c_Groups_Osgn__class_Osgn(X24857,X24856) != c_Groups_Ozero__class_Ozero(X24857)
        | X24856 = c_Groups_Ozero__class_Ozero(X24857)
        | ~ class_Rings_Olinordered__idom(X24857) )
      & ( X24856 != c_Groups_Ozero__class_Ozero(X24857)
        | c_Groups_Osgn__class_Osgn(X24857,X24856) = c_Groups_Ozero__class_Ozero(X24857)
        | ~ class_Rings_Olinordered__idom(X24857) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_11012,plain,
    ! [X33136] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33136)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X33136)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J]) ).

fof(i_0_11013,plain,
    ! [X30231] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30231)),c_List_Olist_ONil(X30231)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(i_0_11014,plain,
    ! [X33404,X33405] : c_Relation_Osym(X33405,c_Relation_OId__on(X33405,X33404)),
    inference(variable_rename,[status(thm)],[fact_sym__Id__on]) ).

fof(i_0_11015,plain,
    ! [X33352,X33353] : c_Relation_Oantisym(X33353,c_Relation_OId__on(X33353,X33352)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id__on]) ).

fof(i_0_11016,plain,
    ! [X33231,X33232] : c_Relation_Otrans(X33232,c_Transitive__Closure_Ortrancl(X33232,X33231)),
    inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).

fof(i_0_11017,plain,
    ! [X33239,X33240] : c_Relation_Otrans(X33240,c_Relation_OId__on(X33240,X33239)),
    inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).

fof(i_0_11018,plain,
    ! [X32450,X32451] : c_Wellfounded_Owf(X32451,c_List_Omeasures(X32451,X32450)),
    inference(variable_rename,[status(thm)],[fact_wf__measures]) ).

fof(i_0_11019,plain,
    ! [X26059] :
      ( ~ class_Rings_Osemiring__1(X26059)
      | ~ c_Int_Oiszero(X26059,c_Groups_Oone__class_Oone(X26059)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6063])]) ).

fof(i_0_11020,plain,
    ! [X32020,X32021] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X32021,X32020)),
    inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).

fof(i_0_11021,plain,
    ! [X28432,X28433] : c_Hilbert__Choice_OEps(X28433,hAPP(c_fequal,X28432)) = X28432,
    inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(i_0_11022,plain,
    ! [X17431,X17432] : c_HOL_OThe(X17432,hAPP(c_fequal,X17431)) = X17431,
    inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(i_0_11023,plain,
    ! [X30228] :
      ( ~ class_Groups_Omonoid__add(X30228)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30228),c_List_Olist_ONil(X30228)) = c_Groups_Ozero__class_Ozero(X30228) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).

fof(i_0_11024,plain,
    ! [X24991] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24991)
      | hAPP(c_Groups_Oabs__class_Oabs(X24991),c_Groups_Ozero__class_Ozero(X24991)) = c_Groups_Ozero__class_Ozero(X24991) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).

fof(i_0_11025,plain,
    ! [X24971] :
      ( ~ class_Rings_Olinordered__idom(X24971)
      | hAPP(c_Groups_Oabs__class_Oabs(X24971),c_Groups_Oone__class_Oone(X24971)) = c_Groups_Oone__class_Oone(X24971) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_11026,plain,
    ! [X22132] :
      ( ~ class_Groups_Ogroup__add(X22132)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22132),c_Groups_Ozero__class_Ozero(X22132)) = c_Groups_Ozero__class_Ozero(X22132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_11027,plain,
    ! [X19789] :
      ( ~ class_Lattices_Oboolean__algebra(X19789)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X19789),c_Orderings_Otop__class_Otop(X19789)) = c_Orderings_Obot__class_Obot(X19789) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).

fof(i_0_11028,plain,
    ! [X19790] :
      ( ~ class_Lattices_Oboolean__algebra(X19790)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X19790),c_Orderings_Obot__class_Obot(X19790)) = c_Orderings_Otop__class_Otop(X19790) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).

fof(i_0_11029,plain,
    ! [X34169,X34170] :
      ( ~ class_Lattices_Obounded__lattice(X34170)
      | class_Lattices_Obounded__lattice(tc_fun(X34169,X34170)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).

fof(i_0_11030,plain,
    ! [X34181,X34182] :
      ( ~ class_Lattices_Odistrib__lattice(X34182)
      | class_Lattices_Odistrib__lattice(tc_fun(X34181,X34182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).

fof(i_0_11031,plain,
    ! [X34179,X34180] :
      ( ~ class_Lattices_Olattice(X34180)
      | class_Lattices_Osemilattice__inf(tc_fun(X34179,X34180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).

fof(i_0_11032,plain,
    ! [X34171,X34172] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X34172)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X34171,X34172)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).

fof(i_0_11033,plain,
    ! [X34175,X34176] :
      ( ~ class_Lattices_Obounded__lattice(X34176)
      | class_Lattices_Obounded__lattice__bot(tc_fun(X34175,X34176)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).

fof(i_0_11034,plain,
    ! [X34177,X34178] :
      ( ~ class_Lattices_Olattice(X34178)
      | class_Lattices_Osemilattice__sup(tc_fun(X34177,X34178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).

fof(i_0_11035,plain,
    ! [X34173,X34174] :
      ( ~ class_Lattices_Obounded__lattice(X34174)
      | class_Lattices_Obounded__lattice__top(tc_fun(X34173,X34174)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).

fof(i_0_11036,plain,
    ! [X34193,X34194] :
      ( ~ class_Orderings_Otop(X34194)
      | class_Orderings_Otop(tc_fun(X34193,X34194)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_11037,plain,
    ! [X34189,X34190] :
      ( ~ class_Lattices_Olattice(X34190)
      | class_Lattices_Olattice(tc_fun(X34189,X34190)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).

fof(i_0_11038,plain,
    ! [X34199,X34200] :
      ( ~ class_Groups_Ouminus(X34200)
      | class_Groups_Ouminus(tc_fun(X34199,X34200)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_11039,plain,
    ! [X34183,X34184] :
      ( ~ class_Lattices_Oboolean__algebra(X34184)
      | class_Lattices_Oboolean__algebra(tc_fun(X34183,X34184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_11040,plain,
    ! [X34191,X34192] :
      ( ~ class_Orderings_Oorder(X34192)
      | class_Orderings_Oorder(tc_fun(X34191,X34192)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_11041,plain,
    ! [X34195,X34196] :
      ( ~ class_Orderings_Oord(X34196)
      | class_Orderings_Oord(tc_fun(X34195,X34196)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_11042,plain,
    ! [X34185,X34186] :
      ( ~ class_Orderings_Opreorder(X34186)
      | class_Orderings_Opreorder(tc_fun(X34185,X34186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_11043,plain,
    ! [X34201,X34202] :
      ( ~ class_Groups_Ominus(X34202)
      | class_Groups_Ominus(tc_fun(X34201,X34202)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).

fof(i_0_11044,plain,
    ! [X34197,X34198] :
      ( ~ class_Orderings_Obot(X34198)
      | class_Orderings_Obot(tc_fun(X34197,X34198)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).

fof(i_0_11045,plain,
    ! [X33440,X33441] :
      ( ~ c_Equiv__Relations_Oequivp(X33441,X33440)
      | c_Equiv__Relations_Opart__equivp(X33441,X33440) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__implies__part__equivp])]) ).

fof(i_0_11046,plain,
    ! [X33324,X33325] :
      ( ( c_Predicate_Oreflp(X33325,X33324)
        | ~ c_Equiv__Relations_Oequivp(X33325,X33324) )
      & ( c_Predicate_Osymp(X33325,X33324)
        | ~ c_Equiv__Relations_Oequivp(X33325,X33324) )
      & ( c_Predicate_Otransp(X33325,X33324)
        | ~ c_Equiv__Relations_Oequivp(X33325,X33324) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6064])])]) ).

fof(i_0_11047,plain,
    ! [X28233,X28234] :
      ( ~ c_Wellfounded_Owf(X28234,X28233)
      | c_Wellfounded_Oacyclic(X28234,X28233) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).

fof(i_0_11048,plain,
    ! [X24030] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24030)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(i_0_11049,plain,
    ! [X33949] : c_Lazy__Sequence_Oflat(X33949,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X33949))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X33949),
    inference(variable_rename,[status(thm)],[fact__04]) ).

fof(i_0_11050,plain,
    ! [X31326] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X31326)) = X31326,
    inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).

fof(i_0_11051,plain,
    ! [X31325] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X31325)) = X31325,
    inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).

fof(i_0_11052,plain,
    ! [X31324] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X31324)) = X31324,
    inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).

fof(i_0_11053,plain,
    ! [X27304] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X27304)) = X27304,
    inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(i_0_11054,plain,
    ! [X26057,X26058] :
      ( ( ~ c_Int_Oiszero(X26058,X26057)
        | X26057 = c_Groups_Ozero__class_Ozero(X26058)
        | ~ class_Rings_Osemiring__1(X26058) )
      & ( X26057 != c_Groups_Ozero__class_Ozero(X26058)
        | c_Int_Oiszero(X26058,X26057)
        | ~ class_Rings_Osemiring__1(X26058) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).

fof(i_0_11055,plain,
    ! [X22857] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22857) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X22857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22857) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])]) ).

fof(i_0_11056,plain,
    ! [X24039] :
      ( ~ class_Rings_Oring__1(X24039)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24039),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X24039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).

fof(i_0_11057,plain,
    ! [X24056] :
      ( ~ class_Rings_Oring__1(X24056)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24056),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X24056) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).

fof(i_0_11058,plain,
    ! [X22904] :
      ( ~ class_Rings_Osemiring__1(X22904)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22904),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X22904) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).

fof(i_0_11059,plain,
    ! [X22923] :
      ( ~ class_Rings_Osemiring__1(X22923)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X22923),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X22923) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).

fof(i_0_11060,plain,
    ! [X25873] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25873) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X25873),
    inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).

fof(i_0_11061,plain,
    ! [X31621,X31622] :
      ( ( c_List_Oremdups(X31622,X31621) != c_List_Olist_ONil(X31622)
        | X31621 = c_List_Olist_ONil(X31622) )
      & ( X31621 != c_List_Olist_ONil(X31622)
        | c_List_Oremdups(X31622,X31621) = c_List_Olist_ONil(X31622) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff])]) ).

fof(i_0_11062,plain,
    ! [X31625,X31626] :
      ( ( c_List_Olist_ONil(X31626) != c_List_Oremdups(X31626,X31625)
        | X31625 = c_List_Olist_ONil(X31626) )
      & ( X31625 != c_List_Olist_ONil(X31626)
        | c_List_Olist_ONil(X31626) = c_List_Oremdups(X31626,X31625) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])]) ).

fof(i_0_11063,plain,
    ! [X34257] :
      ( hBOOL(X34257)
      | hBOOL(hAPP(c_fNot,X34257)) ),
    inference(variable_rename,[status(thm)],[i_0_6065]) ).

fof(i_0_11064,plain,
    ! [X24858] :
      ( ~ class_Groups_Osgn__if(X24858)
      | c_Groups_Osgn__class_Osgn(X24858,c_Groups_Ozero__class_Ozero(X24858)) = c_Groups_Ozero__class_Ozero(X24858) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_11065,plain,
    ! [X19182] :
      ( ~ class_Orderings_Oord(X19182)
      | c_Orderings_Oord__class_Omax(X19182) = c_Orderings_Oord_Omax(X19182,c_Orderings_Oord__class_Oless__eq(X19182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).

fof(i_0_11066,plain,
    ! [X19183] :
      ( ~ class_Orderings_Oord(X19183)
      | c_Orderings_Oord__class_Omin(X19183) = c_Orderings_Oord_Omin(X19183,c_Orderings_Oord__class_Oless__eq(X19183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).

fof(i_0_11067,plain,
    ! [X32139] : hAPP(c_List_Orev(X32139),c_List_Olist_ONil(X32139)) = c_List_Olist_ONil(X32139),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(i_0_11068,plain,
    ! [X30759] : hAPP(c_List_Otl(X30759),c_List_Olist_ONil(X30759)) = c_List_Olist_ONil(X30759),
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(i_0_11069,plain,
    ! [X34216,X34217] : class_Nat_Osize(tc_Nitpick_Opair__box(X34217,X34216)),
    inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize]) ).

fof(i_0_11070,plain,
    ! [X34224,X34225] : class_Nat_Osize(tc_prod(X34225,X34224)),
    inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(i_0_11071,plain,
    ! [X34211,X34212] : class_Nat_Osize(tc_sum(X34212,X34211)),
    inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(i_0_11072,plain,
    ! [X25926] :
      ( ~ class_Int_Onumber__ring(X25926)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25926),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X25926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_11073,plain,
    ! [X25925] :
      ( ~ class_Int_Onumber__ring(X25925)
      | c_Groups_Ozero__class_Ozero(X25925) = hAPP(c_Int_Onumber__class_Onumber__of(X25925),c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_11074,plain,
    ! [X32035] :
      ( ~ class_Orderings_Olinorder(X32035)
      | c_List_Olinorder__class_Osorted(X32035,c_List_Olist_ONil(X32035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).

fof(i_0_11075,plain,
    ! [X32007] :
      ( ~ class_Orderings_Olinorder(X32007)
      | c_List_Olinorder__class_Osorted(X32007,c_List_Olist_ONil(X32007)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).

fof(i_0_11076,plain,
    ! [X26056] :
      ( ~ class_Rings_Osemiring__1(X26056)
      | c_Int_Oiszero(X26056,c_Groups_Ozero__class_Ozero(X26056)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).

fof(i_0_11077,plain,
    ! [X32744,X32745] : hAPP(c_New__DSequence_Opos__empty(X32745),X32744) = c_Lazy__Sequence_Oempty(X32745),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(i_0_11078,plain,
    ! [X31627] : c_List_Oremdups(X31627,c_List_Olist_ONil(X31627)) = c_List_Olist_ONil(X31627),
    inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(i_0_11079,plain,
    ! [X30187] : c_List_Obutlast(X30187,c_List_Olist_ONil(X30187)) = c_List_Olist_ONil(X30187),
    inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(i_0_11080,plain,
    ! [X22136] : hAPP(c_Nat_OSuc,X22136) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_11081,plain,
    ! [X22135] : hAPP(c_Nat_OSuc,X22135) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_11082,plain,
    ! [X22133] : hAPP(c_Nat_OSuc,X22133) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_11083,plain,
    ! [X22138] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22138),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_11084,plain,
    ! [X22137] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22137),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_11085,plain,
    ! [X22134] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22134),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_11086,plain,
    ! [X17404,X17405] : c_Com_Ocom_OWhile(X17405,X17404) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I17_J]) ).

fof(i_0_11087,plain,
    ! [X17400,X17401] : c_Com_Ocom_OSemi(X17401,X17400) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I13_J]) ).

fof(i_0_11088,plain,
    ! [X17402,X17403] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X17403,X17402),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I16_J]) ).

fof(i_0_11089,plain,
    ! [X17398,X17399] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X17399,X17398),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I12_J]) ).

fof(i_0_11090,plain,
    ! [X20718] :
      ( ~ class_Lattices_Osemilattice__inf(X20718)
      | ~ class_Orderings_Olinorder(X20718)
      | c_Lattices_Osemilattice__inf__class_Oinf(X20718) = c_Orderings_Oord__class_Omin(X20718) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).

fof(i_0_11091,plain,
    ! [X19578] :
      ( ~ class_Lattices_Osemilattice__sup(X19578)
      | ~ class_Orderings_Olinorder(X19578)
      | c_Lattices_Osemilattice__sup__class_Osup(X19578) = c_Orderings_Oord__class_Omax(X19578) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).

fof(i_0_11092,plain,
    ! [X21535] : hAPP(c_Nat_OSuc,X21535) != X21535,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_11093,plain,
    ! [X21534] : X21534 != hAPP(c_Nat_OSuc,X21534),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_11094,plain,
    ! [X28027,X28028] : hAPP(c_Fun_Oid(X28028),X28027) = X28027,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

fof(i_0_11095,plain,
    ! [X28025,X28026] : hAPP(c_Fun_Oid(X28026),X28025) = X28025,
    inference(variable_rename,[status(thm)],[fact_id__apply]) ).

fof(i_0_11096,plain,
    ! [X25305,X25306] : hAPP(c_Set_OCollect(X25306),X25305) = X25305,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(i_0_11097,plain,
    ! [X34228,X34229] : hAPP(c_COMBI(X34229),X34228) = X34228,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_11098,plain,
    ! [X22123] :
      ( ~ class_Rings_Ozero__neq__one(X22123)
      | c_Groups_Oone__class_Oone(X22123) != c_Groups_Ozero__class_Ozero(X22123) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_11099,plain,
    ! [X22122] :
      ( ~ class_Rings_Ozero__neq__one(X22122)
      | c_Groups_Ozero__class_Ozero(X22122) != c_Groups_Oone__class_Oone(X22122) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_11100,plain,
    ! [X33613] : c_Quickcheck_Obeyond(X33613,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_beyond__zero]) ).

fof(i_0_11101,plain,
    ! [X27559] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X27559)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(i_0_11102,plain,
    ! [X27560] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X27560)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(i_0_11103,plain,
    ! [X25866] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25866) = X25866,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(i_0_11104,plain,
    ! [X27118] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X27118) = X27118,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_11105,plain,
    ! [X34205] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34205)
      | class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X34205)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_11106,plain,
    ! [X34214] :
      ( ~ class_Enum_Oenum(X34214)
      | class_Enum_Oenum(tc_Option_Ooption(X34214)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum])]) ).

fof(i_0_11107,plain,
    ! [X34213] :
      ( ~ class_Finite__Set_Ofinite(X34213)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X34213)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_11108,plain,
    ! [X27157] : c_Equiv__Relations_Oequivp(X27157,c_fequal),
    inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).

fof(i_0_11109,plain,
    ! [X34227] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X34227)),
    inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(i_0_11110,plain,
    ! [X34206] : class_Nat_Osize(tc_List_Olist(X34206)),
    inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(i_0_11111,plain,
    ! [X34215] : class_Nat_Osize(tc_Option_Ooption(X34215)),
    inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(i_0_11112,plain,
    ! [X34226] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X34226)),
    inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize]) ).

fof(i_0_11113,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_11114,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X1,tc_HOL_Obool)),X4)),X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X2,esk257_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk258_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8),X7),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))
    | ~ c_Equiv__Relations_Ocongruent2(X11,X8,tc_fun(X1,tc_HOL_Obool),X9,X6,X2)
    | ~ c_Equiv__Relations_Oequiv(X8,X7,X6)
    | ~ c_Equiv__Relations_Oequiv(X11,X10,X9) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11115,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk258_11(X2,X3,X4,X5,X6,X7,X8,X1,X9,X10,X11)),X8))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X8),X7)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))
    | ~ c_Equiv__Relations_Ocongruent2(X11,X1,tc_fun(X6,tc_HOL_Obool),X9,X7,X5)
    | ~ c_Equiv__Relations_Oequiv(X1,X8,X7)
    | ~ c_Equiv__Relations_Oequiv(X11,X10,X9) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11116,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk257_11(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X1)),X11))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X9,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X9,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9),X8),X7)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X11),X10)))
    | ~ c_Equiv__Relations_Ocongruent2(X1,X9,tc_fun(X6,tc_HOL_Obool),X10,X7,X5)
    | ~ c_Equiv__Relations_Oequiv(X9,X8,X7)
    | ~ c_Equiv__Relations_Oequiv(X1,X11,X10) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11117,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk551_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk552_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk553_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk554_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
    | hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11118,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk557_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk558_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk559_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk560_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
    | hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6068]),
    [final] ).

cnf(i_0_11119,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk559_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk560_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))
    | hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6068]),
    [final] ).

cnf(i_0_11120,plain,
    c_Divides_Oadjust(X1) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))),
    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_6069,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11121,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X6)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X7)))))))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7))) ),
    inference(split_conjunct,[status(thm)],[i_0_6073]),
    [final] ).

cnf(i_0_11122,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk551_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk552_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))
    | hBOOL(hAPP(hAPP(X5,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X5,X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11123,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5) = hAPP(c_Set_OCollect(tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X3)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X3)))),hAPP(c_COMBC(X2,X3,tc_prod(X2,X3)),c_Product__Type_OPair(X2,X3))))),X5))))),
    inference(split_conjunct,[status(thm)],[i_0_6074]),
    [final] ).

cnf(i_0_11124,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6075]),
    [final] ).

cnf(i_0_11125,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omin(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6076]),
    [final] ).

cnf(i_0_11126,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
    | ~ class_Lattices_Odistrib__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6077]),
    [final] ).

cnf(i_0_11127,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
    | ~ class_Lattices_Odistrib__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6078]),
    [final] ).

cnf(i_0_11128,plain,
    c_List_Oset__Cons(X1,X2,X3) = hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),X3)))))),
    inference(split_conjunct,[status(thm)],[i_0_6079]),
    [final] ).

cnf(i_0_11129,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk308_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk309_8(X3,X4,X5,X2,X1,X6,X7,X8))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X7)),X6),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X8,X7),c_Product__Type_Omap__pair(X1,X8,X2,X7,X5,X4)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6080]),
    [final] ).

cnf(i_0_11130,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk555_7(X3,X4,X5,X6,X7,X2,X1)),esk556_7(X3,X4,X5,X6,X7,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))
    | hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6081]),
    [final] ).

cnf(i_0_11131,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1)))) ),
    inference(rw,[status(thm)],[i_0_6082,c_0_6083]),
    [final] ).

cnf(i_0_11132,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1)))) ),
    inference(rw,[status(thm)],[i_0_6084,c_0_6083]),
    [final] ).

cnf(i_0_11133,plain,
    ( hAPP(c_Set_Oimage(X1,X8,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X5),c_Set_Oimage(X1,X8,X7)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk153_8(X3,X2,X4,X5,X6,X7,X8,X1))),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X4))
    | ~ c_Fun_Oinj__on(X1,X8,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6085]),
    [final] ).

cnf(i_0_11134,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6086]),
    [final] ).

cnf(i_0_11135,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6087]),
    [final] ).

cnf(i_0_11136,plain,
    c_List_Olenlex(X1,X2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2)))))),
    inference(split_conjunct,[status(thm)],[i_0_6088]),
    [final] ).

cnf(i_0_11137,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk555_7(X5,X6,X7,X4,X3,X2,X1)),esk556_7(X5,X6,X7,X4,X3,X2,X1)))),X5))
    | hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6081]),
    [final] ).

cnf(i_0_11138,plain,
    ( hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(X1,esk553_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk554_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | ~ hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11139,plain,
    ( hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X1,esk557_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk558_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6068]),
    [final] ).

cnf(i_0_11140,plain,
    ( hAPP(c_List_Ofoldl(X1,X8,hAPP(c_COMBC(X8,X1,X1),X3),hAPP(X6,X4)),X7) = hAPP(X6,hAPP(c_List_Ofoldl(X2,X8,hAPP(c_COMBC(X8,X2,X2),X5),X4),X7))
    | hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,esk455_8(X4,X5,X6,X3,X2,X1,X7,X8))),X6) != hAPP(c_Fun_Ocomp(X2,X1,X2,X6),hAPP(X5,esk455_8(X4,X5,X6,X3,X2,X1,X7,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_6089]),
    [final] ).

cnf(i_0_11141,plain,
    c_Nitpick_Oplus__frac(X1,X2,X3) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3)))))),c_COMBI(tc_Int_Oint))),
    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_6090,c_0_6091]),c_0_6091]),c_0_6091]),c_0_6091]),c_0_6092]),c_0_6092]),
    [final] ).

cnf(i_0_11142,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6093]),
    [final] ).

cnf(i_0_11143,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6094]),
    [final] ).

cnf(i_0_11144,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X6),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X5)),X6),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6095]),
    [final] ).

cnf(i_0_11145,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4)) ),
    inference(rw,[status(thm)],[i_0_6096,c_0_6097]),
    [final] ).

cnf(i_0_11146,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6086]),
    [final] ).

cnf(i_0_11147,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6087]),
    [final] ).

cnf(i_0_11148,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk265_7(X2,X3,X4,X5,X6,X7,X1)),esk266_7(X2,X3,X4,X5,X6,X7,X1))),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
    | ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6098]),
    [final] ).

cnf(i_0_11149,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk308_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk309_8(X5,X6,X4,X7,X8,X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(c_Set_Oimage(tc_prod(X8,X7),tc_prod(X2,X3),c_Product__Type_Omap__pair(X8,X2,X7,X3,X4,X6)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6080]),
    [final] ).

cnf(i_0_11150,plain,
    ( hBOOL(hAPP(hAPP(X1,esk551_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk552_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11151,plain,
    ( hBOOL(hAPP(hAPP(X1,esk559_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk560_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6068]),
    [final] ).

cnf(i_0_11152,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6093]),
    [final] ).

cnf(i_0_11153,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6094]),
    [final] ).

cnf(i_0_11154,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X5,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBC(X5,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X1,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X5),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X1,X5)))),c_Product__Type_OPair(X1,X5)))),X6),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X5),c_COMBC(X2,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X5,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X2),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X5,X2)))),c_Product__Type_OPair(X5,X2)))),X7)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7))) ),
    inference(split_conjunct,[status(thm)],[i_0_6095]),
    [final] ).

cnf(i_0_11155,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))) ),
    inference(rw,[status(thm)],[i_0_6099,c_0_6097]),
    [final] ).

cnf(i_0_11156,plain,
    hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6100,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11157,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X1)),c_fequal)),X4)))),X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6101]),
    [final] ).

cnf(i_0_11158,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X8),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),X4)
    | hAPP(X1,esk35_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk35_8(X2,X1,X3,X4,X5,X6,X7,X8)))
    | X3 != hAPP(c_Set_Oimage(X7,X6,X5),X4)
    | ~ c_Fun_Oinj__on(X7,X6,X5,X4)
    | ~ class_Groups_Ocomm__monoid__add(X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6102]),
    [final] ).

cnf(i_0_11159,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X2))),c_Transitive__Closure_Ortrancl(X1,X4))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X3))),c_Transitive__Closure_Ortrancl(X1,X4)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6103,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11160,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6105,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11161,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X5)),hAPP(c_Relation_Oconverse(X1,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6106]),
    [final] ).

cnf(i_0_11162,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk455_8(X2,X3,X4,X5,X6,X7,X8,X1)),hAPP(c_List_Oset(X1),X8)))
    | hAPP(c_List_Ofoldl(X7,X1,hAPP(c_COMBC(X1,X7,X7),X5),hAPP(X4,X2)),X8) = hAPP(X4,hAPP(c_List_Ofoldl(X6,X1,hAPP(c_COMBC(X1,X6,X6),X3),X2),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6089]),
    [final] ).

cnf(i_0_11163,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk153_8(X2,X3,X4,X1,X5,X6,X7,X8)),X4))
    | hAPP(c_Set_Oimage(X8,X7,X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X8,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X1),c_Set_Oimage(X8,X7,X6)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ c_Fun_Oinj__on(X8,X7,X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6085]),
    [final] ).

cnf(i_0_11164,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk332_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X8),X3),X5)
    | X4 != hAPP(c_Set_Oimage(X1,X7,X6),X5)
    | ~ c_Fun_Oinj__on(X1,X7,X6,X5)
    | ~ class_Groups_Ocomm__monoid__mult(X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6107]),
    [final] ).

cnf(i_0_11165,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk35_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),X5)
    | X4 != hAPP(c_Set_Oimage(X1,X7,X6),X5)
    | ~ c_Fun_Oinj__on(X1,X7,X6,X5)
    | ~ class_Groups_Ocomm__monoid__add(X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6102]),
    [final] ).

cnf(i_0_11166,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk339_8(X2,X3,X4,X5,X6,X7,X1,X8)),X4))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X6),X4))
    | X5 != X4
    | X7 != X6
    | ~ class_Groups_Ocomm__monoid__add(X8)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6108]),
    [final] ).

cnf(i_0_11167,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(split_conjunct,[status(thm)],[i_0_6109]),
    [final] ).

cnf(i_0_11168,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(X2,esk505_7(X3,X2,X1,X4,X5,X6,X7)),esk506_7(X3,X2,X1,X4,X5,X6,X7))))
    | ~ hBOOL(hAPP(hAPP(X7,hAPP(c_Product__Type_Osnd(X6,X5),X4)),hAPP(c_Product__Type_Ofst(X6,X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6110]),
    [final] ).

cnf(i_0_11169,plain,
    c_FunDef_Orp__inv__image(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBS(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(X2,X1)),c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),c_Relation_Oinv__image(X1,X2))))),c_Relation_Oinv__image(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_6111]),
    [final] ).

cnf(i_0_11170,plain,
    hAPP(hAPP(c_Relation_Oinv__image(X1,X2),X3),X4) = hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),X2),c_COMBB(X1,tc_prod(X1,X1),X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_prod(X1,X1)),X2),c_Product__Type_OPair(X1,X1)),X4))),X4)))),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6112]),
    [final] ).

cnf(i_0_11171,plain,
    hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)) = hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))))),
    inference(split_conjunct,[status(thm)],[i_0_6113]),
    [final] ).

cnf(i_0_11172,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X3))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X4))),c_Com_Ocom_OWhile(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6114]),
    [final] ).

cnf(i_0_11173,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6,X8),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X1),X4)
    | hAPP(X1,esk332_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk332_8(X2,X1,X3,X4,X5,X6,X7,X8))
    | X3 != hAPP(c_Set_Oimage(X7,X6,X5),X4)
    | ~ c_Fun_Oinj__on(X7,X6,X5,X4)
    | ~ class_Groups_Ocomm__monoid__mult(X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6107]),
    [final] ).

cnf(i_0_11174,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X6),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X5),X3))
    | hAPP(X1,esk339_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk339_8(X2,X1,X3,X4,X5,X6,X7,X8))
    | X4 != X3
    | X6 != X5
    | ~ class_Groups_Ocomm__monoid__add(X8)
    | ~ class_Orderings_Oord(X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6108]),
    [final] ).

cnf(i_0_11175,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6115]),
    [final] ).

cnf(i_0_11176,plain,
    hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_6116]),
    [final] ).

cnf(i_0_11177,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X5)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6106]),
    [final] ).

cnf(i_0_11178,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk259_7(X3,X4,X2,X1,X5,X6,X7))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
    | ~ c_Equiv__Relations_Ocongruent(X7,tc_fun(X1,tc_HOL_Obool),X5,X2)
    | ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6117]),
    [final] ).

cnf(i_0_11179,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X6),X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(X1,esk501_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6118]),
    [final] ).

cnf(i_0_11180,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(X1,esk119_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6119]),
    [final] ).

cnf(i_0_11181,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6120]),
    [final] ).

cnf(i_0_11182,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6121]),
    [final] ).

cnf(i_0_11183,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Lattices_Odistrib__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6122]),
    [final] ).

cnf(i_0_11184,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Lattices_Odistrib__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6123]),
    [final] ).

cnf(i_0_11185,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6124]),
    [final] ).

cnf(i_0_11186,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6125]),
    [final] ).

cnf(i_0_11187,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
    inference(split_conjunct,[status(thm)],[i_0_6126]),
    [final] ).

cnf(i_0_11188,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk6_5(X3,X4,X2,X1,X5)))),X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(X3,esk5_5(X3,X4,X2,X1,X5))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6127]),
    [final] ).

cnf(i_0_11189,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),esk395_4(X2,X3,X4,X1)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6128]),
    [final] ).

cnf(i_0_11190,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6129]),
    [final] ).

cnf(i_0_11191,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6130]),
    [final] ).

cnf(i_0_11192,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6131]),
    [final] ).

cnf(i_0_11193,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk339_8(X3,X4,X5,X6,X2,X7,X1,X8)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X6)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))
    | X6 != X5
    | X7 != X2
    | ~ class_Groups_Ocomm__monoid__add(X8)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6108]),
    [final] ).

cnf(i_0_11194,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6132]),
    [final] ).

cnf(i_0_11195,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6115]),
    [final] ).

cnf(i_0_11196,plain,
    ( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),esk25_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk26_7(X6,X7,X5,X4,X3,X2,X1))
    | hAPP(hAPP(X3,X7),X6) = X4
    | ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11197,plain,
    ( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),esk25_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk26_7(X6,X7,X5,X4,X3,X2,X1))
    | X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11198,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk502_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6134]),
    [final] ).

cnf(i_0_11199,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk96_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6135]),
    [final] ).

cnf(i_0_11200,plain,
    c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),hAPP(c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_6136]),
    [final] ).

cnf(i_0_11201,plain,
    hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3)))))),
    inference(split_conjunct,[status(thm)],[i_0_6137]),
    [final] ).

cnf(i_0_11202,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6138,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11203,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6139,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11204,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X1))) ),
    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_6140,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11205,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6128]),
    [final] ).

cnf(i_0_11206,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6129]),
    [final] ).

cnf(i_0_11207,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6130]),
    [final] ).

cnf(i_0_11208,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6131]),
    [final] ).

cnf(i_0_11209,plain,
    hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3))))),
    inference(split_conjunct,[status(thm)],[i_0_6141]),
    [final] ).

cnf(i_0_11210,plain,
    ( hBOOL(hAPP(hAPP(X1,esk506_7(X2,X3,X4,X5,X6,X7,X1)),esk505_7(X2,X3,X4,X5,X6,X7,X1)))
    | hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X6,X2),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X6),X5)),hAPP(c_Product__Type_Ofst(X7,X6),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6110]),
    [final] ).

cnf(i_0_11211,plain,
    ( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6142,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_11212,plain,
    c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6144,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_11213,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X6)))),X4)))),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X5),X6)
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X4),esk241_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk241_6(X5,X4,X6,X3,X2,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6145]),
    [final] ).

cnf(i_0_11214,plain,
    hAPP(c_List_Oset(X1),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_6146]),
    [final] ).

cnf(i_0_11215,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X2),c_Set_Oinsert(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_6147]),
    [final] ).

cnf(i_0_11216,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)))),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6148,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11217,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X6)))),X4)))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),hAPP(c_Finite__Set_Ocard(X3),X6))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X4),esk239_6(X5,X4,X6,X3,X2,X1))))) != X5
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6149]),
    [final] ).

cnf(i_0_11218,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,tc_fun(X4,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),tc_fun(tc_fun(X4,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1)),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5)))),X7)))),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(hAPP(c_COMBS(X4,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X4,X1),X6))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X4,tc_HOL_Obool),X7))))),X5)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6150]),
    [final] ).

cnf(i_0_11219,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X3),X2),tc_prod(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(tc_List_Olist(X3),X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),c_COMBB(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),X3),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_List_Olist(X3)),tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),hAPP(c_COMBB(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_List_Olist(X3)),c_Product__Type_OPair(tc_List_Olist(X3),X2))),c_List_Olist_OCons(X3))))),hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6151]),
    [final] ).

cnf(i_0_11220,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3))),hAPP(X2,X4))),c_Transitive__Closure_Ortrancl(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk341_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk341_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6152]),
    [final] ).

cnf(i_0_11221,plain,
    c_Partial__Function_Ofun__lub(X1,X2,X3,X4,X5,X6) = hAPP(X4,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X3,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X3,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X3,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X3,X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X3,X1))),X5)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X3,X1),X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X3,X1),X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X3,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X3,X1),X3,X1),c_COMBI(tc_fun(X3,X1))),X6)))))),
    inference(split_conjunct,[status(thm)],[i_0_6153]),
    [final] ).

cnf(i_0_11222,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6154]),
    [final] ).

cnf(i_0_11223,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6155]),
    [final] ).

cnf(i_0_11224,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6156]),
    [final] ).

cnf(i_0_11225,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6157]),
    [final] ).

cnf(i_0_11226,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk561_6(X2,X3,X4,X5,X6,X1)),esk562_6(X2,X3,X4,X5,X6,X1))),X6))
    | c_Equiv__Relations_Ocongruent2(X1,X5,X2,X6,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6158]),
    [final] ).

cnf(i_0_11227,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk563_6(X2,X3,X4,X1,X5,X6)),esk564_6(X2,X3,X4,X1,X5,X6))),X4))
    | c_Equiv__Relations_Ocongruent2(X6,X1,X2,X5,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6158]),
    [final] ).

cnf(i_0_11228,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk374_6(X3,X4,X1,X5,X2,X6)),esk375_6(X3,X4,X1,X5,X2,X6))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X2)),X5),hAPP(hAPP(c_Relation_Orel__comp(X6,X1,X2),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6159]),
    [final] ).

cnf(i_0_11229,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk373_6(X3,X4,X2,X5,X6,X1)),esk374_6(X3,X4,X2,X5,X6,X1))),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),X5),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6159]),
    [final] ).

cnf(i_0_11230,plain,
    c_Divides_Odivmod__int__rel(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(split_conjunct,[status(thm)],[i_0_6160]),
    [final] ).

cnf(i_0_11231,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)),
    inference(split_conjunct,[status(thm)],[conj_4]),
    [final] ).

cnf(i_0_11232,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X6),X7)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X5,X1),tc_fun(tc_fun(X5,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X5,X1),tc_fun(X5,X1)),X2),c_COMBB(X1,X1,X5)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3))),X6))),X7)),X4)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6161]),
    [final] ).

cnf(i_0_11233,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X5,X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),X5),c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6))),X3)),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X5,X1),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk301_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6162]),
    [final] ).

cnf(i_0_11234,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6163,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11235,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6164]),
    [final] ).

cnf(i_0_11236,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [final] ).

cnf(i_0_11237,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X2)))
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6166,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11238,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk236_7(X2,X3,X4,X5,X6,X7,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(X7,hAPP(X4,X3)),hAPP(X4,X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ c_Finite__Set_Ofolding__image__simple(X8,X1,X7,X6,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6167]),
    [final] ).

cnf(i_0_11239,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk25_7(X2,X3,X4,X5,X6,X7,X1)),X4))
    | hAPP(hAPP(X6,X3),X2) = X5
    | ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11240,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk25_7(X2,X3,X4,X5,X6,X7,X1)),X4))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11241,plain,
    hAPP(c_Int_Onat,X1) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(split_conjunct,[status(thm)],[i_0_6168]),
    [final] ).

cnf(i_0_11242,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk502_7(X2,X3,X4,X5,X6,X7,X1)),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6134]),
    [final] ).

cnf(i_0_11243,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk96_7(X2,X3,X4,X5,X6,X7,X1)),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6135]),
    [final] ).

cnf(i_0_11244,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk501_7(X2,X3,X4,X5,X6,X7,X1)),X7))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X7),X6),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6118]),
    [final] ).

cnf(i_0_11245,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk119_7(X2,X3,X4,X5,X6,X7,X1)),X5))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6119]),
    [final] ).

cnf(i_0_11246,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk259_7(X2,X3,X4,X5,X6,X7,X1)),X7))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
    | ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6117]),
    [final] ).

cnf(i_0_11247,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk266_7(X2,X3,X4,X5,X6,X7,X1)),X7))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
    | ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6098]),
    [final] ).

cnf(i_0_11248,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk265_7(X2,X3,X4,X5,X6,X7,X1)),X7))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
    | ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6098]),
    [final] ).

cnf(i_0_11249,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk568_7(X2,X3,X4,X5,X6,X7,X1)),X4))
    | hAPP(hAPP(X5,X3),X4) = hAPP(hAPP(X5,X2),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ c_Finite__Set_Ofolding__image(X8,X1,X7,X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6169]),
    [final] ).

cnf(i_0_11250,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk465_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))
    | hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4) = hAPP(c_List_Ofilter(X1,X3),X2)
    | X2 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X7))
    | ~ hBOOL(hAPP(X3,X5))
    | X4 != hAPP(c_List_Ofilter(X1,X3),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_11251,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk468_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))
    | hAPP(c_List_Ofilter(X1,X5),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)
    | X4 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))
    | ~ hBOOL(hAPP(X5,X3))
    | X2 != hAPP(c_List_Ofilter(X1,X5),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_11252,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X1,X2,X3,X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk364_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_11253,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk365_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk364_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_11254,plain,
    ( hAPP(X1,esk365_4(X2,X1,X3,X4)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk364_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk364_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_11255,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),X5))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),X4)))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6173]),
    [final] ).

cnf(i_0_11256,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk301_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X1,X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),X1),c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6))),X2)),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X1,X4),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6162]),
    [final] ).

cnf(i_0_11257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,tc_fun(X1,tc_HOL_Obool)),X4),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk550_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk550_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6174]),
    [final] ).

cnf(i_0_11258,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X1),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk333_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk333_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6175]),
    [final] ).

cnf(i_0_11259,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_fun(X1,tc_HOL_Obool)),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk324_6(X3,X2,X1,X4,X5,X6)),esk325_6(X3,X2,X1,X4,X5,X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6176]),
    [final] ).

cnf(i_0_11260,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    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)],[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_6177,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11261,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    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)],[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_6178,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11262,plain,
    hAPP(c_Relation_Oconverse(X1,X2),X3) = hAPP(c_Set_OCollect(tc_prod(X2,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X2)))),hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))))),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11263,plain,
    ( c_Nitpick_Osetsum_H(X1,X3,X4,X2) = hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6180]),
    [final] ).

cnf(i_0_11264,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk531_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk532_6(X3,X2,X1,X4,X5,X6))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk530_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11265,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X2,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X4))))),
    inference(split_conjunct,[status(thm)],[i_0_6182]),
    [final] ).

cnf(i_0_11266,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X2,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X4))))),
    inference(split_conjunct,[status(thm)],[i_0_6183]),
    [final] ).

cnf(i_0_11267,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk241_6(X2,X3,X4,X1,X5,X6)),X4))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6145]),
    [final] ).

cnf(i_0_11268,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk239_6(X2,X3,X4,X1,X5,X6)),X4))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6149]),
    [final] ).

cnf(i_0_11269,plain,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))) ),
    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_6184,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11270,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),X4))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6185,c_0_6186]),c_0_6186]),
    [final] ).

cnf(i_0_11271,plain,
    ( hAPP(hAPP(X4,X1),X3) = hAPP(hAPP(X4,X2),X3)
    | hAPP(X1,esk568_7(X2,X1,X3,X4,X5,X6,X7)) != hAPP(X2,esk568_7(X2,X1,X3,X4,X5,X6,X7))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))
    | ~ c_Finite__Set_Ofolding__image(X8,X7,X6,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6169]),
    [final] ).

cnf(i_0_11272,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk25_7(X3,X2,X4,X5,X1,X6,X7)),esk26_7(X3,X2,X4,X5,X1,X6,X7))
    | hAPP(hAPP(X1,X2),X3) = X5
    | ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11273,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk25_7(X3,X2,X4,X5,X1,X6,X7)),esk26_7(X3,X2,X4,X5,X1,X6,X7))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11274,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk527_2(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBS(X1,X1,tc_HOL_Obool),X2),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X2)))))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6187]),
    [final] ).

cnf(i_0_11275,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6188,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_11276,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6190]),
    [final] ).

cnf(i_0_11277,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),X1,X5),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X2),c_fequal),X6)))))),hAPP(c_Set_Oimage(X2,X5,X6),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6191]),
    [final] ).

cnf(i_0_11278,plain,
    ( c_Relation_Orefl__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk316_3(X2,X3,X1)),esk316_3(X2,X3,X1))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk315_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_11279,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hBOOL(hAPP(hAPP(c_member(X5),esk530_6(X3,X2,X1,X4,X5,X6)),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk531_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk532_6(X3,X2,X1,X4,X5,X6))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11280,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
    | c_Random__Sequence_ORandom(X2,X3,X1,X4) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X2)),c_Product__Type_Ofst(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6193]),
    [final] ).

cnf(i_0_11281,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk316_3(X2,X3,X1)),X3))
    | c_Relation_Orefl__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk315_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_11282,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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)],[i_0_6194,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11283,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1)),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)],[i_0_6195,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11284,plain,
    hAPP(c_New__DSequence_Opos__not__seq(X1),X2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),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)],[i_0_6196,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11285,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X1,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),X1),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X1),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),c_List_Ozip(X1,X2)),X5))),X3),
    inference(split_conjunct,[status(thm)],[i_0_6197]),
    [final] ).

cnf(i_0_11286,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4)))),X3)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk510_4(X3,X1,X4,X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6173]),
    [final] ).

cnf(i_0_11287,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2)))
    | ~ c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6198]),
    [final] ).

cnf(i_0_11288,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2)))
    | ~ c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6199]),
    [final] ).

cnf(i_0_11289,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X1,X2),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X1),c_Product__Type_OSigma(X3,X4)),X7))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),X2),c_COMBK(tc_fun(X4,tc_HOL_Obool),X3)),X8)))) = hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X6),X8))),
    inference(split_conjunct,[status(thm)],[i_0_6200]),
    [final] ).

cnf(i_0_11290,plain,
    ( c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)
    | ~ c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6201]),
    [final] ).

cnf(i_0_11291,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6202]),
    [final] ).

cnf(i_0_11292,plain,
    ( X3 = X4
    | hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3) != hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6203]),
    [final] ).

cnf(i_0_11293,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk510_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6173]),
    [final] ).

cnf(i_0_11294,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk326_6(X4,X3,X5,X6,X2,X1)),esk327_6(X4,X3,X5,X6,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6204]),
    [final] ).

cnf(i_0_11295,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,X6),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X6)),c_Product__Type_OPair(X1,X2))),X7)))),hAPP(hAPP(c_List_Ozip(X1,X6),X5),X8)),
    inference(split_conjunct,[status(thm)],[i_0_6205]),
    [final] ).

cnf(i_0_11296,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk532_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk530_6(X2,X3,X4,X5,X1,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11297,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk531_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk530_6(X2,X3,X4,X5,X1,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11298,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),esk29_7(X6,X7,X5,X4,X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6206]),
    [final] ).

cnf(i_0_11299,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk34_7(X6,X5,X7,X4,X3,X2,X1)))
    | hBOOL(hAPP(hAPP(c_member(X1),X7),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X7),X5)),X6))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6207]),
    [final] ).

cnf(i_0_11300,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5),
    inference(split_conjunct,[status(thm)],[i_0_6208]),
    [final] ).

cnf(i_0_11301,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6209,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11302,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6210,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11303,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6211,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11304,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    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_6212,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11305,plain,
    ( hAPP(X1,esk265_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk266_7(X2,X3,X1,X4,X5,X6,X7))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X1) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),X1)
    | ~ c_Equiv__Relations_Ocongruent(X7,tc_fun(X4,tc_HOL_Obool),X5,X1)
    | ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6098]),
    [final] ).

cnf(i_0_11306,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),hAPP(X4,esk244_4(X4,X3,X2,X1)))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6213]),
    [final] ).

cnf(i_0_11307,plain,
    ( hBOOL(hAPP(X1,esk465_7(X2,X1,X3,X4,X5,X6,X7)))
    | hAPP(hAPP(c_List_Olist_OCons(X5),X4),X3) = hAPP(c_List_Ofilter(X5,X1),X2)
    | X2 != hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X7))
    | ~ hBOOL(hAPP(X1,X4))
    | X3 != hAPP(c_List_Ofilter(X5,X1),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_11308,plain,
    ( hBOOL(hAPP(X1,esk468_7(X2,X3,X4,X1,X5,X6,X7)))
    | hAPP(c_List_Ofilter(X5,X1),X4) = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X2)
    | X4 != hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))
    | ~ hBOOL(hAPP(X1,X3))
    | X2 != hAPP(c_List_Ofilter(X5,X1),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_11309,plain,
    ( c_Equiv__Relations_Ocongruent2(X6,X4,X2,X5,X3,X1)
    | hAPP(hAPP(X1,esk561_6(X2,X1,X3,X4,X5,X6)),esk563_6(X2,X1,X3,X4,X5,X6)) != hAPP(hAPP(X1,esk562_6(X2,X1,X3,X4,X5,X6)),esk564_6(X2,X1,X3,X4,X5,X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6158]),
    [final] ).

cnf(i_0_11310,plain,
    ( c_Wellfounded_Owf(X3,hAPP(c_Set_OCollect(tc_prod(X3,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X4))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X3)),c_fequal)),X2)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,hAPP(X2,esk291_4(X3,X2,X1,X4)))),hAPP(X1,esk291_4(X3,X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6214]),
    [final] ).

cnf(i_0_11311,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6215]),
    [final] ).

cnf(i_0_11312,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6216]),
    [final] ).

cnf(i_0_11313,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X7)),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X7),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6217]),
    [final] ).

cnf(i_0_11314,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X2),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,esk7_6(X2,X3,X4,X1,X5,X6)),esk8_6(X2,X3,X4,X1,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6218]),
    [final] ).

cnf(i_0_11315,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,esk11_6(X1,X2,X3,X4,X5,X6)),esk12_6(X1,X2,X3,X4,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6219]),
    [final] ).

cnf(i_0_11316,plain,
    ( X2 = X3
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
    | hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk430_3(X3,X2,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6220,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_11317,plain,
    ( X2 = X3
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
    | hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk429_3(X2,X3,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6221,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_11318,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk532_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | hBOOL(hAPP(hAPP(c_member(X1),esk530_6(X2,X3,X4,X5,X1,X6)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11319,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk531_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | hBOOL(hAPP(hAPP(c_member(X1),esk530_6(X2,X3,X4,X5,X1,X6)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11320,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5))),X4)),c_Groups_Ozero__class_Ozero(X1))),X3)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6222]),
    [final] ).

cnf(i_0_11321,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))
    | ~ c_Relation_Orefl__on(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_11322,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))),
    inference(rw,[status(thm)],[i_0_6223,c_0_6224]),
    [final] ).

cnf(i_0_11323,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | esk531_6(X1,X2,X3,X4,X5,X6) != esk532_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X2,esk530_6(X1,X2,X3,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11324,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6225,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11325,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8)) = hAPP(hAPP(c_List_Omap(tc_prod(X3,X6),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X6,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),X3),c_COMBB(X2,tc_prod(X1,X2),X6)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4))),X7))),hAPP(hAPP(c_List_Ozip(X3,X6),X5),X8)),
    inference(split_conjunct,[status(thm)],[i_0_6226]),
    [final] ).

cnf(i_0_11326,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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_6227,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11327,plain,
    ( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(X6,hAPP(X4,X3)),hAPP(X4,X2))
    | hAPP(X1,esk236_7(X2,X3,X4,X1,X5,X6,X7)) != X5
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))
    | ~ c_Finite__Set_Ofolding__image__simple(X8,X7,X6,X5,X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6167]),
    [final] ).

cnf(i_0_11328,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    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_6228,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11329,plain,
    ( hBOOL(hAPP(X1,esk291_4(X2,X3,X4,X1)))
    | c_Wellfounded_Owf(X2,hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X2),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X1))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(X2,tc_HOL_Obool,X2)),c_fequal)),X3))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6214]),
    [final] ).

cnf(i_0_11330,plain,
    c_Wellfounded_Ofinite__psubset(X1) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_6229]),
    [final] ).

cnf(i_0_11331,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
    inference(rw,[status(thm)],[i_0_6230,c_0_6224]),
    [final] ).

cnf(i_0_11332,plain,
    ( hAPP(c_Nat_OSuc,X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
    inference(rw,[status(thm)],[i_0_6231,c_0_6224]),
    [final] ).

cnf(i_0_11333,plain,
    ( c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6198]),
    [final] ).

cnf(i_0_11334,plain,
    ( c_Nitpick_Ocard_H(X1,X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6232]),
    [final] ).

cnf(i_0_11335,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6233]),
    [final] ).

cnf(i_0_11336,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X7)),hAPP(hAPP(c_Product__Type_OPair(X6,X7),hAPP(X8,X3)),hAPP(X9,X4))),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X6,X7),c_Product__Type_Omap__pair(X1,X6,X2,X7,X8,X9)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6234]),
    [final] ).

cnf(i_0_11337,plain,
    ( c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6199]),
    [final] ).

cnf(i_0_11338,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    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_6235,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11339,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    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_6236,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11340,plain,
    c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X4,X5,X6,X7) = c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6237]),
    [final] ).

cnf(i_0_11341,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_member(X2))),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6238]),
    [final] ).

cnf(i_0_11342,plain,
    ( c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))
    | ~ c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6201]),
    [final] ).

cnf(i_0_11343,plain,
    ( c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6202]),
    [final] ).

cnf(i_0_11344,plain,
    ( c_Equiv__Relations_Ocongruent(X1,X2,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3))),X3)),esk320_4(X3,X4,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6239]),
    [final] ).

cnf(i_0_11345,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),X5))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))))
    | ~ hBOOL(hAPP(X3,X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6240]),
    [final] ).

cnf(i_0_11346,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6)),X3)),X2)),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk302_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6241]),
    [final] ).

cnf(i_0_11347,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6)),X3)),X2)),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk303_6(X3,X2,X1,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6242]),
    [final] ).

cnf(i_0_11348,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5))),X4)),c_Groups_Ozero__class_Ozero(X1))),X3)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6243]),
    [final] ).

cnf(i_0_11349,plain,
    ( hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6244]),
    [final] ).

cnf(i_0_11350,plain,
    ( hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X5)
    | hBOOL(hAPP(hAPP(c_member(X1),X6),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6244]),
    [final] ).

cnf(i_0_11351,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = X5
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6244]),
    [final] ).

cnf(i_0_11352,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6244]),
    [final] ).

cnf(i_0_11353,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk150_4(X2,X3,X4,X1))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk150_4(X2,X3,X4,X1)),X3))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6245]),
    [final] ).

cnf(i_0_11354,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6246,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11355,plain,
    c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X4,X5,X6,X7) = c_New__DSequence_Opos__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X4),X5)),X6)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6247]),
    [final] ).

cnf(i_0_11356,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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)],[i_0_6248,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11357,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6249,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11358,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),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)],[i_0_6250,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11359,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),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)],[i_0_6251,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11360,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),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)],[i_0_6252,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11361,plain,
    hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6) = hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6))),
    inference(split_conjunct,[status(thm)],[i_0_6253]),
    [final] ).

cnf(i_0_11362,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3)),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6254,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11363,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hBOOL(hAPP(hAPP(c_member(X5),esk530_6(X1,X2,X3,X4,X5,X6)),X4))
    | esk531_6(X1,X2,X3,X4,X5,X6) != esk532_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11364,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2) = c_Lazy__Sequence_Oappend(tc_List_Olist(X1),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),c_Lazy__Sequence_Oproduct(X1,tc_List_Olist(X1),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1)),tc_List_Olist(X1)),c_Lazy__Sequence_Osingle(tc_List_Olist(X1)))),c_List_Olist_OCons(X1))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X1))))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6255]),
    [final] ).

cnf(i_0_11365,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,X2) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6256]),
    [final] ).

cnf(i_0_11366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk165_6(X3,X4,X2,X5,X6,X1))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X1),X2),X5) != X4
    | ~ hBOOL(hAPP(hAPP(c_member(X6),X3),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6257]),
    [final] ).

cnf(i_0_11367,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(X5,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6258]),
    [final] ).

cnf(i_0_11368,plain,
    ( hBOOL(hAPP(hAPP(X1,esk11_6(X2,X1,X3,X4,X5,X6)),esk12_6(X2,X1,X3,X4,X5,X6)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6219]),
    [final] ).

cnf(i_0_11369,plain,
    ( hBOOL(hAPP(hAPP(X1,esk7_6(X1,X2,X3,X4,X5,X6)),esk8_6(X1,X2,X3,X4,X5,X6)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6218]),
    [final] ).

cnf(i_0_11370,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6259]),
    [final] ).

cnf(i_0_11371,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6260]),
    [final] ).

cnf(i_0_11372,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Finite__Set_Ocard(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6258]),
    [final] ).

cnf(i_0_11373,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = c_Groups_Oone__class_Oone(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6259]),
    [final] ).

cnf(i_0_11374,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6260]),
    [final] ).

cnf(i_0_11375,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,X2) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),c_Orderings_Oord__class_Oless__eq(X1)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6261]),
    [final] ).

cnf(i_0_11376,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),X2),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4))),X7))),
    inference(split_conjunct,[status(thm)],[i_0_6262]),
    [final] ).

cnf(i_0_11377,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),X2),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4))),X7))),
    inference(split_conjunct,[status(thm)],[i_0_6263]),
    [final] ).

cnf(i_0_11378,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
    inference(rw,[status(thm)],[i_0_6264,c_0_6224]),
    [final] ).

cnf(i_0_11379,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
    inference(rw,[status(thm)],[i_0_6265,c_0_6224]),
    [final] ).

cnf(i_0_11380,plain,
    hAPP(c_Product__Type_Omap__pair(X5,X3,X2,X2,X6,c_Fun_Oid(X2)),hAPP(c_Product__Type_Omap__pair(X5,X5,X1,X2,c_Fun_Oid(X5),X4),X7)) = hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6266,c_0_6267]),c_0_6267]),c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11381,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X4),X5),X6),X7) = c_New__DSequence_Oneg__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6268]),
    [final] ).

cnf(i_0_11382,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X4))),X3)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk240_4(X3,X1,X4,X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6240]),
    [final] ).

cnf(i_0_11383,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk34_7(X1,X4,X3,X5,X2,X6,X7))
    | hBOOL(hAPP(hAPP(c_member(X7),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,hAPP(hAPP(c_Set_Oinsert(X7),X3),X4)),X1))
    | ~ c_Finite__Set_Ofun__left__comm(X7,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6207]),
    [final] ).

cnf(i_0_11384,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk29_7(X3,X1,X4,X5,X2,X6,X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,X4),X1))
    | ~ c_Finite__Set_Ofun__left__comm(X7,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6206]),
    [final] ).

cnf(i_0_11385,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk414_5(X5,X4,X3,X2,X1)),esk414_5(X5,X4,X3,X2,X1))),X5))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6269]),
    [final] ).

cnf(i_0_11386,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X1,tc_HOL_Obool))),X2)))),c_member(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_6270]),
    [final] ).

cnf(i_0_11387,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X1,tc_HOL_Obool))),X2)))),c_member(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_6271]),
    [final] ).

cnf(i_0_11388,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk356_5(X2,X3,X4,X5,X1)),esk357_5(X2,X3,X4,X5,X1))),X2))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6272]),
    [final] ).

cnf(i_0_11389,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk355_5(X2,X3,X4,X5,X1)),esk354_5(X2,X3,X4,X5,X1))),X2))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6273]),
    [final] ).

cnf(i_0_11390,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X2),X5),X6)) = hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,X2),tc_fun(X4,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X4,X2),tc_fun(X4,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X4)),c_Product__Type_OPair(X1,X2))),X5))),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6274]),
    [final] ).

cnf(i_0_11391,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6275,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11392,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(rw,[status(thm)],[i_0_6276,c_0_6224]),
    [final] ).

cnf(i_0_11393,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
    inference(rw,[status(thm)],[i_0_6277,c_0_6224]),
    [final] ).

cnf(i_0_11394,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk233_3(X1,X2,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk232_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk232_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_11395,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk225_3(X1,X2,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk224_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk224_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11396,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk349_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk350_5(X2,X3,X4,X5,X1)),X2)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11397,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk349_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk350_5(X2,X3,X4,X5,X1)),X2)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11398,plain,
    ( hAPP(X1,esk233_3(X2,X1,X3)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk232_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk232_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_11399,plain,
    ( hAPP(X1,esk225_3(X2,X1,X3)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk224_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk224_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11400,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[fact_Nitpick_OFrac__def]),
    [final] ).

cnf(i_0_11401,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk302_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X6)),X2)),X3)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6241]),
    [final] ).

cnf(i_0_11402,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk303_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X6)),X2)),X3)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6242]),
    [final] ).

cnf(i_0_11403,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4))),X4)),X5))
    | ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6239]),
    [final] ).

cnf(i_0_11404,plain,
    ( hBOOL(hAPP(X1,esk240_4(X2,X3,X1,X4)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X1))),X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6240]),
    [final] ).

cnf(i_0_11405,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6281]),
    [final] ).

cnf(i_0_11406,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X4),X5),X6),X7) = c_New__DSequence_Opos__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X4),X5)),X6)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6282]),
    [final] ).

cnf(i_0_11407,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6283]),
    [final] ).

cnf(i_0_11408,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6284]),
    [final] ).

cnf(i_0_11409,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6285]),
    [final] ).

cnf(i_0_11410,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6286]),
    [final] ).

cnf(i_0_11411,plain,
    c_Nitpick_Oprod(X1,X2,X3,X4) = hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6287]),
    [final] ).

cnf(i_0_11412,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    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_6288,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11413,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(c_Product__Type_Omap__pair(X7,X1,X8,X3,X9,X10),X11)) = hAPP(c_Product__Type_Omap__pair(X7,X2,X8,X4,hAPP(c_Fun_Ocomp(X1,X2,X7,X5),X9),hAPP(c_Fun_Ocomp(X3,X4,X8,X6),X10)),X11),
    inference(split_conjunct,[status(thm)],[i_0_6289]),
    [final] ).

cnf(i_0_11414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6290]),
    [final] ).

cnf(i_0_11415,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6291]),
    [final] ).

cnf(i_0_11416,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk550_6(X2,X3,X4,X5,X6,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6174]),
    [final] ).

cnf(i_0_11417,plain,
    ( c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2))),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_6292,c_0_6293]),
    [final] ).

cnf(i_0_11418,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk331_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6294]),
    [final] ).

cnf(i_0_11419,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk330_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6294]),
    [final] ).

cnf(i_0_11420,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk333_6(X2,X3,X4,X5,X6,X1)),X6))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6175]),
    [final] ).

cnf(i_0_11421,plain,
    hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(c_Set_OCollect(X1),X3)))),hAPP(c_Set_Oimage(X1,X2,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3))))),
    inference(split_conjunct,[status(thm)],[i_0_6295]),
    [final] ).

cnf(i_0_11422,plain,
    hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X1,c_Fun_Oid(X3),X6),X7)) = hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X2,c_Fun_Oid(X3),hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6296,c_0_6083]),c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11423,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X5,X1,X3,X3,X6,c_Fun_Oid(X3)),X7)) = hAPP(c_Product__Type_Omap__pair(X5,X2,X3,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6),c_Fun_Oid(X3)),X7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6297,c_0_6267]),c_0_6267]),c_0_6267]),
    [final] ).

cnf(i_0_11424,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_6298]),
    [final] ).

cnf(i_0_11425,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk254_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X4),X2),X5) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Oab__semigroup__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6299]),
    [final] ).

cnf(i_0_11426,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6300,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11427,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6301,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11428,plain,
    ( c_Wellfounded_Owf(X3,hAPP(c_Set_Oimage(tc_prod(X1,X1),tc_prod(X3,X3),c_Product__Type_Omap__pair(X1,X3,X1,X3,X4,X4)),X2))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ c_Fun_Oinj__on(X1,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6302]),
    [final] ).

cnf(i_0_11429,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk235_6(X2,X3,X4,X5,X1,X6)),X6))
    | c_Fun_Oinj__on(X5,X4,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X6),X2))
    | X6 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6303]),
    [final] ).

cnf(i_0_11430,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk165_6(X2,X3,X4,X5,X1,X6)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6),hAPP(X4,X2)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X4),X5) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Oordered__ab__group__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6257]),
    [final] ).

cnf(i_0_11431,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X2),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X3),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk421_5(X3,X2,X4,X5,X1))),hAPP(X3,esk421_5(X3,X2,X4,X5,X1))))
    | ~ class_Groups_Omonoid__add(X1)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6304]),
    [final] ).

cnf(i_0_11432,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk459_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk459_5(X1,X4,X5,X3,X2))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6305]),
    [final] ).

cnf(i_0_11433,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk424_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk424_5(X4,X3,X1,X5,X2))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6306]),
    [final] ).

cnf(i_0_11434,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X3),X4)))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk37_5(X3,X2,X4,X5,X1))),hAPP(X3,esk37_5(X3,X2,X4,X5,X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6307]),
    [final] ).

cnf(i_0_11435,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk66_5(X3,X2,X4,X5,X1))),hAPP(X3,esk66_5(X3,X2,X4,X5,X1))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6308]),
    [final] ).

cnf(i_0_11436,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X2),X4)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X4)))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6309]),
    [final] ).

cnf(i_0_11437,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk354_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6273]),
    [final] ).

cnf(i_0_11438,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(rw,[status(thm)],[i_0_6310,c_0_6224]),
    [final] ).

cnf(i_0_11439,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(rw,[status(thm)],[i_0_6311,c_0_6224]),
    [final] ).

cnf(i_0_11440,plain,
    ( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X4,hAPP(X3,X5)) = hAPP(X3,hAPP(c_Set_Oimage(X1,X1,X4),X5))
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | hAPP(X4,hAPP(hAPP(X2,esk13_5(X5,X4,X3,X2,X1)),esk14_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk13_5(X5,X4,X3,X2,X1))),hAPP(X4,esk14_5(X5,X4,X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6312]),
    [final] ).

cnf(i_0_11441,plain,
    ( X3 = c_List_Olist_ONil(tc_List_Olist(X2))
    | c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6313,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_11442,plain,
    ( c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6314,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_11443,plain,
    ( X2 = c_List_Olist_ONil(tc_List_Olist(X1))
    | c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk434_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6315,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_11444,plain,
    ( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk434_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6316,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_11445,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    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_6317,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11446,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk268_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk267_3(X1,X2,X3)),esk268_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,esk267_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk268_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6318,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11447,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6319]),
    [final] ).

cnf(i_0_11448,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6320]),
    [final] ).

cnf(i_0_11449,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = c_Groups_Oone__class_Oone(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6319]),
    [final] ).

cnf(i_0_11450,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6320]),
    [final] ).

cnf(i_0_11451,plain,
    hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)) = hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),hAPP(c_List_Oset(X1),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6321]),
    [final] ).

cnf(i_0_11452,plain,
    hAPP(c_Fun_Ocomp(tc_prod(X1,X2),tc_prod(X3,X4),tc_prod(X5,X6),c_Product__Type_Omap__pair(X1,X3,X2,X4,X7,X8)),c_Product__Type_Omap__pair(X5,X1,X6,X2,X9,X10)) = c_Product__Type_Omap__pair(X5,X3,X6,X4,hAPP(c_Fun_Ocomp(X1,X3,X5,X7),X9),hAPP(c_Fun_Ocomp(X2,X4,X6,X8),X10)),
    inference(split_conjunct,[status(thm)],[i_0_6322]),
    [final] ).

cnf(i_0_11453,plain,
    c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10)) = hAPP(c_Fun_Ocomp(tc_prod(X5,X8),tc_prod(X2,X4),tc_prod(X1,X3),c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9)),c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10)),
    inference(split_conjunct,[status(thm)],[i_0_6323]),
    [final] ).

cnf(i_0_11454,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk386_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk386_4(X3,X4,X2,X1)))),X3))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6324]),
    [final] ).

cnf(i_0_11455,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk270_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk269_3(X1,X2,X3)),esk270_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk269_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk270_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6325,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11456,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk383_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6326]),
    [final] ).

cnf(i_0_11457,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    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_6327,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11458,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk382_5(X2,X3,X4,X5,X1)),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6326]),
    [final] ).

cnf(i_0_11459,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk359_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6328]),
    [final] ).

cnf(i_0_11460,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk358_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6329]),
    [final] ).

cnf(i_0_11461,plain,
    c_Nitpick_Otimes__frac(X1,X2,X3) = hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6330,c_0_6091]),c_0_6091]),c_0_6092]),c_0_6092]),
    [final] ).

cnf(i_0_11462,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk351_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk352_5(X3,X4,X5,X2,X1)),X3)))
    | X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_11463,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk351_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk352_5(X3,X4,X5,X2,X1)),X3)))
    | X2 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_11464,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk360_5(X2,X3,X4,X5,X1)),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6332]),
    [final] ).

cnf(i_0_11465,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6333,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11466,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6334,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11467,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk351_5(X2,X3,X4,X5,X1)),X4)),X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_11468,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk351_5(X2,X3,X4,X5,X1)),X4)),X2))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_11469,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6335,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11470,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6336,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11471,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6337,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11472,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6338,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11473,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6339,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11474,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
    inference(rw,[status(thm)],[i_0_6340,c_0_6224]),
    [final] ).

cnf(i_0_11475,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
    inference(rw,[status(thm)],[i_0_6341,c_0_6224]),
    [final] ).

cnf(i_0_11476,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6342,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11477,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6343]),
    [final] ).

cnf(i_0_11478,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))
    | ~ class_Rings_Osemiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6344,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11479,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6345,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11480,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6346,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11481,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6347,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11482,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6348,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11483,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Oring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6349,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11484,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))
    | ~ class_Rings_Oring__1(X1) ),
    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_6350,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11485,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6351,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11486,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),
    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_6352,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11487,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)))),
    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_6353,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11488,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk280_5(X3,X4,X1,X5,X2)),X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6354]),
    [final] ).

cnf(i_0_11489,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk260_5(X3,X4,X1,X5,X2)),X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6355]),
    [final] ).

cnf(i_0_11490,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X6),X1),hAPP(c_Set_Oimage(X5,X3,X2),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X3,X6,X5,X1),X2)),X4)
    | hAPP(X1,hAPP(X2,esk330_6(X3,X1,X2,X4,X5,X6))) != c_Groups_Ozero__class_Ozero(X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6294]),
    [final] ).

cnf(i_0_11491,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X4)),X4))
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X2,esk9_4(X4,X3,X2,X1)),esk10_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk9_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk10_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6356]),
    [final] ).

cnf(i_0_11492,plain,
    c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X2),X3) = hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X3)),c_Enum_On__lists(X1,X2,X3))),
    inference(rw,[status(thm)],[i_0_6357,c_0_6143]),
    [final] ).

cnf(i_0_11493,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))),
    inference(rw,[status(thm)],[i_0_6358,c_0_6224]),
    [final] ).

cnf(i_0_11494,plain,
    hAPP(c_Relation_OImage(X1,X2,hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))),X4) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6359]),
    [final] ).

cnf(i_0_11495,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6360,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11496,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))
    | ~ c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6361]),
    [final] ).

cnf(i_0_11497,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X1),X2),X4) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X4)
    | hAPP(X1,esk254_6(X2,X3,X1,X4,X5,X6)) != hAPP(X3,esk254_6(X2,X3,X1,X4,X5,X6))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Oab__semigroup__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6299]),
    [final] ).

cnf(i_0_11498,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X4))
    | X6 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(X4,esk235_6(X4,X3,X2,X1,X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6303]),
    [final] ).

cnf(i_0_11499,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fimplies),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),X4))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4))),
    inference(split_conjunct,[status(thm)],[i_0_6362]),
    [final] ).

cnf(i_0_11500,plain,
    c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X4)),c_List_Osublist(X1,X3,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6363]),
    [final] ).

cnf(i_0_11501,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk326_6(X1,X4,X3,X2,X5,X6)),esk327_6(X1,X4,X3,X2,X5,X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6204]),
    [final] ).

cnf(i_0_11502,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),X4)),hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6364]),
    [final] ).

cnf(i_0_11503,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk373_6(X4,X5,X6,X1,X3,X2)),esk375_6(X4,X5,X6,X1,X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Relation_Orel__comp(X2,X6,X3),X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6159]),
    [final] ).

cnf(i_0_11504,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    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_6365,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11505,plain,
    ( hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))
    | hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),X5) != hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X6),X5) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6366,c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11506,plain,
    ( hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5)) = hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))
    | hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5) != hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X6,c_Fun_Oid(X3)),X5) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6367,c_0_6267]),c_0_6267]),
    [final] ).

cnf(i_0_11507,plain,
    c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))),
    inference(rw,[status(thm)],[i_0_6368,c_0_6097]),
    [final] ).

cnf(i_0_11508,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk324_6(X4,X5,X6,X3,X2,X1)),esk325_6(X4,X5,X6,X3,X2,X1))
    | hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6176]),
    [final] ).

cnf(i_0_11509,plain,
    hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6369,c_0_6267]),c_0_6083]),
    [final] ).

cnf(i_0_11510,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6370,c_0_6267]),c_0_6083]),
    [final] ).

cnf(i_0_11511,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)) = hAPP(c_Finite__Set_Ocard(X1),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6371]),
    [final] ).

cnf(i_0_11512,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1))),X3))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6372]),
    [final] ).

cnf(i_0_11513,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6373]),
    [final] ).

cnf(i_0_11514,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6283]),
    [final] ).

cnf(i_0_11515,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6374]),
    [final] ).

cnf(i_0_11516,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6284]),
    [final] ).

cnf(i_0_11517,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6285]),
    [final] ).

cnf(i_0_11518,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6286]),
    [final] ).

cnf(i_0_11519,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6283]),
    [final] ).

cnf(i_0_11520,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6284]),
    [final] ).

cnf(i_0_11521,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6285]),
    [final] ).

cnf(i_0_11522,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6286]),
    [final] ).

cnf(i_0_11523,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6290]),
    [final] ).

cnf(i_0_11524,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6291]),
    [final] ).

cnf(i_0_11525,plain,
    ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6375]),
    [final] ).

cnf(i_0_11526,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6376,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11527,plain,
    ( c_FunDef_Oreduction__pair(X1,X2)
    | ~ c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6377]),
    [final] ).

cnf(i_0_11528,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2)))),
    inference(rw,[status(thm)],[i_0_6378,c_0_6224]),
    [final] ).

cnf(i_0_11529,plain,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6379,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11530,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2)))),
    inference(rw,[status(thm)],[i_0_6380,c_0_6224]),
    [final] ).

cnf(i_0_11531,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk100_5(X3,X2,X4,X5,X1))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6381]),
    [final] ).

cnf(i_0_11532,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X5),X4))),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk140_5(X3,X2,X4,X5,X1))),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6382]),
    [final] ).

cnf(i_0_11533,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat)))),
    inference(rw,[status(thm)],[i_0_6383,c_0_6224]),
    [final] ).

cnf(i_0_11534,plain,
    c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X2,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X4),tc_fun(X3,tc_prod(X2,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(tc_fun(X3,X4),tc_fun(X3,tc_prod(X2,X4))),X1),c_COMBB(X4,tc_prod(X2,X4),X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X5))),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6384]),
    [final] ).

cnf(i_0_11535,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6385]),
    [final] ).

cnf(i_0_11536,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk101_5(X3,X2,X4,X5,X1))),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6386]),
    [final] ).

cnf(i_0_11537,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) = c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6387,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11538,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6388,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11539,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6389,c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11540,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk390_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk390_4(X3,X4,X2,X1)))),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_11541,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk390_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk390_4(X3,X4,X2,X1)))),X3))
    | hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_11542,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(rw,[status(thm)],[i_0_6391,c_0_6143]),
    [final] ).

cnf(i_0_11543,plain,
    hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6392]),
    [final] ).

cnf(i_0_11544,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_6393]),
    [final] ).

cnf(i_0_11545,plain,
    c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4)))) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_6394]),
    [final] ).

cnf(i_0_11546,plain,
    c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4)))) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_6395]),
    [final] ).

cnf(i_0_11547,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    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_6396,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11548,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X3,X1),X4))),X6)),X5)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6397]),
    [final] ).

cnf(i_0_11549,plain,
    hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_OCollect(X2),X4))),
    inference(split_conjunct,[status(thm)],[i_0_6398]),
    [final] ).

cnf(i_0_11550,plain,
    ( hAPP(c_Set_Oimage(X1,X3,X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X3,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_Set_Oinsert(X3)),X4)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6399]),
    [final] ).

cnf(i_0_11551,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(rw,[status(thm)],[i_0_6400,c_0_6143]),
    [final] ).

cnf(i_0_11552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6401]),
    [final] ).

cnf(i_0_11553,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2)) ),
    inference(rw,[status(thm)],[i_0_6402,c_0_6097]),
    [final] ).

cnf(i_0_11554,plain,
    c_Relation_OId__on(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6403]),
    [final] ).

cnf(i_0_11555,plain,
    c_Int_Oint__ge__less__than(X1) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_6404]),
    [final] ).

cnf(i_0_11556,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,tc_prod(X2,X3)),X7),X8)),X9) = hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,X4),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X2,X3)),tc_fun(tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),X5),c_Product__Type_Oscomp(X6,X2,X3,X4)),X8)),X9)),
    inference(split_conjunct,[status(thm)],[i_0_6405]),
    [final] ).

cnf(i_0_11557,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk356_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6272]),
    [final] ).

cnf(i_0_11558,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__weak)) ),
    inference(split_conjunct,[status(thm)],[i_0_6406]),
    [final] ).

cnf(i_0_11559,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__strict)) ),
    inference(split_conjunct,[status(thm)],[i_0_6407]),
    [final] ).

cnf(i_0_11560,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rw,[status(thm)],[i_0_6408,c_0_6224]),
    [final] ).

cnf(i_0_11561,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rw,[status(thm)],[i_0_6409,c_0_6224]),
    [final] ).

cnf(i_0_11562,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X2),c_fequal),X3)),hAPP(X4,X5))),X5)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6410]),
    [final] ).

cnf(i_0_11563,plain,
    ( hAPP(X1,esk330_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk331_6(X2,X3,X1,X4,X5,X6))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X5,X2,X1),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X2,X6,X5,X3),X1)),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6294]),
    [final] ).

cnf(i_0_11564,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk385_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6411]),
    [final] ).

cnf(i_0_11565,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    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_6412,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11566,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6413]),
    [final] ).

cnf(i_0_11567,plain,
    c_List_Osublist(X1,X2,X3) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))),
    inference(rw,[status(thm)],[i_0_6414,c_0_6189]),
    [final] ).

cnf(i_0_11568,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk336_5(X3,X4,X5,X1,X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_11569,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk384_5(X3,X4,X5,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6411]),
    [final] ).

cnf(i_0_11570,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6416]),
    [final] ).

cnf(i_0_11571,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X1,X6),tc_prod(X2,X7),c_Product__Type_Omap__pair(X1,X2,X6,X7,X3,X8)),hAPP(hAPP(c_Product__Type_OSigma(X1,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X1),X9))) = hAPP(hAPP(c_Product__Type_OSigma(X2,X7),X5),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X2),X10))
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5
    | hAPP(c_Set_Oimage(X6,X7,X8),X9) != X10 ),
    inference(split_conjunct,[status(thm)],[i_0_6417]),
    [final] ).

cnf(i_0_11572,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__weak)) ),
    inference(split_conjunct,[status(thm)],[i_0_6418]),
    [final] ).

cnf(i_0_11573,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__strict)) ),
    inference(split_conjunct,[status(thm)],[i_0_6419]),
    [final] ).

cnf(i_0_11574,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk32_5(X3,X4,X5,X2,X1),esk33_5(X3,X4,X5,X2,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6420]),
    [final] ).

cnf(i_0_11575,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk30_5(X3,X4,X5,X2,X1),esk31_5(X3,X4,X5,X2,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6421]),
    [final] ).

cnf(i_0_11576,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk400_4(X3,X4,X2,X1))),esk399_4(X3,X4,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6422]),
    [final] ).

cnf(i_0_11577,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X1,X4),tc_prod(X2,X5),c_Product__Type_Omap__pair(X1,X2,X4,X5,X3,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X4),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X5),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X4,X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6423]),
    [final] ).

cnf(i_0_11578,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6424]),
    [final] ).

cnf(i_0_11579,plain,
    ( hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X1),X4) = hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X5),X4)
    | hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6425,c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11580,plain,
    ( hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X1,c_Fun_Oid(X3)),X4) = hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X5,c_Fun_Oid(X3)),X4)
    | hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6426,c_0_6267]),c_0_6267]),
    [final] ).

cnf(i_0_11581,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk360_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6332]),
    [final] ).

cnf(i_0_11582,plain,
    c_Nitpick_Ouminus__frac(X1,X2) = c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6427,c_0_6091]),c_0_6092]),
    [final] ).

cnf(i_0_11583,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X1,X1,X3,X2,c_Fun_Oid(X1),X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X3),X5)),
    inference(rw,[status(thm)],[i_0_6428,c_0_6083]),
    [final] ).

cnf(i_0_11584,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X2,X2,X4,c_Fun_Oid(X2)),X5)) = hAPP(X4,hAPP(c_Product__Type_Ofst(X3,X2),X5)),
    inference(rw,[status(thm)],[i_0_6429,c_0_6267]),
    [final] ).

cnf(i_0_11585,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7)) = hAPP(X5,hAPP(c_Product__Type_Ofst(X3,X4),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6430]),
    [final] ).

cnf(i_0_11586,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X4),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6431]),
    [final] ).

cnf(i_0_11587,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X1,X1,X3,X2,c_Fun_Oid(X1),X4),X5)) = hAPP(c_Product__Type_Ofst(X1,X3),X5),
    inference(rw,[status(thm)],[i_0_6432,c_0_6083]),
    [final] ).

cnf(i_0_11588,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X2,X2,X4,c_Fun_Oid(X2)),X5)) = hAPP(c_Product__Type_Osnd(X3,X2),X5),
    inference(rw,[status(thm)],[i_0_6433,c_0_6267]),
    [final] ).

cnf(i_0_11589,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk32_5(X2,X3,X4,X5,X1)),esk33_5(X2,X3,X4,X5,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6420]),
    [final] ).

cnf(i_0_11590,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk30_5(X2,X3,X4,X5,X1)),esk31_5(X2,X3,X4,X5,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6421]),
    [final] ).

cnf(i_0_11591,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_4(X2,X3,X4,X1)),esk387_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6434]),
    [final] ).

cnf(i_0_11592,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk387_4(X2,X3,X4,X1)),esk388_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6434]),
    [final] ).

cnf(i_0_11593,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk359_5(X3,X4,X5,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6328]),
    [final] ).

cnf(i_0_11594,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk358_5(X3,X4,X5,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6329]),
    [final] ).

cnf(i_0_11595,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_6435]),
    [final] ).

cnf(i_0_11596,plain,
    c_Relation_OId__on(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_prod(X1,X1))),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6436]),
    [final] ).

cnf(i_0_11597,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk349_5(X3,X4,X5,X2,X1))),X3))
    | X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11598,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk349_5(X3,X4,X5,X2,X1))),X3))
    | X2 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11599,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat))),
    inference(rw,[status(thm)],[i_0_6437,c_0_6224]),
    [final] ).

cnf(i_0_11600,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_6438]),
    [final] ).

cnf(i_0_11601,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat)))),
    inference(rw,[status(thm)],[i_0_6439,c_0_6224]),
    [final] ).

cnf(i_0_11602,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),c_Int_Onat)))),
    inference(rw,[status(thm)],[i_0_6440,c_0_6224]),
    [final] ).

cnf(i_0_11603,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X5,X1),X6),X7)),X8)) = hAPP(hAPP(c_List_Omap(tc_prod(X5,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X5),c_Product__Type_OPair(X1,X2)),X6)))),hAPP(hAPP(c_List_Ozip(X5,X2),X7),X8)),
    inference(split_conjunct,[status(thm)],[i_0_6441]),
    [final] ).

cnf(i_0_11604,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))
    | ~ class_Orderings_Oorder(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6442]),
    [final] ).

cnf(i_0_11605,plain,
    c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X3,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6443]),
    [final] ).

cnf(i_0_11606,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6444,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11607,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X2),hAPP(c_Set_Oimage(X5,X1,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X1,X6,X5,X2),X3)),X4)
    | esk330_6(X1,X2,X3,X4,X5,X6) != esk331_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6294]),
    [final] ).

cnf(i_0_11608,plain,
    ( hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4) = hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6445]),
    [final] ).

cnf(i_0_11609,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6446,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11610,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6447,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11611,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6448,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11612,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6449,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11613,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    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_6450,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11614,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6451,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11615,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6452,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11616,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6453,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11617,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6454,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11618,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk114_5(X3,X2,X4,X5,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6455]),
    [final] ).

cnf(i_0_11619,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk94_5(X2,X3,X4,X5,X1)),hAPP(X3,esk93_5(X2,X3,X4,X5,X1))))
    | hBOOL(hAPP(X2,X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11620,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
    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_6457,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11621,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X6))),c_Wellfounded_Omax__ext(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X6)),c_Wellfounded_Omax__ext(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6458]),
    [final] ).

cnf(i_0_11622,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk307_5(X2,X3,X4,X1,X5)),hAPP(X2,esk306_5(X2,X3,X4,X1,X5))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6459]),
    [final] ).

cnf(i_0_11623,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Omap(X5,X2),X6),X7)) = hAPP(c_List_Ofoldl(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X5,X2),tc_fun(X5,X1)),X1),c_COMBB(X2,X1,X5)),X3)),X6),X4),X7),
    inference(split_conjunct,[status(thm)],[i_0_6460]),
    [final] ).

cnf(i_0_11624,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)),X7) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),c_Relation_Orel__comp(X1,X2,X3)),X6)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6461]),
    [final] ).

cnf(i_0_11625,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
    | ~ c_FunDef_Oreduction__pair(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6377]),
    [final] ).

cnf(i_0_11626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_6462]),
    [final] ).

cnf(i_0_11627,plain,
    hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)))),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4),X5))),X5)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6463,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_11628,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6464]),
    [final] ).

cnf(i_0_11629,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X3)),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6464]),
    [final] ).

cnf(i_0_11630,plain,
    ( hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X4),esk529_5(X5,X1,X4,X3,X2))))
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6465]),
    [final] ).

cnf(i_0_11631,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6466]),
    [final] ).

cnf(i_0_11632,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6467]),
    [final] ).

cnf(i_0_11633,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X4)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11634,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X4)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11635,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_6469]),
    [final] ).

cnf(i_0_11636,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2)))),hAPP(c_List_Orev(X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_6470,c_0_6293]),
    [final] ).

cnf(i_0_11637,plain,
    ( hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk548_3(X3,X2,X1)),X4)) = hAPP(X2,esk548_3(X3,X2,X1))
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk547_3(X3,X2,X1)))),hAPP(X2,esk547_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(rw,[status(thm)],[i_0_6471,c_0_6104]),
    [final] ).

cnf(i_0_11638,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X4))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6472]),
    [final] ).

cnf(i_0_11639,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6473]),
    [final] ).

cnf(i_0_11640,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X9),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X10),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8)) = hAPP(hAPP(X8,X9),X10)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X4,X5,X6)
    | ~ c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X9),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X10),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6474]),
    [final] ).

cnf(i_0_11641,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6475]),
    [final] ).

cnf(i_0_11642,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),X4),
    inference(rw,[status(thm)],[i_0_6476,c_0_6143]),
    [final] ).

cnf(i_0_11643,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X2),hAPP(c_List_Onth(X1),X3))))),
    inference(split_conjunct,[status(thm)],[i_0_6477]),
    [final] ).

cnf(i_0_11644,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),c_Groups_Oone__class_Oone(X1)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6478]),
    [final] ).

cnf(i_0_11645,plain,
    ( c_Fun_Obij__betw(X1,X2,esk539_6(X6,X5,X4,X3,X2,X1),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Oinj__on(X2,X1,X6,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6479]),
    [final] ).

cnf(i_0_11646,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11647,plain,
    ( c_List_Olist__all2(X1,X3,X4,X6,hAPP(hAPP(c_List_Omap(X2,X3),X5),X7))
    | ~ c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X3,tc_HOL_Obool,X2)),X4)),X5),X6,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6481]),
    [final] ).

cnf(i_0_11648,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk151_4(X2,X3,X4,X1))),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk151_4(X2,X3,X4,X1)),X3))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6482]),
    [final] ).

cnf(i_0_11649,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk337_4(X4,X3,X5,X1)),X2)),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_11650,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk292_4(X4,X3,X5,X1)),X2)),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6483]),
    [final] ).

cnf(i_0_11651,plain,
    ( hBOOL(hAPP(hAPP(X1,esk287_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6484]),
    [final] ).

cnf(i_0_11652,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk338_3(X3,X2,X1)))),hAPP(X3,esk338_3(X3,X2,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6485]),
    [final] ).

cnf(i_0_11653,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk289_3(X2,X1,X3)))),hAPP(X3,esk289_3(X2,X1,X3)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6486]),
    [final] ).

cnf(i_0_11654,plain,
    ( c_Equiv__Relations_Ocongruent(X1,tc_fun(X7,tc_HOL_Obool),X3,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X4,X5,X6)
    | ~ c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X9),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6487]),
    [final] ).

cnf(i_0_11655,plain,
    ( c_Nitpick_Oless__eq__frac(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[i_0_6488,c_0_6092]),
    [final] ).

cnf(i_0_11656,plain,
    ( c_Nitpick_Oless__frac(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[i_0_6489,c_0_6092]),
    [final] ).

cnf(i_0_11657,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(X3,X6),X7)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6490]),
    [final] ).

cnf(i_0_11658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk138_5(X2,X3,X4,X5,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6491]),
    [final] ).

cnf(i_0_11659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk133_5(X2,X3,X4,X5,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6492]),
    [final] ).

cnf(i_0_11660,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6493]),
    [final] ).

cnf(i_0_11661,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6494]),
    [final] ).

cnf(i_0_11662,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6495]),
    [final] ).

cnf(i_0_11663,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6496]),
    [final] ).

cnf(i_0_11664,plain,
    ( c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,X7,hAPP(hAPP(X1,X2),X3))
    | hAPP(hAPP(X1,X2),X3) != hAPP(hAPP(X1,X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X6),X4),X7))
    | ~ c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X6),X4),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_11665,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olistrel1(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X6),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11666,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3))
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6416]),
    [final] ).

cnf(i_0_11667,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6497,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11668,plain,
    ( c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,X3,hAPP(hAPP(X5,X2),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6498]),
    [final] ).

cnf(i_0_11669,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,esk549_5(X3,X2,X1,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6499]),
    [final] ).

cnf(i_0_11670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,esk107_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6500]),
    [final] ).

cnf(i_0_11671,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))
    | ~ c_Relation_Orefl__on(X1,hAPP(X2,esk492_5(X3,X2,X1,X4,X5)),hAPP(X3,esk492_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6501]),
    [final] ).

cnf(i_0_11672,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))
    | ~ c_Relation_Orefl__on(X1,hAPP(X2,esk542_5(X3,X2,X1,X4,X5)),hAPP(X3,esk542_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6502]),
    [final] ).

cnf(i_0_11673,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6503]),
    [final] ).

cnf(i_0_11674,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6504,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11675,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk287_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6484]),
    [final] ).

cnf(i_0_11676,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk106_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6505]),
    [final] ).

cnf(i_0_11677,plain,
    hAPP(c_Set_Ovimage(X1,tc_prod(X2,X3),X4),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X2,X1,c_Product__Type_Ofst(X2,X3)),X4)),X5)),hAPP(c_Set_Ovimage(X1,X3,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X3,X1,c_Product__Type_Osnd(X2,X3)),X4)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6506]),
    [final] ).

cnf(i_0_11678,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11679,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6507]),
    [final] ).

cnf(i_0_11680,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6508]),
    [final] ).

cnf(i_0_11681,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk120_5(X2,X1,X3,X4,X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6509]),
    [final] ).

cnf(i_0_11682,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_6510]),
    [final] ).

cnf(i_0_11683,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6511]),
    [final] ).

cnf(i_0_11684,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,esk113_5(X3,X4,X5,X2,X1))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6512]),
    [final] ).

cnf(i_0_11685,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X4) = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,esk462_5(X3,X2,X4,X5,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6513]),
    [final] ).

cnf(i_0_11686,plain,
    ( hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk157_5(X3,X2,X4,X5,X1))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4) != c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6514]),
    [final] ).

cnf(i_0_11687,plain,
    ( hBOOL(hAPP(hAPP(X1,esk5_5(X2,X3,X4,X5,X1)),esk6_5(X2,X3,X4,X5,X1)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6127]),
    [final] ).

cnf(i_0_11688,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),
    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_6515,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11689,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) = c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X5))),
    inference(split_conjunct,[status(thm)],[i_0_6516]),
    [final] ).

cnf(i_0_11690,plain,
    hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X5))),
    inference(split_conjunct,[status(thm)],[i_0_6517]),
    [final] ).

cnf(i_0_11691,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk463_5(X3,X4,X5,X6,X1))))
    | ~ hBOOL(hAPP(X4,X2))
    | hAPP(hAPP(c_List_Olist_OCons(X1),X6),X5) != hAPP(c_List_Ofilter(X1,X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_11692,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk466_5(X3,X4,X5,X6,X1))))
    | ~ hBOOL(hAPP(X6,X2))
    | hAPP(c_List_Ofilter(X1,X6),X5) != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_11693,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    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_6518,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11694,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk410_4(X2,X3,X4,X1)),esk411_4(X2,X3,X4,X1))),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6519]),
    [final] ).

cnf(i_0_11695,plain,
    ( X7 = X6
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6520]),
    [final] ).

cnf(i_0_11696,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6521]),
    [final] ).

cnf(i_0_11697,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6522]),
    [final] ).

cnf(i_0_11698,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6523]),
    [final] ).

cnf(i_0_11699,plain,
    ( X1 = X2
    | X3 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X1),hAPP(hAPP(c_List_Olist_OCons(X5),X3),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X2),hAPP(hAPP(c_List_Olist_OCons(X5),X4),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11700,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk336_5(X2,X3,X4,X1,X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_11701,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_6508]),
    [final] ).

cnf(i_0_11702,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[fact_min__weak__def]),
    [final] ).

cnf(i_0_11703,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[fact_max__weak__def]),
    [final] ).

cnf(i_0_11704,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6524]),
    [final] ).

cnf(i_0_11705,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6525]),
    [final] ).

cnf(i_0_11706,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),X4)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6526]),
    [final] ).

cnf(i_0_11707,plain,
    c_Int_Oint__ge__less__than2(X1) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_6527]),
    [final] ).

cnf(i_0_11708,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk103_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6528]),
    [final] ).

cnf(i_0_11709,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6529]),
    [final] ).

cnf(i_0_11710,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6530]),
    [final] ).

cnf(i_0_11711,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Set_OCollect(X1),X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6531]),
    [final] ).

cnf(i_0_11712,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3,X3,hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot)),c_fequal)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6438]),
    [final] ).

cnf(i_0_11713,plain,
    ( c_Nitpick_Oof__frac(X2,X1,X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3)))
    | ~ class_Rings_Oring__1(X1)
    | ~ class_Rings_Oinverse(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6532,c_0_6091]),c_0_6092]),
    [final] ).

cnf(i_0_11714,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6533]),
    [final] ).

cnf(i_0_11715,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oorder(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6442]),
    [final] ).

cnf(i_0_11716,plain,
    c_List_Omeasures(X1,X2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X1),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X1),c_List_Omap(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X1,tc_Nat_Onat),X1,tc_Nat_Onat),c_COMBI(tc_fun(X1,tc_Nat_Onat))))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6534]),
    [final] ).

cnf(i_0_11717,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7),X2))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X7)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6535]),
    [final] ).

cnf(i_0_11718,plain,
    c_Random__Sequence_Omap(X1,X2,X3,X4) = c_Random__Sequence_Obind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X1,c_Random__Sequence_Osingle(X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6536]),
    [final] ).

cnf(i_0_11719,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk164_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Fields_Ofield(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6537]),
    [final] ).

cnf(i_0_11720,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7),X2))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X7))) ),
    inference(split_conjunct,[status(thm)],[i_0_6538]),
    [final] ).

cnf(i_0_11721,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6539]),
    [final] ).

cnf(i_0_11722,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6540]),
    [final] ).

cnf(i_0_11723,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6495]),
    [final] ).

cnf(i_0_11724,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6496]),
    [final] ).

cnf(i_0_11725,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk376_4(X3,X4,X1,X2)),esk377_4(X3,X4,X1,X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6541]),
    [final] ).

cnf(i_0_11726,plain,
    ( c_Fun_Oinj__on(tc_prod(X1,X5),tc_prod(X2,X6),c_Product__Type_Omap__pair(X1,X2,X5,X6,X3,X7),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X1),X8)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X5,X6,X7,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6542]),
    [final] ).

cnf(i_0_11727,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4),X2))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6543]),
    [final] ).

cnf(i_0_11728,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X2))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6544]),
    [final] ).

cnf(i_0_11729,plain,
    c_Lazy__Sequence_Oproduct(X1,X2,X3,X4) = hAPP(c_Lazy__Sequence_Obind(X1,tc_prod(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X1),c_Lazy__Sequence_Obind(X2,tc_prod(X1,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X2),c_Lazy__Sequence_Osingle(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6545]),
    [final] ).

cnf(i_0_11730,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(X4,X1)),hAPP(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ class_Groups_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6546]),
    [final] ).

cnf(i_0_11731,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,tc_prod(X1,X2),esk300_4(X3,X4,X1,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X3))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6547]),
    [final] ).

cnf(i_0_11732,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4)))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6548]),
    [final] ).

cnf(i_0_11733,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X1,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X1,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),X4))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6549]),
    [final] ).

cnf(i_0_11734,plain,
    hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X1,tc_prod(X3,X4),c_Product__Type_Ofst(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6)) = hAPP(c_Fun_Ocomp(X3,X1,tc_prod(X3,X4),X5),c_Product__Type_Ofst(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_6550]),
    [final] ).

cnf(i_0_11735,plain,
    hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X2,tc_prod(X3,X4),c_Product__Type_Osnd(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6)) = hAPP(c_Fun_Ocomp(X4,X2,tc_prod(X3,X4),X6),c_Product__Type_Osnd(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_6551]),
    [final] ).

cnf(i_0_11736,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_6552]),
    [final] ).

cnf(i_0_11737,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_6553]),
    [final] ).

cnf(i_0_11738,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6554]),
    [final] ).

cnf(i_0_11739,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6555]),
    [final] ).

cnf(i_0_11740,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6556]),
    [final] ).

cnf(i_0_11741,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(X5,X2),X7)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,X3),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6557]),
    [final] ).

cnf(i_0_11742,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk565_4(X2,X3,X4,X1)),esk566_4(X2,X3,X4,X1))),X4))
    | c_Equiv__Relations_Ocongruent(X1,X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6558]),
    [final] ).

cnf(i_0_11743,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X2)),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk380_2(X1,X2)),hAPP(X2,esk380_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6559]),
    [final] ).

cnf(i_0_11744,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(X3)
    | ~ class_Groups_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6546]),
    [final] ).

cnf(i_0_11745,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6464]),
    [final] ).

cnf(i_0_11746,plain,
    ( hAPP(hAPP(X6,X7),X9) = hAPP(hAPP(X6,X8),X10)
    | ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X8)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X10)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6560]),
    [final] ).

cnf(i_0_11747,plain,
    ( c_List_Olist__all2(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X5)),X3)),X6),X4,X7)
    | ~ c_List_Olist__all2(X1,X2,X3,X4,hAPP(hAPP(c_List_Omap(X5,X2),X6),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6481]),
    [final] ).

cnf(i_0_11748,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk371_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_OCollect(X1),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6561]),
    [final] ).

cnf(i_0_11749,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X4)),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11750,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk152_3(X2,X3,X1))),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6562]),
    [final] ).

cnf(i_0_11751,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6563]),
    [final] ).

cnf(i_0_11752,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6564]),
    [final] ).

cnf(i_0_11753,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3)),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6564]),
    [final] ).

cnf(i_0_11754,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6466]),
    [final] ).

cnf(i_0_11755,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6467]),
    [final] ).

cnf(i_0_11756,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk384_5(X3,X1,X4,X5,X2)),esk385_5(X3,X1,X4,X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)),X1)),c_List_Olistrel(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6411]),
    [final] ).

cnf(i_0_11757,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2),
    inference(split_conjunct,[status(thm)],[i_0_6565]),
    [final] ).

cnf(i_0_11758,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk362_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_6566,c_0_6104]),
    [final] ).

cnf(i_0_11759,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk421_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),X4))))
    | ~ class_Groups_Omonoid__add(X5)
    | ~ class_Groups_Oordered__ab__semigroup__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6304]),
    [final] ).

cnf(i_0_11760,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk361_4(X2,X3,X4,X1)),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_6567,c_0_6104]),
    [final] ).

cnf(i_0_11761,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X7),X8)) = hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(X5,X7)),hAPP(X6,X8)),
    inference(split_conjunct,[status(thm)],[i_0_6568]),
    [final] ).

cnf(i_0_11762,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,X5)),X6),
    inference(rw,[status(thm)],[i_0_6569,c_0_6267]),
    [final] ).

cnf(i_0_11763,plain,
    hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),X5),hAPP(X4,X6)),
    inference(rw,[status(thm)],[i_0_6570,c_0_6083]),
    [final] ).

cnf(i_0_11764,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
    | X5 != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11765,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk425_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X4))))
    | c_List_Olist__all2(X1,X2,X3,X5,X4)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6571]),
    [final] ).

cnf(i_0_11766,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk423_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X3))))
    | c_List_Olist__all2(X1,X2,X5,X4,X3)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6572]),
    [final] ).

cnf(i_0_11767,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6524]),
    [final] ).

cnf(i_0_11768,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6525]),
    [final] ).

cnf(i_0_11769,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk138_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Oordered__ab__semigroup__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6491]),
    [final] ).

cnf(i_0_11770,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk133_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6492]),
    [final] ).

cnf(i_0_11771,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6493]),
    [final] ).

cnf(i_0_11772,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6494]),
    [final] ).

cnf(i_0_11773,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_6573]),
    [final] ).

cnf(i_0_11774,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk140_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X1),X4))),X2)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X5)
    | ~ class_Rings_Osemiring__1(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6382]),
    [final] ).

cnf(i_0_11775,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk100_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6381]),
    [final] ).

cnf(i_0_11776,plain,
    ( hAPP(hAPP(X3,hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8))),hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8))) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6574]),
    [final] ).

cnf(i_0_11777,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk105_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6575]),
    [final] ).

cnf(i_0_11778,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk104_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6576]),
    [final] ).

cnf(i_0_11779,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk135_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6577]),
    [final] ).

cnf(i_0_11780,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk134_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6578]),
    [final] ).

cnf(i_0_11781,plain,
    hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X4))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6579]),
    [final] ).

cnf(i_0_11782,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11783,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk382_5(X3,X4,X5,X1,X2)),esk383_5(X3,X4,X5,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4))),c_List_Olistrel(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6326]),
    [final] ).

cnf(i_0_11784,plain,
    ( c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ c_List_Olist__ex1(X1,X2,X3)
    | ~ c_List_Olist__all(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))),hAPP(c_fequal,X4)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6580]),
    [final] ).

cnf(i_0_11785,plain,
    hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),c_List_Otranspose(X1,X2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
    inference(rw,[status(thm)],[i_0_6581,c_0_6186]),
    [final] ).

cnf(i_0_11786,plain,
    ( hAPP(X6,X7) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6582]),
    [final] ).

cnf(i_0_11787,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)))
    | c_List_Olist__all2(X5,X3,X1,X4,X2)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6305]),
    [final] ).

cnf(i_0_11788,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk424_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)))
    | c_List_Olist__all2(X5,X4,X3,X2,X1)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6306]),
    [final] ).

cnf(i_0_11789,plain,
    ( c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X1))),hAPP(c_fequal,X2)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6580]),
    [final] ).

cnf(i_0_11790,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk22_5(X2,X3,X1,X4,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6583]),
    [final] ).

cnf(i_0_11791,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))),X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6584,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_11792,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk97_5(X3,X4,X5,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6585]),
    [final] ).

cnf(i_0_11793,plain,
    ( hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6586]),
    [final] ).

cnf(i_0_11794,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk93_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(X2,X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11795,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7) = hAPP(hAPP(c_Fun_Ocomp(X1,X4,X2,c_Hilbert__Choice_Oinv__into(X4,X1,X6,X5)),c_Hilbert__Choice_Oinv__into(X1,X2,hAPP(c_Set_Oimage(X4,X1,X5),X6),X3)),X7)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))
    | ~ c_Fun_Oinj__on(X4,X1,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6587]),
    [final] ).

cnf(i_0_11796,plain,
    ( hAPP(c_Fun_Othe__inv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7) = hAPP(hAPP(c_Fun_Ocomp(X1,X4,X2,c_Fun_Othe__inv__into(X4,X1,X6,X5)),c_Fun_Othe__inv__into(X1,X2,hAPP(c_Set_Oimage(X4,X1,X5),X6),X3)),X7)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))
    | ~ c_Fun_Oinj__on(X4,X1,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6588]),
    [final] ).

cnf(i_0_11797,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk114_5(X2,X3,X4,X1,X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X5)
    | ~ class_Orderings_Olinorder(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6455]),
    [final] ).

cnf(i_0_11798,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk97_5(X2,X3,X1,X4,X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6585]),
    [final] ).

cnf(i_0_11799,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk37_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6307]),
    [final] ).

cnf(i_0_11800,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),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)],[i_0_6589,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11801,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk87_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6590]),
    [final] ).

cnf(i_0_11802,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk86_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6591]),
    [final] ).

cnf(i_0_11803,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk207_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6592]),
    [final] ).

cnf(i_0_11804,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk206_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6593]),
    [final] ).

cnf(i_0_11805,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))
    | esk356_5(X1,X2,X3,X4,X5) != esk357_5(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6272]),
    [final] ).

cnf(i_0_11806,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))
    | esk355_5(X1,X2,X3,X4,X5) != esk354_5(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6273]),
    [final] ).

cnf(i_0_11807,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_6594,c_0_6092]),
    [final] ).

cnf(i_0_11808,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_6595,c_0_6092]),
    [final] ).

cnf(i_0_11809,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk66_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Oordered__ab__semigroup__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6308]),
    [final] ).

cnf(i_0_11810,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk542_5(X2,X3,X4,X5,X1)),X5))
    | c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6502]),
    [final] ).

cnf(i_0_11811,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk492_5(X2,X3,X4,X5,X1)),X5))
    | c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6501]),
    [final] ).

cnf(i_0_11812,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk95_5(X2,X3,X4,X5,X1)),X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6596]),
    [final] ).

cnf(i_0_11813,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk529_5(X2,X3,X4,X1,X5)),hAPP(c_Set_Oimage(X5,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | hBOOL(hAPP(X3,X2))
    | ~ c_Fun_Oinj__on(X5,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6465]),
    [final] ).

cnf(i_0_11814,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4)))
    | ~ class_Orderings_Oorder(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6597]),
    [final] ).

cnf(i_0_11815,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk92_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hBOOL(hAPP(X2,X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11816,plain,
    ( hBOOL(hAPP(hAPP(X1,esk95_5(X2,X1,X3,X4,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6596]),
    [final] ).

cnf(i_0_11817,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk306_5(X2,X3,X4,X5,X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6459]),
    [final] ).

cnf(i_0_11818,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk549_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6499]),
    [final] ).

cnf(i_0_11819,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk107_5(X2,X3,X1,X4,X5)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6500]),
    [final] ).

cnf(i_0_11820,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6598]),
    [final] ).

cnf(i_0_11821,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X5),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6599]),
    [final] ).

cnf(i_0_11822,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X5),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6600]),
    [final] ).

cnf(i_0_11823,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X6))),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)))),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6601]),
    [final] ).

cnf(i_0_11824,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk280_5(X2,X3,X1,X4,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6354]),
    [final] ).

cnf(i_0_11825,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk260_5(X2,X3,X1,X4,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6355]),
    [final] ).

cnf(i_0_11826,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_Int_Ointrel)) ),
    inference(split_conjunct,[status(thm)],[i_0_6602]),
    [final] ).

cnf(i_0_11827,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6603]),
    [final] ).

cnf(i_0_11828,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk101_5(X2,X3,X4,X1,X5)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X4),X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6386]),
    [final] ).

cnf(i_0_11829,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk106_5(X2,X3,X1,X4,X5)),X3))
    | hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6505]),
    [final] ).

cnf(i_0_11830,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk102_5(X3,X4,X5,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X3)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_11831,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X1))))
    | ~ hBOOL(hAPP(X1,esk371_5(X1,X2,X3,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6561]),
    [final] ).

cnf(i_0_11832,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6508]),
    [final] ).

cnf(i_0_11833,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6508]),
    [final] ).

cnf(i_0_11834,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk120_5(X2,X3,X4,X5,X1)),X4))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6509]),
    [final] ).

cnf(i_0_11835,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk102_5(X2,X3,X1,X4,X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X3),X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X5)
    | ~ class_Orderings_Olinorder(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_11836,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,tc_prod(X1,X2)),X7),X8)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))),X7)),X8),
    inference(split_conjunct,[status(thm)],[i_0_6605]),
    [final] ).

cnf(i_0_11837,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    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_6606,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11838,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Rings_Oring__1(X1) ),
    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_6607,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11839,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
    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_6608,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11840,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk27_4(X1,X3,X4,X2)),esk28_4(X1,X3,X4,X2))))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_11841,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X4,X1,X3)),c_List_Olist_Olist__size(X4,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,esk398_4(X2,X1,X3,X4))),hAPP(X2,esk398_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6610]),
    [final] ).

cnf(i_0_11842,plain,
    c_Fun_Oinj__on(tc_fun(X1,X2),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Set_OCollect(tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool)),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_6611]),
    [final] ).

cnf(i_0_11843,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    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_6612,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11844,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6613,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11845,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6614,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11846,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk443_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),hAPP(c_List_Ofilter(X1,X3),X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),X4))
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6615]),
    [final] ).

cnf(i_0_11847,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6616,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11848,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6617,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11849,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk516_5(X2,X3,X4,X1,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
    | ~ c_Wellfounded_Omax__extp(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_11850,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk285_5(X2,X3,X4,X1,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
    | ~ c_Wellfounded_Omax__extp(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_11851,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6620]),
    [final] ).

cnf(i_0_11852,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6621]),
    [final] ).

cnf(i_0_11853,plain,
    ( hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8)) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6622]),
    [final] ).

cnf(i_0_11854,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk113_5(X2,X3,X1,X4,X5)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X3),X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6512]),
    [final] ).

cnf(i_0_11855,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk157_5(X2,X3,X4,X1,X5)),X4))
    | hAPP(X3,X2) = c_Groups_Ozero__class_Ozero(X5)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Groups_Oordered__ab__group__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6514]),
    [final] ).

cnf(i_0_11856,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
    inference(rw,[status(thm)],[i_0_6623,c_0_6293]),
    [final] ).

cnf(i_0_11857,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk462_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X5,X3),X2),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)
    | ~ class_Orderings_Olinorder(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6513]),
    [final] ).

cnf(i_0_11858,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6624]),
    [final] ).

cnf(i_0_11859,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6625]),
    [final] ).

cnf(i_0_11860,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Relation_OImage(X2,X1,X3)),X6)))),
    inference(split_conjunct,[status(thm)],[i_0_6626]),
    [final] ).

cnf(i_0_11861,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6529]),
    [final] ).

cnf(i_0_11862,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6530]),
    [final] ).

cnf(i_0_11863,plain,
    ( hAPP(hAPP(X3,hAPP(X6,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6627]),
    [final] ).

cnf(i_0_11864,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk19_4(X3,X2,X4,X1))),hAPP(X3,esk19_4(X3,X2,X4,X1))))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6628]),
    [final] ).

cnf(i_0_11865,plain,
    ( hAPP(X6,X7) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X5),X4),X7)
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6629]),
    [final] ).

cnf(i_0_11866,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk420_5(X2,X3,X4,X5,X1)),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_List_Omap(X1,X5),X4),X3) = hAPP(hAPP(c_List_Omap(X1,X5),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6630]),
    [final] ).

cnf(i_0_11867,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X6,X7,X8,X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6484]),
    [final] ).

cnf(i_0_11868,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X6,X7,X8,X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6631]),
    [final] ).

cnf(i_0_11869,plain,
    ( hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8)) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6632]),
    [final] ).

cnf(i_0_11870,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk463_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk464_5(X1,X3,X4,X5,X2)))
    | hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4) != hAPP(c_List_Ofilter(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_11871,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk466_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk467_5(X3,X4,X1,X5,X2)))
    | hAPP(c_List_Ofilter(X2,X5),X1) != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_11872,plain,
    ( c_Equiv__Relations_Ocongruent(X4,X5,X6,hAPP(X7,X8))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Equiv__Relations_Ocongruent2(X1,X4,X5,X3,X6,X7)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6633]),
    [final] ).

cnf(i_0_11873,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk409_5(X3,X4,X1,X5,X2)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),esk408_5(X3,X4,X1,X5,X2)),X1) = X3
    | hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_11874,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X8),X7))
    | hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6635]),
    [final] ).

cnf(i_0_11875,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk75_4(X3,X1,X4,X2)),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X4)),hAPP(c_Finite__Set_Ocard(X1),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6636]),
    [final] ).

cnf(i_0_11876,plain,
    ( hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6637]),
    [final] ).

cnf(i_0_11877,plain,
    c_Enum_Osublists(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X3)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X1)),tc_fun(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(tc_List_Olist(X1))),c_List_Oappend(tc_List_Olist(X1))),hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Olist_OCons(X1),X2)))),c_COMBI(tc_List_Olist(tc_List_Olist(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_6638]),
    [final] ).

cnf(i_0_11878,plain,
    ( hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6639]),
    [final] ).

cnf(i_0_11879,plain,
    ( c_List_Olist__all2(X1,X2,X3,X5,X4)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk425_5(X3,X4,X5,X2,X1)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6571]),
    [final] ).

cnf(i_0_11880,plain,
    ( c_List_Olist__all2(X1,X2,X3,X5,X4)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk423_5(X4,X5,X3,X2,X1)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6572]),
    [final] ).

cnf(i_0_11881,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6640]),
    [final] ).

cnf(i_0_11882,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6641]),
    [final] ).

cnf(i_0_11883,plain,
    ( hAPP(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X4
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6642]),
    [final] ).

cnf(i_0_11884,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(split_conjunct,[status(thm)],[fact_max__rpair__set]),
    [final] ).

cnf(i_0_11885,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(split_conjunct,[status(thm)],[fact_min__rpair__set]),
    [final] ).

cnf(i_0_11886,plain,
    ( hAPP(hAPP(X3,X7),X7) = X7
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6643]),
    [final] ).

cnf(i_0_11887,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6644]),
    [final] ).

cnf(i_0_11888,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6624]),
    [final] ).

cnf(i_0_11889,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6625]),
    [final] ).

cnf(i_0_11890,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),X3)))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6645]),
    [final] ).

cnf(i_0_11891,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),X1)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,esk168_3(X2,X3,X1))),hAPP(X3,esk168_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6646]),
    [final] ).

cnf(i_0_11892,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk24_4(X3,X1,X2,X4)),X4)),X3))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X1,X2,X5),X3) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_6647]),
    [final] ).

cnf(i_0_11893,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk296_4(X4,X3,X2,X1)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6648]),
    [final] ).

cnf(i_0_11894,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk294_4(X4,X3,X2,X1)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6649]),
    [final] ).

cnf(i_0_11895,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6650]),
    [final] ).

cnf(i_0_11896,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6651]),
    [final] ).

cnf(i_0_11897,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6652]),
    [final] ).

cnf(i_0_11898,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6653]),
    [final] ).

cnf(i_0_11899,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6654]),
    [final] ).

cnf(i_0_11900,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6655]),
    [final] ).

cnf(i_0_11901,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6656]),
    [final] ).

cnf(i_0_11902,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
    inference(split_conjunct,[status(thm)],[i_0_6657]),
    [final] ).

cnf(i_0_11903,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
    inference(split_conjunct,[status(thm)],[i_0_6658]),
    [final] ).

cnf(i_0_11904,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
    inference(split_conjunct,[status(thm)],[i_0_6659]),
    [final] ).

cnf(i_0_11905,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6660]),
    [final] ).

cnf(i_0_11906,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6661]),
    [final] ).

cnf(i_0_11907,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6662]),
    [final] ).

cnf(i_0_11908,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X6),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X3),X7)),hAPP(hAPP(c_Product__Type_OSigma(X1,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X1),X8))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X6),tc_HOL_Obool)),X7),hAPP(hAPP(c_Product__Type_OSigma(X2,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X2),X8)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6663]),
    [final] ).

cnf(i_0_11909,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_11910,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6665]),
    [final] ).

cnf(i_0_11911,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_11912,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6667]),
    [final] ).

cnf(i_0_11913,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6668]),
    [final] ).

cnf(i_0_11914,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6669]),
    [final] ).

cnf(i_0_11915,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6670]),
    [final] ).

cnf(i_0_11916,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6671]),
    [final] ).

cnf(i_0_11917,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6672]),
    [final] ).

cnf(i_0_11918,plain,
    ( hAPP(hAPP(X5,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X7)),X8)),X6) = hAPP(hAPP(X3,hAPP(hAPP(X5,X7),X6)),hAPP(hAPP(X5,X8),X6))
    | ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6673]),
    [final] ).

cnf(i_0_11919,plain,
    ( hBOOL(hAPP(X1,X6))
    | ~ hBOOL(hAPP(X1,esk94_5(X1,X2,X3,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11920,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olexord(X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))
    | hAPP(hAPP(c_List_Otake(X2),X1),X3) != hAPP(hAPP(c_List_Otake(X2),X1),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_11921,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6674,c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11922,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6675]),
    [final] ).

cnf(i_0_11923,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6676]),
    [final] ).

cnf(i_0_11924,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6677]),
    [final] ).

cnf(i_0_11925,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6678]),
    [final] ).

cnf(i_0_11926,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))),
    inference(split_conjunct,[status(thm)],[i_0_6679]),
    [final] ).

cnf(i_0_11927,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6680,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11928,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6681,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11929,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),X1) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat)))),
    inference(split_conjunct,[status(thm)],[i_0_6682]),
    [final] ).

cnf(i_0_11930,plain,
    c_List_Olenlex(X1,X2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X1)),tc_List_Olist(X1)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X1),c_Wellfounded_Oless__than,c_List_Olex(X1,X2))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X1))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_COMBI(tc_List_Olist(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_6683]),
    [final] ).

cnf(i_0_11931,plain,
    ( c_Fun_Obij__betw(X1,X3,X5,X6,X8)
    | ~ c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X5),X6)),X8))
    | ~ c_Fun_Obij__betw(X3,X2,X4,X8,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6684]),
    [final] ).

cnf(i_0_11932,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
    | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X7))
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X6,X4,X5),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6421]),
    [final] ).

cnf(i_0_11933,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6651]),
    [final] ).

cnf(i_0_11934,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6652]),
    [final] ).

cnf(i_0_11935,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6653]),
    [final] ).

cnf(i_0_11936,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk312_3(X2,X3,X1)),esk312_3(X2,X3,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6685]),
    [final] ).

cnf(i_0_11937,plain,
    ( c_Relation_Orefl__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk310_3(X2,X3,X1)),esk310_3(X2,X3,X1))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6686]),
    [final] ).

cnf(i_0_11938,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6687]),
    [final] ).

cnf(i_0_11939,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_6688]),
    [final] ).

cnf(i_0_11940,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk361_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
    inference(rw,[status(thm)],[i_0_6689,c_0_6104]),
    [final] ).

cnf(i_0_11941,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6671]),
    [final] ).

cnf(i_0_11942,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6672]),
    [final] ).

cnf(i_0_11943,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6690]),
    [final] ).

cnf(i_0_11944,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk306_5(X4,X5,X1,X3,X2)),esk307_5(X4,X5,X1,X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6459]),
    [final] ).

cnf(i_0_11945,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk362_4(X3,X4,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
    inference(rw,[status(thm)],[i_0_6691,c_0_6104]),
    [final] ).

cnf(i_0_11946,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6692]),
    [final] ).

cnf(i_0_11947,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6693,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_11948,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk32_5(X4,X3,X2,X5,X1)),esk33_5(X4,X3,X2,X5,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6420]),
    [final] ).

cnf(i_0_11949,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk30_5(X4,X3,X2,X5,X1)),esk31_5(X4,X3,X2,X5,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6421]),
    [final] ).

cnf(i_0_11950,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X2))
    | hAPP(X1,esk103_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6528]),
    [final] ).

cnf(i_0_11951,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_11952,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6694,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11953,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6695,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11954,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_11955,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),hAPP(c_List_Ofilter(X4,X1),X3))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),X3))
    | ~ hBOOL(hAPP(X1,esk443_5(X2,X1,X3,X4,X5)))
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6615]),
    [final] ).

cnf(i_0_11956,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    inference(split_conjunct,[status(thm)],[i_0_6696]),
    [final] ).

cnf(i_0_11957,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_6697]),
    [final] ).

cnf(i_0_11958,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(split_conjunct,[status(thm)],[i_0_6698]),
    [final] ).

cnf(i_0_11959,plain,
    ( hBOOL(hAPP(X1,X7))
    | ~ hBOOL(hAPP(X1,esk92_5(X1,X2,X3,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(X2,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11960,plain,
    ( c_Fun_Obij__betw(X1,X6,hAPP(c_Fun_Ocomp(X2,X6,X1,X7),X3),X4,X8)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Obij__betw(X2,X6,X7,X5,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6684]),
    [final] ).

cnf(i_0_11961,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5) = X6
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6699]),
    [final] ).

cnf(i_0_11962,plain,
    ( X5 = X4
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6700]),
    [final] ).

cnf(i_0_11963,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6701]),
    [final] ).

cnf(i_0_11964,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6702]),
    [final] ).

cnf(i_0_11965,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6703]),
    [final] ).

cnf(i_0_11966,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6702]),
    [final] ).

cnf(i_0_11967,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6703]),
    [final] ).

cnf(i_0_11968,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X3)
    | hAPP(X1,esk209_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk209_5(X2,X1,X3,X4,X5))
    | ~ c_Nat__Transfer_Onat__set(X3)
    | X4 != X3
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6704]),
    [final] ).

cnf(i_0_11969,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X3)
    | hAPP(X1,esk218_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk218_5(X2,X1,X3,X4,X5))
    | ~ c_Nat__Transfer_Onat__set(X3)
    | X4 != X3
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6705]),
    [final] ).

cnf(i_0_11970,plain,
    ( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
    | hAPP(X1,esk420_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk420_5(X2,X3,X1,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6630]),
    [final] ).

cnf(i_0_11971,plain,
    c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2)) = c_Random_Oselect__weight(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_6706]),
    [final] ).

cnf(i_0_11972,plain,
    c_Random_Opick(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2)) = c_Random_Opick(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_6707]),
    [final] ).

cnf(i_0_11973,plain,
    ( hBOOL(hAPP(X1,esk371_5(X2,X1,X3,X4,X5)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6561]),
    [final] ).

cnf(i_0_11974,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
    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_6708,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11975,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
    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_6709,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_11976,plain,
    ( c_Hilbert__Choice_Oinv__into(X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)) = hAPP(c_Fun_Ocomp(X1,X4,X2,c_Hilbert__Choice_Oinv__into(X4,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X5)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6710]),
    [final] ).

cnf(i_0_11977,plain,
    hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6711,c_0_6712]),c_0_6712]),c_0_6712]),
    [final] ).

cnf(i_0_11978,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6713]),
    [final] ).

cnf(i_0_11979,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6714]),
    [final] ).

cnf(i_0_11980,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6715]),
    [final] ).

cnf(i_0_11981,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6716]),
    [final] ).

cnf(i_0_11982,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6717]),
    [final] ).

cnf(i_0_11983,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6718]),
    [final] ).

cnf(i_0_11984,plain,
    hAPP(c_List_Orotate1(X1),X2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2),
    inference(split_conjunct,[status(thm)],[i_0_6719]),
    [final] ).

cnf(i_0_11985,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6720]),
    [final] ).

cnf(i_0_11986,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6721]),
    [final] ).

cnf(i_0_11987,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6722]),
    [final] ).

cnf(i_0_11988,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X5))),X4))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6723]),
    [final] ).

cnf(i_0_11989,plain,
    c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_6724]),
    [final] ).

cnf(i_0_11990,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olistrel1(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_11991,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6665]),
    [final] ).

cnf(i_0_11992,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_11993,plain,
    c_Random_Oselect__weight(X1,X2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_6725]),
    [final] ).

cnf(i_0_11994,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk409_5(X3,X4,X5,X2,X1)) = X4
    | hAPP(hAPP(c_List_Oappend(X1),esk408_5(X3,X4,X5,X2,X1)),X5) = X3
    | hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_11995,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk409_5(X3,X4,X1,X5,X2)),X3)
    | X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk408_5(X3,X4,X1,X5,X2))
    | hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_11996,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6)))),
    inference(split_conjunct,[status(thm)],[i_0_6726]),
    [final] ).

cnf(i_0_11997,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X3)),X5)),X4)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6727]),
    [final] ).

cnf(i_0_11998,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X5)),X4)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6728]),
    [final] ).

cnf(i_0_11999,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X5))),X4))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6729]),
    [final] ).

cnf(i_0_12000,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6730]),
    [final] ).

cnf(i_0_12001,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X3)) = hAPP(c_List_Orev(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),c_List_Orotate1(X1)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6731,c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_12002,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6733]),
    [final] ).

cnf(i_0_12003,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6734,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12004,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6735,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12005,plain,
    ( c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X1))),hAPP(c_fequal,X2)),X4)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6580]),
    [final] ).

cnf(i_0_12006,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oorder(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6597]),
    [final] ).

cnf(i_0_12007,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))
    | ~ c_FunDef_Oreduction__pair(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
    | ~ c_Wellfounded_Owf(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6736]),
    [final] ).

cnf(i_0_12008,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6737]),
    [final] ).

cnf(i_0_12009,plain,
    ( X1 = X2
    | c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X1,X6),X2,X7) = c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X2,X7),X1,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6738]),
    [final] ).

cnf(i_0_12010,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X3,X4),X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X1,hAPP(c_Relation_Oconverse(X1,X3),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X5))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6739]),
    [final] ).

cnf(i_0_12011,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6740,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12012,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6741,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12013,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Set_Oinsert(X2)),X3)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6742]),
    [final] ).

cnf(i_0_12014,plain,
    ( hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6743]),
    [final] ).

cnf(i_0_12015,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6744]),
    [final] ).

cnf(i_0_12016,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6743]),
    [final] ).

cnf(i_0_12017,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6745]),
    [final] ).

cnf(i_0_12018,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6746]),
    [final] ).

cnf(i_0_12019,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6747]),
    [final] ).

cnf(i_0_12020,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olexord(X1,X4)))
    | ~ c_Relation_Otrans(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6748]),
    [final] ).

cnf(i_0_12021,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5)))),
    inference(split_conjunct,[status(thm)],[i_0_6749]),
    [final] ).

cnf(i_0_12022,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))),
    inference(split_conjunct,[status(thm)],[i_0_6750]),
    [final] ).

cnf(i_0_12023,plain,
    ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))
    | ~ hBOOL(hAPP(X1,esk370_2(X2,X1)))
    | ~ hBOOL(hAPP(X2,esk370_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6751]),
    [final] ).

cnf(i_0_12024,plain,
    hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X7),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6))) = hAPP(c_List_Ofoldl(X2,X4,hAPP(c_COMBC(X4,X2,X2),hAPP(c_Fun_Ocomp(X1,tc_fun(X2,X2),X4,X3),X5)),X7),hAPP(c_List_Orev(X4),X6)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6752,c_0_6186]),c_0_6186]),
    [final] ).

cnf(i_0_12025,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6753]),
    [final] ).

cnf(i_0_12026,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6754]),
    [final] ).

cnf(i_0_12027,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6602]),
    [final] ).

cnf(i_0_12028,plain,
    ( hBOOL(hAPP(X1,esk370_2(X2,X1)))
    | hBOOL(hAPP(X2,esk370_2(X2,X1)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6751]),
    [final] ).

cnf(i_0_12029,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk370_2(X1,X2)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6751]),
    [final] ).

cnf(i_0_12030,plain,
    c_List_Olists(X1,X2) = hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6755]),
    [final] ).

cnf(i_0_12031,plain,
    ( hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_Set_Oimage(X1,X4,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6756]),
    [final] ).

cnf(i_0_12032,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
    | X5 != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6757]),
    [final] ).

cnf(i_0_12033,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),X4)),hAPP(hAPP(c_List_Oappend(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6757]),
    [final] ).

cnf(i_0_12034,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_12035,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olexord(X3,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olexord(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6665]),
    [final] ).

cnf(i_0_12036,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olex(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_12037,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X2)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6758]),
    [final] ).

cnf(i_0_12038,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6759]),
    [final] ).

cnf(i_0_12039,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk412_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk411_4(X3,X1,X4,X2)),esk413_4(X3,X1,X4,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X4),X1)),c_List_Olistrel1(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6519]),
    [final] ).

cnf(i_0_12040,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk412_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk410_4(X3,X4,X1,X2)),esk413_4(X3,X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X4)),c_List_Olistrel1(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6519]),
    [final] ).

cnf(i_0_12041,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
    inference(rw,[status(thm)],[i_0_6760,c_0_6104]),
    [final] ).

cnf(i_0_12042,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))),
    inference(split_conjunct,[status(thm)],[i_0_6761]),
    [final] ).

cnf(i_0_12043,plain,
    ( c_Fun_Obij__betw(X3,X2,X4,X8,X7)
    | ~ c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)
    | ~ c_Fun_Obij__betw(X1,X3,X5,X6,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6762]),
    [final] ).

cnf(i_0_12044,plain,
    ( X1 = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_12045,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),X6) = hAPP(hAPP(c_List_Omap(tc_prod(X3,X2),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4))),hAPP(hAPP(c_List_Ozip(X3,X2),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6763]),
    [final] ).

cnf(i_0_12046,plain,
    c_Wellfounded_Omlex__prod(X1,X2,X3) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1),c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X3)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1),c_Product__Type_OPair(tc_Nat_Onat,X1)),X2)),c_COMBI(X1))),
    inference(split_conjunct,[status(thm)],[i_0_6764]),
    [final] ).

cnf(i_0_12047,plain,
    ( hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),esk18_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk17_3(X1,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6765]),
    [final] ).

cnf(i_0_12048,plain,
    ( X1 = X2
    | X3 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X5),X2),X4))),c_List_Olistrel1(X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_12049,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olistrel(X2,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6324]),
    [final] ).

cnf(i_0_12050,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6766]),
    [final] ).

cnf(i_0_12051,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk315_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk316_3(X2,X3,X1)),esk316_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_12052,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)))),c_COMBI(X2)))
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6767,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12053,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6)),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X6),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6768]),
    [final] ).

cnf(i_0_12054,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X6)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6769]),
    [final] ).

cnf(i_0_12055,plain,
    ( c_Fun_Obij__betw(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X2,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6770]),
    [final] ).

cnf(i_0_12056,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3)),hAPP(c_Set_OPow(X2),X4))),hAPP(c_Set_OPow(X1),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6771]),
    [final] ).

cnf(i_0_12057,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X6)),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | X6 != hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6422]),
    [final] ).

cnf(i_0_12058,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6772]),
    [final] ).

cnf(i_0_12059,plain,
    hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X5))) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),X5))),hAPP(c_List_Orev(X1),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6773,c_0_6186]),c_0_6186]),c_0_6186]),
    [final] ).

cnf(i_0_12060,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Ofst(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X1,X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6774]),
    [final] ).

cnf(i_0_12061,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6775]),
    [final] ).

cnf(i_0_12062,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6776]),
    [final] ).

cnf(i_0_12063,plain,
    hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4)) = hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3)),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_6777]),
    [final] ).

cnf(i_0_12064,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6778]),
    [final] ).

cnf(i_0_12065,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))),
    inference(split_conjunct,[status(thm)],[i_0_6779]),
    [final] ).

cnf(i_0_12066,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_12067,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk381_3(X2,X3,X1)),esk381_3(X2,X3,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6781]),
    [final] ).

cnf(i_0_12068,hypothesis,
    ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X1)),hAPP(v_c0,X1)),hAPP(v_Q,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X1)),hAPP(v_c0,X1)),hAPP(v_Q_H,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6782]),
    [final] ).

cnf(i_0_12069,plain,
    c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_6783]),
    [final] ).

cnf(i_0_12070,plain,
    ( c_Nitpick_Ofold__graph_H(X2,X7,X3,X6,X1,hAPP(hAPP(X3,X4),X5))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(X3,X4),X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6133]),
    [final] ).

cnf(i_0_12071,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))),c_Int_OMin),
    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_6784,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6224]),c_0_6224]),
    [final] ).

cnf(i_0_12072,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6785]),
    [final] ).

cnf(i_0_12073,plain,
    ( hAPP(X1,esk164_5(X1,X2,X3,X4,X5)) = c_Groups_Ozero__class_Ozero(X5)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Fields_Ofield(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6537]),
    [final] ).

cnf(i_0_12074,plain,
    hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),tc_prod(X1,X2)),X5),hAPP(hAPP(c_COMBB(X1,X4,tc_prod(X1,X2)),X6),c_Product__Type_Ofst(X1,X2)))),c_Product__Type_Osnd(X1,X2)) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),X1),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_6786]),
    [final] ).

cnf(i_0_12075,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_4(X1,X2,X3,X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_12076,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X5),X3),c_List_Oremove1(X2,X3,X4)) = X4
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))
    | hAPP(c_List_Ohd(X2),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_fequal,hAPP(X5,X3))),X5)),X4)) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_6787]),
    [final] ).

cnf(i_0_12077,plain,
    ( c_Fun_Obij__betw(X1,X4,X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X5),X6))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X5),X6) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X4,X7,X2,X5)
    | ~ c_Fun_Obij__betw(X1,X4,X7,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6788]),
    [final] ).

cnf(i_0_12078,plain,
    ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel)) ),
    inference(split_conjunct,[status(thm)],[i_0_6789]),
    [final] ).

cnf(i_0_12079,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk500_4(X2,X3,X1,X4)),esk499_4(X2,X3,X1,X4)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk497_4(X2,X3,X1,X4)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12080,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk500_4(X2,X3,X1,X4)),esk498_4(X2,X3,X1,X4)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk497_4(X2,X3,X1,X4)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12081,plain,
    c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
    inference(split_conjunct,[status(thm)],[i_0_6791]),
    [final] ).

cnf(i_0_12082,plain,
    c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
    inference(split_conjunct,[status(thm)],[i_0_6792]),
    [final] ).

cnf(i_0_12083,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6793]),
    [final] ).

cnf(i_0_12084,plain,
    c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6794]),
    [final] ).

cnf(i_0_12085,plain,
    c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
    inference(rw,[status(thm)],[i_0_6795,c_0_6267]),
    [final] ).

cnf(i_0_12086,plain,
    c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6796]),
    [final] ).

cnf(i_0_12087,plain,
    c_Product__Type_Omap__pair(X2,X2,X1,X1,c_Fun_Oid(X2),c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X2,X1)),
    inference(rw,[status(thm)],[i_0_6797,c_0_6083]),
    [final] ).

cnf(i_0_12088,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X5,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4)))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6798]),
    [final] ).

cnf(i_0_12089,plain,
    ( c_Fun_Obij__betw(X1,X6,hAPP(c_Fun_Ocomp(X2,X6,X1,X7),X3),X4,X8)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X2,X6,X7,X5,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_12090,plain,
    ( c_Fun_Obij__betw(X6,X2,hAPP(c_Fun_Ocomp(X1,X2,X6,X3),X7),X8,X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X6,X1,X7,X8,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6762]),
    [final] ).

cnf(i_0_12091,plain,
    c_Divides_OnegateSnd = c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(rw,[status(thm)],[i_0_6800,c_0_6083]),
    [final] ).

cnf(i_0_12092,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6801]),
    [final] ).

cnf(i_0_12093,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_12094,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X3),X6)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X4),X7)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X6),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6802]),
    [final] ).

cnf(i_0_12095,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6803]),
    [final] ).

cnf(i_0_12096,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)),X6))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6804]),
    [final] ).

cnf(i_0_12097,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X2,X4,hAPP(hAPP(c_COMBB(X1,X4,X2),X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6805]),
    [final] ).

cnf(i_0_12098,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6806]),
    [final] ).

cnf(i_0_12099,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_12100,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olists(X1,X3)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_List_Olist(X1)),c_List_Olists(X1,X3)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6807]),
    [final] ).

cnf(i_0_12101,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X6),X7),hAPP(c_Set_Oimage(X2,X4,X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Fun_Ocomp(X4,X1,X2,X6),X5)),X7),X3)
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ c_Fun_Oinj__on(X2,X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6808]),
    [final] ).

cnf(i_0_12102,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6809]),
    [final] ).

cnf(i_0_12103,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6666]),
    [final] ).

cnf(i_0_12104,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk256_4(X2,X3,X4,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6810]),
    [final] ).

cnf(i_0_12105,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk64_4(X2,X3,X4,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6811]),
    [final] ).

cnf(i_0_12106,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X5),X7))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X6,X7)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X5),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6812]),
    [final] ).

cnf(i_0_12107,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_4(X1,X2,X3,X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))
    | hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_12108,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6813,c_0_6097]),c_0_6104]),
    [final] ).

cnf(i_0_12109,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_12110,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | X5 != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6664]),
    [final] ).

cnf(i_0_12111,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5))),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6815]),
    [final] ).

cnf(i_0_12112,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6665]),
    [final] ).

cnf(i_0_12113,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6816,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12114,plain,
    ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6817,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12115,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X5)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6739]),
    [final] ).

cnf(i_0_12116,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X3)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6818]),
    [final] ).

cnf(i_0_12117,plain,
    c_Hilbert__Choice_OEps(tc_prod(X1,X2),X3) = c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6819]),
    [final] ).

cnf(i_0_12118,plain,
    c_HOL_OThe(tc_prod(X1,X2),X3) = c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6820]),
    [final] ).

cnf(i_0_12119,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X6)),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6821]),
    [final] ).

cnf(i_0_12120,plain,
    ( c_Relation_Ototal__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_3(X2,X3,X1)),esk347_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_12121,plain,
    ( c_Relation_Ototal__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk347_3(X2,X3,X1)),esk348_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_12122,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6823]),
    [final] ).

cnf(i_0_12123,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ c_Relation_Osingle__valued(X1,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6824]),
    [final] ).

cnf(i_0_12124,plain,
    ( c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6825]),
    [final] ).

cnf(i_0_12125,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6826]),
    [final] ).

cnf(i_0_12126,plain,
    c_Random_Oselect(X1,X2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of))),
    inference(split_conjunct,[status(thm)],[i_0_6827]),
    [final] ).

cnf(i_0_12127,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_12128,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6829]),
    [final] ).

cnf(i_0_12129,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_12130,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk27_4(X2,X3,X4,X1)),esk28_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_12131,plain,
    ( c_List_OtakeWhile(X1,X3,X2) = hAPP(c_List_Ofilter(X1,X3),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),esk446_3(X2,X3,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)))) ),
    inference(rw,[status(thm)],[i_0_6830,c_0_6293]),
    [final] ).

cnf(i_0_12132,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk337_4(X2,X3,X4,X1)),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_12133,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk292_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6483]),
    [final] ).

cnf(i_0_12134,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(rw,[status(thm)],[i_0_6831,c_0_6104]),
    [final] ).

cnf(i_0_12135,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(rw,[status(thm)],[i_0_6832,c_0_6104]),
    [final] ).

cnf(i_0_12136,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6833]),
    [final] ).

cnf(i_0_12137,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_12138,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_6834]),
    [final] ).

cnf(i_0_12139,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk516_5(X3,X4,X1,X5,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X2),X4))
    | ~ c_Wellfounded_Omax__extp(X5,X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_12140,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk285_5(X3,X4,X1,X5,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X2),X4))
    | ~ c_Wellfounded_Omax__extp(X5,X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_12141,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6835,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12142,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Groups_Omonoid__mult(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6836,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12143,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(rw,[status(thm)],[i_0_6837,c_0_6104]),
    [final] ).

cnf(i_0_12144,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk500_4(X2,X3,X1,X4)),esk499_4(X2,X3,X1,X4)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk497_4(X2,X3,X1,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12145,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk500_4(X2,X3,X1,X4)),esk498_4(X2,X3,X1,X4)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk497_4(X2,X3,X1,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12146,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X5)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4))) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6838]),
    [final] ).

cnf(i_0_12147,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12148,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk298_4(X4,X3,X2,X1))),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6840]),
    [final] ).

cnf(i_0_12149,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk297_4(X4,X3,X2,X1))),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6841]),
    [final] ).

cnf(i_0_12150,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6842]),
    [final] ).

cnf(i_0_12151,plain,
    ( hAPP(c_Fun_Ocomp(X2,X4,X1,hAPP(c_Fun_Ocomp(X1,X4,X2,X5),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))),X3) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6843]),
    [final] ).

cnf(i_0_12152,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X4)),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6844]),
    [final] ).

cnf(i_0_12153,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6845,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12154,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Random_Opick(X2,X3),X1)),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),X2),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2)),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6846]),
    [final] ).

cnf(i_0_12155,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X6),X3),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X5),X8)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X6)),hAPP(hAPP(c_Product__Type_OPair(X2,X6),X4),X7)),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6847]),
    [final] ).

cnf(i_0_12156,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X3,X5,X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6848]),
    [final] ).

cnf(i_0_12157,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,X6,X7)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6849]),
    [final] ).

cnf(i_0_12158,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk68_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk67_4(X2,X3,X4,X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12159,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6851,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12160,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk72_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk71_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12161,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6853,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12162,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6854,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12163,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X2)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6855,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12164,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk499_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk497_4(X2,X3,X1,X4)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12165,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk498_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk497_4(X2,X3,X1,X4)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12166,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk352_5(X2,X1,X3,X4,X5))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_12167,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk350_5(X2,X1,X3,X4,X5))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_12168,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk352_5(X2,X1,X3,X4,X5))
    | X4 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6331]),
    [final] ).

cnf(i_0_12169,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk350_5(X2,X1,X3,X4,X5))
    | X4 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_12170,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6119]),
    [final] ).

cnf(i_0_12171,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6856]),
    [final] ).

cnf(i_0_12172,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6857]),
    [final] ).

cnf(i_0_12173,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6858,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12174,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6859,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12175,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_12176,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6860,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12177,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6861,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12178,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_12179,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6415]),
    [final] ).

cnf(i_0_12180,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6862,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12181,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6863,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12182,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))
    | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6789]),
    [final] ).

cnf(i_0_12183,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,X6,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6864]),
    [final] ).

cnf(i_0_12184,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6865,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12185,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk390_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk390_4(X2,X3,X4,X1)),X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_12186,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_List_Omap(X1,X4),c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(hAPP(c_List_Omap(X1,X4),X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6866]),
    [final] ).

cnf(i_0_12187,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X6,X4,X1,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6702]),
    [final] ).

cnf(i_0_12188,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X6,X1,X4,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6703]),
    [final] ).

cnf(i_0_12189,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(c_Set_Oimage(X1,X4,X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6756]),
    [final] ).

cnf(i_0_12190,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4),c_Fun_Ofun__upd(X3,X1,X5,X6,X7)) = c_Fun_Ofun__upd(X3,X2,hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6,hAPP(X4,X7)),
    inference(split_conjunct,[status(thm)],[i_0_6867]),
    [final] ).

cnf(i_0_12191,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12192,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6868,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12193,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6869]),
    [final] ).

cnf(i_0_12194,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5)) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6870]),
    [final] ).

cnf(i_0_12195,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk209_5(X1,X2,X3,X4,X5)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X3)
    | ~ c_Nat__Transfer_Onat__set(X3)
    | X4 != X3
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6704]),
    [final] ).

cnf(i_0_12196,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk218_5(X1,X2,X3,X4,X5)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X3)
    | ~ c_Nat__Transfer_Onat__set(X3)
    | X4 != X3
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6705]),
    [final] ).

cnf(i_0_12197,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6871]),
    [final] ).

cnf(i_0_12198,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6871]),
    [final] ).

cnf(i_0_12199,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk409_5(X3,X4,X5,X2,X1)) = X4
    | X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk408_5(X3,X4,X5,X2,X1))
    | hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_12200,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk407_5(X3,X4,X1,X5,X2)),X3)
    | hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) = X3
    | hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_12201,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk406_5(X2,X3,X4,X5,X1)),X4) = X2
    | X4 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)
    | hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_12202,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk395_4(X2,X3,X4,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X3))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6128]),
    [final] ).

cnf(i_0_12203,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6874]),
    [final] ).

cnf(i_0_12204,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk52_2(X2,X1)),esk53_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk52_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk53_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6875]),
    [final] ).

cnf(i_0_12205,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk50_2(X2,X1)),esk51_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk50_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk51_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6876]),
    [final] ).

cnf(i_0_12206,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),X2)),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk304_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6877]),
    [final] ).

cnf(i_0_12207,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6878]),
    [final] ).

cnf(i_0_12208,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6879]),
    [final] ).

cnf(i_0_12209,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6880]),
    [final] ).

cnf(i_0_12210,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk406_5(X2,X3,X4,X5,X1)),X4) = X2
    | X5 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_12211,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk407_5(X3,X4,X1,X5,X2)),X3)
    | X4 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_12212,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),X2))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk48_2(X2,X1)),esk49_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk48_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk49_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6881]),
    [final] ).

cnf(i_0_12213,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6882,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12214,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6883]),
    [final] ).

cnf(i_0_12215,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6733]),
    [final] ).

cnf(i_0_12216,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6884]),
    [final] ).

cnf(i_0_12217,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X4,X5,X3)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6885]),
    [final] ).

cnf(i_0_12218,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))
    | hAPP(X1,esk105_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6575]),
    [final] ).

cnf(i_0_12219,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))
    | hAPP(X1,esk104_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6576]),
    [final] ).

cnf(i_0_12220,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2))
    | hAPP(X1,esk135_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6577]),
    [final] ).

cnf(i_0_12221,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2))
    | hAPP(X1,esk134_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6578]),
    [final] ).

cnf(i_0_12222,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),c_List_Otranspose(X2,X3)),X1) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),X2),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_Nat_Onat,X2),c_List_Onth(X2)),X1)),hAPP(c_List_Ofilter(tc_List_Olist(X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Nat_Osize__class_Osize(tc_List_Olist(X2)))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6886]),
    [final] ).

cnf(i_0_12223,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6887]),
    [final] ).

cnf(i_0_12224,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk390_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk390_4(X2,X3,X4,X1)),X3)
    | hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3) = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_12225,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Oinj__on(X2,X1,X6,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6888]),
    [final] ).

cnf(i_0_12226,plain,
    c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)) = c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_6889]),
    [final] ).

cnf(i_0_12227,plain,
    c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)) = c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_6890]),
    [final] ).

cnf(i_0_12228,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X5,X2)),hAPP(X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X5),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6891]),
    [final] ).

cnf(i_0_12229,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6892]),
    [final] ).

cnf(i_0_12230,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6893]),
    [final] ).

cnf(i_0_12231,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6894]),
    [final] ).

cnf(i_0_12232,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk400_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel1(X4,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6422]),
    [final] ).

cnf(i_0_12233,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X1,X2,X3,X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12234,plain,
    c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4,X6) = c_Fun_Ofun__upd(X1,X2,X3,X4,X6),
    inference(split_conjunct,[status(thm)],[i_0_6895]),
    [final] ).

cnf(i_0_12235,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6896]),
    [final] ).

cnf(i_0_12236,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6897]),
    [final] ).

cnf(i_0_12237,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6898,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12238,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_Fun_Ocomp(X1,X1,X2,c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6899]),
    [final] ).

cnf(i_0_12239,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),esk71_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk72_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12240,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk72_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X2,esk71_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12241,plain,
    c_New__Random__Sequence_Oneg__map(X1,X2,X3,X4) = c_New__Random__Sequence_Oneg__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X1,c_New__Random__Sequence_Oneg__single(X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6900]),
    [final] ).

cnf(i_0_12242,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6901]),
    [final] ).

cnf(i_0_12243,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6902]),
    [final] ).

cnf(i_0_12244,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6903]),
    [final] ).

cnf(i_0_12245,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6904]),
    [final] ).

cnf(i_0_12246,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))),c_Groups_Ozero__class_Ozero(X2)))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6904]),
    [final] ).

cnf(i_0_12247,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk115_2(X2,X1)),esk116_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk115_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk116_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6905]),
    [final] ).

cnf(i_0_12248,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk82_2(X2,X1)),esk83_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk82_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk83_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6906]),
    [final] ).

cnf(i_0_12249,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk46_2(X2,X1)),esk47_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk46_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk47_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6907]),
    [final] ).

cnf(i_0_12250,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk44_2(X2,X1)),esk45_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk44_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk45_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6908]),
    [final] ).

cnf(i_0_12251,plain,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6909]),
    [final] ).

cnf(i_0_12252,plain,
    ( hAPP(hAPP(X5,X8),hAPP(c_Set_Oimage(X2,X2,X7),X6)) = hAPP(hAPP(X5,hAPP(c_Fun_Ocomp(X2,X1,X2,X8),X7)),X6)
    | ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))
    | ~ c_Fun_Oinj__on(X2,X2,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6910]),
    [final] ).

cnf(i_0_12253,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk256_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6810]),
    [final] ).

cnf(i_0_12254,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk64_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6811]),
    [final] ).

cnf(i_0_12255,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6911]),
    [final] ).

cnf(i_0_12256,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),hAPP(hAPP(X7,X3),X4)),hAPP(c_Set_Oimage(tc_prod(X1,X2),X6,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X6),X7)),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6912]),
    [final] ).

cnf(i_0_12257,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6913]),
    [final] ).

cnf(i_0_12258,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk499_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk497_4(X2,X3,X1,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12259,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk498_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk497_4(X2,X3,X1,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12260,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))),
    inference(rw,[status(thm)],[i_0_6914,c_0_6104]),
    [final] ).

cnf(i_0_12261,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X5),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6915]),
    [final] ).

cnf(i_0_12262,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X6))
    | hBOOL(hAPP(hAPP(X4,X5),X6))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6916]),
    [final] ).

cnf(i_0_12263,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
    inference(split_conjunct,[status(thm)],[i_0_6917]),
    [final] ).

cnf(i_0_12264,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6918]),
    [final] ).

cnf(i_0_12265,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)
    | hAPP(X1,esk87_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6590]),
    [final] ).

cnf(i_0_12266,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2)
    | hAPP(X1,esk86_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6591]),
    [final] ).

cnf(i_0_12267,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)
    | hAPP(X1,esk207_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6592]),
    [final] ).

cnf(i_0_12268,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2)
    | hAPP(X1,esk206_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
    | ~ class_Groups_Ocomm__monoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6593]),
    [final] ).

cnf(i_0_12269,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3,X1,X4),X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))
    | ~ c_Fun_Obij__betw(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6897]),
    [final] ).

cnf(i_0_12270,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X4),c_Transitive__Closure_Ortrancl(X3,X4)))) ),
    inference(rw,[status(thm)],[i_0_6919,c_0_6104]),
    [final] ).

cnf(i_0_12271,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
    inference(rw,[status(thm)],[i_0_6920,c_0_6104]),
    [final] ).

cnf(i_0_12272,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6921]),
    [final] ).

cnf(i_0_12273,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6922]),
    [final] ).

cnf(i_0_12274,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X6),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X3),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))
    | ~ c_List_Olist__all2(X1,X2,X6,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6572]),
    [final] ).

cnf(i_0_12275,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6923]),
    [final] ).

cnf(i_0_12276,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6923]),
    [final] ).

cnf(i_0_12277,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X6))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6924]),
    [final] ).

cnf(i_0_12278,plain,
    ( hBOOL(hAPP(hAPP(X4,X5),X6))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6925]),
    [final] ).

cnf(i_0_12279,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk430_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
    | hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6926,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_12280,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk429_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
    | hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6927,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_12281,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X1,X3))))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk448_4(X3,X2,X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6928]),
    [final] ).

cnf(i_0_12282,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    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_6929,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12283,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    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_6930,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12284,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    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_6931,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12285,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    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_6932,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12286,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6766]),
    [final] ).

cnf(i_0_12287,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6933]),
    [final] ).

cnf(i_0_12288,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6934]),
    [final] ).

cnf(i_0_12289,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6935]),
    [final] ).

cnf(i_0_12290,plain,
    ( hAPP(c_Fun_Ocomp(X5,X6,X7,X8),hAPP(c_Fun_Ocomp(X9,X5,X7,X10),X11)) = hAPP(c_Fun_Ocomp(X9,X6,X7,hAPP(c_Fun_Ocomp(X5,X6,X9,X8),X10)),X11)
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6936]),
    [final] ).

cnf(i_0_12291,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X3))),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_6937,c_0_6712]),
    [final] ).

cnf(i_0_12292,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X2))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6938]),
    [final] ).

cnf(i_0_12293,plain,
    hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_6939]),
    [final] ).

cnf(i_0_12294,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6940]),
    [final] ).

cnf(i_0_12295,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6941]),
    [final] ).

cnf(i_0_12296,plain,
    hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6942]),
    [final] ).

cnf(i_0_12297,plain,
    ( c_Wellfounded_OwfP(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X2))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Predicate_ODomainP(X1,X1,hAPP(X2,esk322_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk323_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk321_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6943]),
    [final] ).

cnf(i_0_12298,plain,
    c_List_Opartition(X1,X2,X3) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6944]),
    [final] ).

cnf(i_0_12299,plain,
    ( hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X4))),X5)) = hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6945,c_0_6712]),c_0_6712]),
    [final] ).

cnf(i_0_12300,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))),X4))
    | hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6364]),
    [final] ).

cnf(i_0_12301,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),hAPP(c_List_Ofilter(X4,X2),X3))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),X3))
    | hAPP(X1,esk443_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6615]),
    [final] ).

cnf(i_0_12302,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk404_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk405_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk404_3(X1,X2,X3)),esk405_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6946]),
    [final] ).

cnf(i_0_12303,plain,
    ( c_List_Olist__all2(X3,X2,X4,hAPP(hAPP(c_List_Omap(X1,X3),X5),X6),X7)
    | ~ c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_HOL_Obool),X1),X4),X5),X6,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6947]),
    [final] ).

cnf(i_0_12304,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_6948,c_0_6104]),
    [final] ).

cnf(i_0_12305,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6949]),
    [final] ).

cnf(i_0_12306,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6950]),
    [final] ).

cnf(i_0_12307,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6951]),
    [final] ).

cnf(i_0_12308,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6952]),
    [final] ).

cnf(i_0_12309,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6941]),
    [final] ).

cnf(i_0_12310,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5)))),hAPP(hAPP(c_List_Oappend(X1),X3),X5)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,X3))),X3)),X5)
    | hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6953,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_12311,plain,
    ( hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk72_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X1,esk71_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12312,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_6954]),
    [final] ).

cnf(i_0_12313,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2)))),hAPP(hAPP(c_List_Oappend(X1),X4),X2)) = hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),esk458_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6955,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_12314,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))
    | c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6793]),
    [final] ).

cnf(i_0_12315,plain,
    ( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk400_4(X4,X1,X3,X2)),esk399_4(X4,X1,X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X1)),c_List_Olistrel1(X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6422]),
    [final] ).

cnf(i_0_12316,plain,
    ( hBOOL(hAPP(X1,esk68_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(X4),esk67_4(X1,X2,X3,X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12317,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk68_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,esk67_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12318,plain,
    ( hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X4))),X5)) = hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6956,c_0_6712]),c_0_6712]),
    [final] ).

cnf(i_0_12319,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6957]),
    [final] ).

cnf(i_0_12320,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2)),
    inference(rw,[status(thm)],[i_0_6958,c_0_6186]),
    [final] ).

cnf(i_0_12321,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk346_3(X3,X2,X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
    inference(rw,[status(thm)],[i_0_6959,c_0_6104]),
    [final] ).

cnf(i_0_12322,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X2),X1)),c_List_Olexord(X4,X3)))
    | X2 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X1),X2)),c_List_Olexord(X4,X3)))
    | esk387_4(X1,X2,X3,X4) != esk388_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6434]),
    [final] ).

cnf(i_0_12323,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_12324,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),hAPP(c_List_Oset(X2),X3)),X4) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6960]),
    [final] ).

cnf(i_0_12325,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),hAPP(c_List_Oset(X2),X3)),X4) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6961]),
    [final] ).

cnf(i_0_12326,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Oappend(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6962,c_0_6143]),c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_12327,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk245_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6963]),
    [final] ).

cnf(i_0_12328,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk88_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6964]),
    [final] ).

cnf(i_0_12329,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool),X5),hAPP(c_Relation_Orel__comp(X1,X2,X3),X4)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6965]),
    [final] ).

cnf(i_0_12330,plain,
    ( c_List_Olist__all2(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X4),X3),X5),X6,X7)
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6947]),
    [final] ).

cnf(i_0_12331,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4),hAPP(c_Fun_Ocomp(X5,X1,X3,X6),X7)) = hAPP(c_Fun_Ocomp(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
    inference(split_conjunct,[status(thm)],[i_0_6966]),
    [final] ).

cnf(i_0_12332,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6967]),
    [final] ).

cnf(i_0_12333,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_12334,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_Oimage(X1,X2,X3)),X6))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6968]),
    [final] ).

cnf(i_0_12335,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),hAPP(hAPP(c_Relation_Oinv__image(X1,X6),X5),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12336,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6970]),
    [final] ).

cnf(i_0_12337,plain,
    ( hAPP(X4,X5) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6971]),
    [final] ).

cnf(i_0_12338,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6891]),
    [final] ).

cnf(i_0_12339,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X6)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6972]),
    [final] ).

cnf(i_0_12340,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,hAPP(c_List_Otl(X1),X3),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1)),X3))),X2),
    inference(split_conjunct,[status(thm)],[i_0_6973]),
    [final] ).

cnf(i_0_12341,plain,
    c_New__Random__Sequence_Opos__map(X1,X2,X3,X4) = c_New__Random__Sequence_Opos__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X1,c_New__Random__Sequence_Opos__single(X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6974]),
    [final] ).

cnf(i_0_12342,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6975]),
    [final] ).

cnf(i_0_12343,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk386_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel(X4,X1)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6324]),
    [final] ).

cnf(i_0_12344,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6976]),
    [final] ).

cnf(i_0_12345,plain,
    ( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6977]),
    [final] ).

cnf(i_0_12346,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X8),X6),hAPP(hAPP(c_List_Olist__update(X2,X5),X8),X7))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(X3,X6),X7))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6978]),
    [final] ).

cnf(i_0_12347,plain,
    ( c_List_Olist__all2(X2,X4,X5,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X7),hAPP(hAPP(c_List_Olist__update(X4,X6),X1),X8))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ c_List_Olist__all2(X2,X4,X5,X3,X6)
    | ~ hBOOL(hAPP(hAPP(X5,X7),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6979]),
    [final] ).

cnf(i_0_12348,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_OCollect(X1),X4)) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6980]),
    [final] ).

cnf(i_0_12349,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X4),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6981]),
    [final] ).

cnf(i_0_12350,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Finite__Set_Ocard(X2),X4)))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6982]),
    [final] ).

cnf(i_0_12351,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk378_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6983]),
    [final] ).

cnf(i_0_12352,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk379_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6984]),
    [final] ).

cnf(i_0_12353,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk304_4(X2,X3,X4,X1)),X4))
    | hAPP(c_Finite__Set_Ocard(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),X2)),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6877]),
    [final] ).

cnf(i_0_12354,plain,
    c_Predicate_Oconversep(X1,X2,c_Predicate_Opred__comp(X1,X3,X2,X4,X5)) = c_Predicate_Opred__comp(X2,X3,X1,c_Predicate_Oconversep(X3,X2,X5),c_Predicate_Oconversep(X1,X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_6985]),
    [final] ).

cnf(i_0_12355,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(rw,[status(thm)],[i_0_6986,c_0_6104]),
    [final] ).

cnf(i_0_12356,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(rw,[status(thm)],[i_0_6987,c_0_6104]),
    [final] ).

cnf(i_0_12357,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),X8))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6988]),
    [final] ).

cnf(i_0_12358,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(X4,X1),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12359,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4) = c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6989]),
    [final] ).

cnf(i_0_12360,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk365_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X2,X3,X4,X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12361,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk365_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk364_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12362,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk305_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_12363,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6991]),
    [final] ).

cnf(i_0_12364,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6992]),
    [final] ).

cnf(i_0_12365,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk175_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6993]),
    [final] ).

cnf(i_0_12366,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))
    | c_List_OtakeWhile(X2,X1,X3) = hAPP(hAPP(c_List_Otake(X2),X4),X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk447_4(X1,X3,X2,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12367,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6)) = hAPP(hAPP(hAPP(X4,X5),X6),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,X6)),
    inference(split_conjunct,[status(thm)],[i_0_6995]),
    [final] ).

cnf(i_0_12368,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Wellfounded_Omax__extp(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,esk517_4(X3,X5,X4,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_12369,plain,
    ( c_Wellfounded_Omax__extp(X1,X4,X5,X3)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,esk515_4(X4,X3,X5,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6996]),
    [final] ).

cnf(i_0_12370,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Wellfounded_Omax__extp(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,esk286_4(X3,X5,X4,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_12371,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),X8))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6997]),
    [final] ).

cnf(i_0_12372,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X8)),c_List_Olistrel1(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | X5 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X7))
    | X8 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6998]),
    [final] ).

cnf(i_0_12373,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk546_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))
    | ~ hBOOL(hAPP(X3,X5))
    | ~ hBOOL(hAPP(X2,esk545_4(X2,X3,X4,X1)))
    | ~ c_Equiv__Relations_Oequivp(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6999]),
    [final] ).

cnf(i_0_12374,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | c_List_OtakeWhile(X2,X4,X3) = hAPP(hAPP(c_List_Otake(X2),X1),X3)
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),esk447_4(X4,X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12375,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(rw,[status(thm)],[i_0_7000,c_0_6104]),
    [final] ).

cnf(i_0_12376,plain,
    ( hAPP(X1,X2) = hAPP(X1,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6891]),
    [final] ).

cnf(i_0_12377,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk497_4(X1,X2,X3,X4)),X2))
    | hAPP(X1,esk500_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12378,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk426_4(X4,X1,X3,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7001]),
    [final] ).

cnf(i_0_12379,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk255_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7002]),
    [final] ).

cnf(i_0_12380,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk65_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7003]),
    [final] ).

cnf(i_0_12381,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12382,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk497_4(X1,X2,X3,X4)),X2))
    | esk498_4(X1,X2,X3,X4) != esk499_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12383,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7004]),
    [final] ).

cnf(i_0_12384,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X6,X7)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))
    | hAPP(c_Set_Oimage(X1,X2,X3),X6) != X7 ),
    inference(split_conjunct,[status(thm)],[i_0_7005]),
    [final] ).

cnf(i_0_12385,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7006]),
    [final] ).

cnf(i_0_12386,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7006]),
    [final] ).

cnf(i_0_12387,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X8))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7007]),
    [final] ).

cnf(i_0_12388,plain,
    ( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk22_5(X5,X4,X2,X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X3,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6583]),
    [final] ).

cnf(i_0_12389,plain,
    ( hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)))),hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X1,X2))),X2)
    | ~ hBOOL(hAPP(X1,esk458_4(X2,X1,X3,X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7008,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_12390,plain,
    ( X1 = hAPP(X2,esk74_5(X1,X2,X3,X4,X5))
    | hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X5)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7009]),
    [final] ).

cnf(i_0_12391,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))
    | ~ class_Groups_Oab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7010]),
    [final] ).

cnf(i_0_12392,plain,
    ( hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = hAPP(hAPP(c_List_Olist__update(X2,hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7011]),
    [final] ).

cnf(i_0_12393,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | c_Groups_Oone__class_Oone(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7012,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12394,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7013,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12395,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))),hAPP(c_Set_OCollect(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7014]),
    [final] ).

cnf(i_0_12396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12397,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12398,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk342_3(X3,X2,X1)),esk344_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7017]),
    [final] ).

cnf(i_0_12399,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk342_3(X3,X2,X1)),esk343_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7017]),
    [final] ).

cnf(i_0_12400,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk290_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk290_2(X2,X1),X3))),X2))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6486]),
    [final] ).

cnf(i_0_12401,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_12402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_12403,plain,
    c_Product__Type_Oprod_Oprod__size(X1,X2,X3,X4,X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,hAPP(c_Product__Type_Ofst(X1,X2),X5))),hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X2),X5)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_7020]),
    [final] ).

cnf(i_0_12404,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X5))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7021]),
    [final] ).

cnf(i_0_12405,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7022]),
    [final] ).

cnf(i_0_12406,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7023]),
    [final] ).

cnf(i_0_12407,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
    | c_Fun_Oinj__on(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X6,X5),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7024]),
    [final] ).

cnf(i_0_12408,plain,
    ( X4 = X5
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X7),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X7)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7025]),
    [final] ).

cnf(i_0_12409,plain,
    ( X5 = X6
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
    | ~ c_Equiv__Relations_Oequiv(X1,X7,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7026]),
    [final] ).

cnf(i_0_12410,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk208_3(X2,X3,X1)),X3)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7027]),
    [final] ).

cnf(i_0_12411,plain,
    c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X2,c_fequal)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_7028]),
    [final] ).

cnf(i_0_12412,plain,
    ( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12413,plain,
    ( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7030]),
    [final] ).

cnf(i_0_12414,plain,
    hAPP(c_Relation_OImage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X1,X2,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7031]),
    [final] ).

cnf(i_0_12415,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7032]),
    [final] ).

cnf(i_0_12416,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_4(X1,X2,X3,X4)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6993]),
    [final] ).

cnf(i_0_12417,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7033]),
    [final] ).

cnf(i_0_12418,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7034]),
    [final] ).

cnf(i_0_12419,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7035]),
    [final] ).

cnf(i_0_12420,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),X5,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7036]),
    [final] ).

cnf(i_0_12421,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X5,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X6) = hAPP(X3,X6)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7037]),
    [final] ).

cnf(i_0_12422,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X8,tc_HOL_Obool))),X3),X4),X5),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6135]),
    [final] ).

cnf(i_0_12423,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X8,tc_HOL_Obool))),X3),X4),X5),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7038]),
    [final] ).

cnf(i_0_12424,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X4,X5),X6),X7))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_7039]),
    [final] ).

cnf(i_0_12425,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12426,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12427,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7040]),
    [final] ).

cnf(i_0_12428,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X6)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7041]),
    [final] ).

cnf(i_0_12429,plain,
    ( c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6849]),
    [final] ).

cnf(i_0_12430,plain,
    ( c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X6),X4),hAPP(hAPP(c_List_Oappend(X2),X7),X5))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6849]),
    [final] ).

cnf(i_0_12431,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5)) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X5)),X4),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7042]),
    [final] ).

cnf(i_0_12432,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X5)) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X5)),X4),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7043]),
    [final] ).

cnf(i_0_12433,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7044]),
    [final] ).

cnf(i_0_12434,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7045]),
    [final] ).

cnf(i_0_12435,plain,
    ( hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7046]),
    [final] ).

cnf(i_0_12436,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7047]),
    [final] ).

cnf(i_0_12437,plain,
    ( hAPP(c_Set_Oimage(X2,X1,esk23_4(X5,X2,X1,X4)),X5) = X4
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6647]),
    [final] ).

cnf(i_0_12438,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7048]),
    [final] ).

cnf(i_0_12439,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7049]),
    [final] ).

cnf(i_0_12440,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))
    | ~ c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7050]),
    [final] ).

cnf(i_0_12441,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6887]),
    [final] ).

cnf(i_0_12442,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk453_2(X2,X1))),hAPP(c_List_Oset(X1),esk454_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_7051,c_0_6143]),
    [final] ).

cnf(i_0_12443,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6838]),
    [final] ).

cnf(i_0_12444,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))),X3))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7052]),
    [final] ).

cnf(i_0_12445,plain,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_Set_Oimage(X1,X2,X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7053]),
    [final] ).

cnf(i_0_12446,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6892]),
    [final] ).

cnf(i_0_12447,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6893]),
    [final] ).

cnf(i_0_12448,plain,
    ( c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_List_Olist__all2(X4,X5,X1,X6,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_7054]),
    [final] ).

cnf(i_0_12449,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7055]),
    [final] ).

cnf(i_0_12450,plain,
    ( hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7056]),
    [final] ).

cnf(i_0_12451,plain,
    ( c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7054]),
    [final] ).

cnf(i_0_12452,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk255_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7002]),
    [final] ).

cnf(i_0_12453,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk65_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7003]),
    [final] ).

cnf(i_0_12454,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),
    inference(rw,[status(thm)],[i_0_7057,c_0_6732]),
    [final] ).

cnf(i_0_12455,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_4(X1,X2,X3,X4)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7022]),
    [final] ).

cnf(i_0_12456,plain,
    ( ~ c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_7058,c_0_6104]),
    [final] ).

cnf(i_0_12457,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7059]),
    [final] ).

cnf(i_0_12458,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(c_List_Oset(tc_prod(X1,X4)),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7060]),
    [final] ).

cnf(i_0_12459,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OPair(X4,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X4,X1)),hAPP(hAPP(c_List_Ozip(X4,X1),X6),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7060]),
    [final] ).

cnf(i_0_12460,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7061]),
    [final] ).

cnf(i_0_12461,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7062]),
    [final] ).

cnf(i_0_12462,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6))) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7063]),
    [final] ).

cnf(i_0_12463,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_12464,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_12465,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7064]),
    [final] ).

cnf(i_0_12466,plain,
    ( X1 = X2
    | hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7065,c_0_6712]),c_0_6712]),
    [final] ).

cnf(i_0_12467,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7066]),
    [final] ).

cnf(i_0_12468,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7067]),
    [final] ).

cnf(i_0_12469,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7068]),
    [final] ).

cnf(i_0_12470,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7069]),
    [final] ).

cnf(i_0_12471,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_12472,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7071,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12473,plain,
    ( X5 = X6
    | ~ c_Relation_Osingle__valued(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7017]),
    [final] ).

cnf(i_0_12474,plain,
    ( X5 = X6
    | ~ c_Relation_Osingle__valued(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7072]),
    [final] ).

cnf(i_0_12475,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7073]),
    [final] ).

cnf(i_0_12476,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7074]),
    [final] ).

cnf(i_0_12477,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk366_3(X3,X1,X4))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ c_Wellfounded_Owf(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7075]),
    [final] ).

cnf(i_0_12478,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7076,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12479,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7077,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12480,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7078,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12481,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7079,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12482,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk312_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6685]),
    [final] ).

cnf(i_0_12483,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk310_3(X2,X3,X1)),X3))
    | c_Relation_Orefl__on(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6686]),
    [final] ).

cnf(i_0_12484,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7056]),
    [final] ).

cnf(i_0_12485,plain,
    c_Nitpick_Oint__lcm(X1,X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))),
    inference(rw,[status(thm)],[i_0_7080,c_0_7081]),
    [final] ).

cnf(i_0_12486,plain,
    hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))) = hAPP(hAPP(X3,X4),hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),X5))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7082,c_0_6186]),c_0_6186]),
    [final] ).

cnf(i_0_12487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,X6)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6381]),
    [final] ).

cnf(i_0_12488,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Odrop(X1),X6),X4),hAPP(hAPP(c_List_Odrop(X2),X6),X5))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7083]),
    [final] ).

cnf(i_0_12489,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Otake(X1),X6),X4),hAPP(hAPP(c_List_Otake(X2),X6),X5))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7084]),
    [final] ).

cnf(i_0_12490,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(split_conjunct,[status(thm)],[fact_pred__nat__def]),
    [final] ).

cnf(i_0_12491,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7085]),
    [final] ).

cnf(i_0_12492,plain,
    ( X3 = X4
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7086]),
    [final] ).

cnf(i_0_12493,plain,
    ( X3 = X4
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7087]),
    [final] ).

cnf(i_0_12494,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7088]),
    [final] ).

cnf(i_0_12495,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7089]),
    [final] ).

cnf(i_0_12496,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7090]),
    [final] ).

cnf(i_0_12497,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),hAPP(c_Relation_OImage(X1,X2,X4),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7091]),
    [final] ).

cnf(i_0_12498,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12499,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7093]),
    [final] ).

cnf(i_0_12500,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12501,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_12502,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X2),X4),c_Transitive__Closure_Ortrancl(X2,X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))) ),
    inference(rw,[status(thm)],[i_0_7096,c_0_6104]),
    [final] ).

cnf(i_0_12503,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7097]),
    [final] ).

cnf(i_0_12504,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))),c_Int_OMin),
    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_7098,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6224]),c_0_6224]),
    [final] ).

cnf(i_0_12505,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7099]),
    [final] ).

cnf(i_0_12506,plain,
    ( hAPP(X1,esk365_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk364_4(X2,X1,X3,X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12507,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7100]),
    [final] ).

cnf(i_0_12508,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12509,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7059]),
    [final] ).

cnf(i_0_12510,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk546_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))
    | hBOOL(hAPP(X3,esk545_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(X3,X5))
    | ~ c_Equiv__Relations_Oequivp(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6999]),
    [final] ).

cnf(i_0_12511,plain,
    ( c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7101]),
    [final] ).

cnf(i_0_12512,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6901]),
    [final] ).

cnf(i_0_12513,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk453_2(X2,X1))),hAPP(c_List_Oset(X1),esk454_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7102,c_0_6143]),
    [final] ).

cnf(i_0_12514,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk272_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk273_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk273_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7103]),
    [final] ).

cnf(i_0_12515,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk189_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7104]),
    [final] ).

cnf(i_0_12516,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7105]),
    [final] ).

cnf(i_0_12517,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5)
    | ~ c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7106]),
    [final] ).

cnf(i_0_12518,plain,
    ( c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5))
    | ~ c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7106]),
    [final] ).

cnf(i_0_12519,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | esk74_5(X1,X2,X3,X4,X5) != X5
    | X1 != hAPP(X2,X5)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7009]),
    [final] ).

cnf(i_0_12520,plain,
    ( c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7101]),
    [final] ).

cnf(i_0_12521,plain,
    ( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk416_3(X3,X2,X1)),esk417_3(X3,X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olexord(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7107]),
    [final] ).

cnf(i_0_12522,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Set_Ovimage(X2,X1,X3),X4))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7108]),
    [final] ).

cnf(i_0_12523,plain,
    ( X4 = X5
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_List_Oset(X2),X4)),hAPP(c_List_Oset(X2),X5)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5)))
    | hAPP(c_List_Oset(X2),X4) != hAPP(c_List_Oset(X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7109]),
    [final] ).

cnf(i_0_12524,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7110]),
    [final] ).

cnf(i_0_12525,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7111]),
    [final] ).

cnf(i_0_12526,plain,
    ( hBOOL(hAPP(X1,esk68_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,esk67_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12527,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)
    | hAPP(X1,esk500_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk497_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12528,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6)) = hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7112]),
    [final] ).

cnf(i_0_12529,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk454_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_7113,c_0_6143]),
    [final] ).

cnf(i_0_12530,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk452_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk453_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_7114,c_0_6143]),
    [final] ).

cnf(i_0_12531,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7115]),
    [final] ).

cnf(i_0_12532,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)
    | esk498_4(X1,X2,X3,X4) != esk499_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk497_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6790]),
    [final] ).

cnf(i_0_12533,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk490_3(X1,X2,X3)),esk491_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk490_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk491_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7116]),
    [final] ).

cnf(i_0_12534,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),X5) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X5))),hAPP(hAPP(c_List_Ozip(X1,X2),X4),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X5))),
    inference(split_conjunct,[status(thm)],[i_0_7117]),
    [final] ).

cnf(i_0_12535,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7118]),
    [final] ).

cnf(i_0_12536,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))) ),
    inference(rw,[status(thm)],[i_0_7119,c_0_6104]),
    [final] ).

cnf(i_0_12537,plain,
    ( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk247_4(X3,X4,X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7120]),
    [final] ).

cnf(i_0_12538,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7121,c_0_7122]),c_0_7122]),
    [final] ).

cnf(i_0_12539,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7123,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12540,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X4)) = X4
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7124]),
    [final] ).

cnf(i_0_12541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12542,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_12543,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk448_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6928]),
    [final] ).

cnf(i_0_12544,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk199_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7125]),
    [final] ).

cnf(i_0_12545,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk191_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7126]),
    [final] ).

cnf(i_0_12546,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk176_4(X2,X3,X4,X1)),esk175_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6993]),
    [final] ).

cnf(i_0_12547,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),X5)
    | hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2
    | hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) != X5
    | X3 != hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)
    | X4 != hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_12548,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7128]),
    [final] ).

cnf(i_0_12549,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7129]),
    [final] ).

cnf(i_0_12550,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7130]),
    [final] ).

cnf(i_0_12551,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7131,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7132,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12553,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7133,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12554,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7134,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12555,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7135,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12556,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7136]),
    [final] ).

cnf(i_0_12557,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7100]),
    [final] ).

cnf(i_0_12558,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7137]),
    [final] ).

cnf(i_0_12559,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7138]),
    [final] ).

cnf(i_0_12560,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X5))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7139]),
    [final] ).

cnf(i_0_12561,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
    | ~ c_Equiv__Relations_Oequiv(X3,X7,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7026]),
    [final] ).

cnf(i_0_12562,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7140]),
    [final] ).

cnf(i_0_12563,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7141]),
    [final] ).

cnf(i_0_12564,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk369_3(X2,X1,X3)),X3)),X2))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk367_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7075]),
    [final] ).

cnf(i_0_12565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6904]),
    [final] ).

cnf(i_0_12566,plain,
    X1 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk282_1(X1)),esk283_1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7142]),
    [final] ).

cnf(i_0_12567,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk4_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7143]),
    [final] ).

cnf(i_0_12568,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk190_4(X1,X2,X3,X4)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7104]),
    [final] ).

cnf(i_0_12569,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7144]),
    [final] ).

cnf(i_0_12570,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X6)) = X6
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7145]),
    [final] ).

cnf(i_0_12571,plain,
    ( c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | hAPP(c_Fun_Ocomp(X1,X2,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X3) != c_Fun_Oid(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7146]),
    [final] ).

cnf(i_0_12572,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1))),
    inference(rw,[status(thm)],[i_0_7147,c_0_6143]),
    [final] ).

cnf(i_0_12573,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,X3),X1,X5),X6)),X7) = hAPP(hAPP(X5,hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X2),X7))),hAPP(c_Product__Type_Osnd(X1,X2),X7)),
    inference(split_conjunct,[status(thm)],[i_0_7148]),
    [final] ).

cnf(i_0_12574,plain,
    ( c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)) = X3
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7149]),
    [final] ).

cnf(i_0_12575,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7150,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12576,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7151,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12577,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7152]),
    [final] ).

cnf(i_0_12578,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7153]),
    [final] ).

cnf(i_0_12579,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk244_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6213]),
    [final] ).

cnf(i_0_12580,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk56_3(X3,X2,X1)),esk57_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk56_3(X3,X2,X1))),hAPP(X2,esk57_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7154]),
    [final] ).

cnf(i_0_12581,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk54_3(X3,X2,X1)),esk55_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk54_3(X3,X2,X1))),hAPP(X2,esk55_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7155]),
    [final] ).

cnf(i_0_12582,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6952]),
    [final] ).

cnf(i_0_12583,plain,
    ( hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_List_Onth(X1),X4),X6)),hAPP(hAPP(c_List_Onth(X2),X5),X6)))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7156]),
    [final] ).

cnf(i_0_12584,plain,
    ( hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_List_Onth(X1),X4),X6)),hAPP(hAPP(c_List_Onth(X2),X5),X6)))
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7157]),
    [final] ).

cnf(i_0_12585,plain,
    ( hBOOL(hAPP(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X5),X6),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ c_List_Olist__all2(X2,X5,X4,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6306]),
    [final] ).

cnf(i_0_12586,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7158]),
    [final] ).

cnf(i_0_12587,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),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_7159,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12588,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),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_7160,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12589,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),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_7161,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12590,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),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_7162,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12591,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_12592,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_12593,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7144]),
    [final] ).

cnf(i_0_12594,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7165]),
    [final] ).

cnf(i_0_12595,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7166]),
    [final] ).

cnf(i_0_12596,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,X3),X4)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7167]),
    [final] ).

cnf(i_0_12597,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk245_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6963]),
    [final] ).

cnf(i_0_12598,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk88_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6964]),
    [final] ).

cnf(i_0_12599,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7168]),
    [final] ).

cnf(i_0_12600,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7169]),
    [final] ).

cnf(i_0_12601,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7170]),
    [final] ).

cnf(i_0_12602,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7169]),
    [final] ).

cnf(i_0_12603,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_12604,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7172]),
    [final] ).

cnf(i_0_12605,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7173]),
    [final] ).

cnf(i_0_12606,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3)) = hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk62_3(X3,X2,X1)),esk63_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk62_3(X3,X2,X1))),hAPP(X2,esk63_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7174]),
    [final] ).

cnf(i_0_12607,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(c_Set_Oimage(X2,X2,X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_Fun_Ocomp(X2,X1,X2,X5),X4)),X3)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ c_Fun_Oinj__on(X2,X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7175]),
    [final] ).

cnf(i_0_12608,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(c_Set_Oimage(X2,X2,X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(X2,X1,X2,X5),X4)),X3)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ c_Fun_Oinj__on(X2,X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7176]),
    [final] ).

cnf(i_0_12609,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk335_3(X2,X3,X1)),X3)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7177]),
    [final] ).

cnf(i_0_12610,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk334_3(X2,X3,X1)),X3)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7178]),
    [final] ).

cnf(i_0_12611,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk284_3(X2,X3,X1)),X3)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7179]),
    [final] ).

cnf(i_0_12612,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7180]),
    [final] ).

cnf(i_0_12613,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk454_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7181,c_0_6143]),
    [final] ).

cnf(i_0_12614,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk453_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk452_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7182,c_0_6143]),
    [final] ).

cnf(i_0_12615,plain,
    hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4),X5) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,tc_List_Olist(X1)),c_List_Olist__update(X1,X3)),X5)),X4),
    inference(split_conjunct,[status(thm)],[i_0_7183]),
    [final] ).

cnf(i_0_12616,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk398_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X3,X4)),c_List_Olist_Olist__size(X1,X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6610]),
    [final] ).

cnf(i_0_12617,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2))) = X4,
    inference(split_conjunct,[status(thm)],[i_0_7184]),
    [final] ).

cnf(i_0_12618,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk201_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7185]),
    [final] ).

cnf(i_0_12619,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7186]),
    [final] ).

cnf(i_0_12620,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk178_4(X2,X3,X4,X1)),esk177_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7022]),
    [final] ).

cnf(i_0_12621,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
    | c_Partial__Function_Oflat__lub(X1,X3,X2) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7187]),
    [final] ).

cnf(i_0_12622,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk69_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
    | ~ hBOOL(hAPP(X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12623,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk69_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_12624,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X1,X2,X3,X4)),X4))
    | hAPP(hAPP(c_List_Otake(X3),X4),X2) = hAPP(hAPP(c_List_Otake(X3),X4),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7188]),
    [final] ).

cnf(i_0_12625,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7189]),
    [final] ).

cnf(i_0_12626,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[fact_Zero__int__def]),
    [final] ).

cnf(i_0_12627,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[fact_One__int__def]),
    [final] ).

cnf(i_0_12628,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X4,X5),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X3),X2))),hAPP(c_Product__Type_Ofst(X4,X5),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X3),X2))))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7190]),
    [final] ).

cnf(i_0_12629,plain,
    ( c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))
    | ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)
    | ~ c_Fun_Oinj__on(X1,X3,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7191]),
    [final] ).

cnf(i_0_12630,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk247_4(X2,X3,X4,X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7120]),
    [final] ).

cnf(i_0_12631,plain,
    ( hAPP(c_Set_Oimage(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X2,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7192]),
    [final] ).

cnf(i_0_12632,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk365_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk364_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12633,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_7193]),
    [final] ).

cnf(i_0_12634,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk70_4(X4,X3,X5,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12635,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk70_4(X4,X5,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_12636,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X6),hAPP(c_Set_Oimage(X2,X3,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_Fun_Ocomp(X3,X1,X2,X6),X4)),X5)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7194]),
    [final] ).

cnf(i_0_12637,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X6),hAPP(c_Set_Oimage(X2,X3,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(X3,X1,X2,X6),X4)),X5)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7195]),
    [final] ).

cnf(i_0_12638,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7196]),
    [final] ).

cnf(i_0_12639,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7197]),
    [final] ).

cnf(i_0_12640,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk27_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_12641,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk200_4(X1,X2,X3,X4)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7125]),
    [final] ).

cnf(i_0_12642,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk192_4(X1,X2,X3,X4)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7126]),
    [final] ).

cnf(i_0_12643,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),hAPP(c_List_Olexn(X1,X5),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7198]),
    [final] ).

cnf(i_0_12644,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),hAPP(c_List_Olexn(X1,X5),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7198]),
    [final] ).

cnf(i_0_12645,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12646,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12647,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7199]),
    [final] ).

cnf(i_0_12648,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7166]),
    [final] ).

cnf(i_0_12649,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7200]),
    [final] ).

cnf(i_0_12650,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X5)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6636]),
    [final] ).

cnf(i_0_12651,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7201,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12652,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X1,X2,X3,X4)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7138]),
    [final] ).

cnf(i_0_12653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7202]),
    [final] ).

cnf(i_0_12654,plain,
    ( c_List_Otranspose(X1,c_List_Otranspose(X1,X2)) = c_List_OtakeWhile(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1))),X2)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7203]),
    [final] ).

cnf(i_0_12655,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olattice__class_OInf__fin(X1,X3)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Lattices_Olattice(X1)
    | hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk117_3(X3,X2,X1)),esk118_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk117_3(X3,X2,X1))),hAPP(X2,esk118_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7204]),
    [final] ).

cnf(i_0_12656,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olattice__class_OSup__fin(X1,X3)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Lattices_Olattice(X1)
    | hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk84_3(X3,X2,X1)),esk85_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk84_3(X3,X2,X1))),hAPP(X2,esk85_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7205]),
    [final] ).

cnf(i_0_12657,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olinorder__class_OMin(X1,X3)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk60_3(X3,X2,X1)),esk61_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk60_3(X3,X2,X1))),hAPP(X2,esk61_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7206]),
    [final] ).

cnf(i_0_12658,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X2,c_Big__Operators_Olinorder__class_OMax(X1,X3)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk58_3(X3,X2,X1)),esk59_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk58_3(X3,X2,X1))),hAPP(X2,esk59_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7207]),
    [final] ).

cnf(i_0_12659,plain,
    ( hBOOL(hAPP(X3,esk198_2(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,esk195_2(X3,X2)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X3,X2)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_12660,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7209]),
    [final] ).

cnf(i_0_12661,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk452_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))
    | hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)))
    | esk454_2(X1,X2) != esk453_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(rw,[status(thm)],[i_0_7210,c_0_6143]),
    [final] ).

cnf(i_0_12662,plain,
    c_Set_Othe__elem(X1,X2) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7211]),
    [final] ).

cnf(i_0_12663,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_12664,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_12665,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk353_2(X2,X1)),esk353_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_7212,c_0_6104]),
    [final] ).

cnf(i_0_12666,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk340_2(X2,X1)),esk340_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_7213,c_0_6104]),
    [final] ).

cnf(i_0_12667,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7214]),
    [final] ).

cnf(i_0_12668,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7215]),
    [final] ).

cnf(i_0_12669,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7118]),
    [final] ).

cnf(i_0_12670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7216]),
    [final] ).

cnf(i_0_12671,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7217]),
    [final] ).

cnf(i_0_12672,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X4)),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7218]),
    [final] ).

cnf(i_0_12673,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7219]),
    [final] ).

cnf(i_0_12674,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7220]),
    [final] ).

cnf(i_0_12675,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7221]),
    [final] ).

cnf(i_0_12676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7222]),
    [final] ).

cnf(i_0_12677,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X4),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7223]),
    [final] ).

cnf(i_0_12678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12679,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12680,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_12681,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_12682,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X5),X4))),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7224]),
    [final] ).

cnf(i_0_12683,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7225]),
    [final] ).

cnf(i_0_12684,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7226]),
    [final] ).

cnf(i_0_12685,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
    inference(split_conjunct,[status(thm)],[i_0_7227]),
    [final] ).

cnf(i_0_12686,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
    inference(split_conjunct,[status(thm)],[i_0_7228]),
    [final] ).

cnf(i_0_12687,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
    inference(split_conjunct,[status(thm)],[i_0_7229]),
    [final] ).

cnf(i_0_12688,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X5)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7230]),
    [final] ).

cnf(i_0_12689,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk250_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X1,c_Groups_Otimes__class_Otimes(X4)),X2),c_Groups_Oone__class_Oone(X4)),X3) = c_Groups_Oone__class_Oone(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7231]),
    [final] ).

cnf(i_0_12690,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk471_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7232]),
    [final] ).

cnf(i_0_12691,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7233]),
    [final] ).

cnf(i_0_12692,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7234]),
    [final] ).

cnf(i_0_12693,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7235]),
    [final] ).

cnf(i_0_12694,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7236]),
    [final] ).

cnf(i_0_12695,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7237]),
    [final] ).

cnf(i_0_12696,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7238]),
    [final] ).

cnf(i_0_12697,plain,
    ( hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7239]),
    [final] ).

cnf(i_0_12698,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk166_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7240]),
    [final] ).

cnf(i_0_12699,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk167_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X2),X3) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7241]),
    [final] ).

cnf(i_0_12700,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6128]),
    [final] ).

cnf(i_0_12701,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6324]),
    [final] ).

cnf(i_0_12702,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7242]),
    [final] ).

cnf(i_0_12703,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7243]),
    [final] ).

cnf(i_0_12704,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6941]),
    [final] ).

cnf(i_0_12705,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7244]),
    [final] ).

cnf(i_0_12706,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7245]),
    [final] ).

cnf(i_0_12707,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X3)))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(rw,[status(thm)],[i_0_7246,c_0_6186]),
    [final] ).

cnf(i_0_12708,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_6390]),
    [final] ).

cnf(i_0_12709,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
    inference(rw,[status(thm)],[i_0_7247,c_0_6097]),
    [final] ).

cnf(i_0_12710,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12711,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12712,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk15_3(X1,X3,X2)),esk16_3(X1,X3,X2))))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7248]),
    [final] ).

cnf(i_0_12713,plain,
    ( hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3)),X4) = c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3),X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7249]),
    [final] ).

cnf(i_0_12714,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_12715,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_12716,plain,
    ( hBOOL(hAPP(X1,esk546_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X1,esk545_4(X1,X2,X3,X4)))
    | ~ c_Equiv__Relations_Oequivp(X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6999]),
    [final] ).

cnf(i_0_12717,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7250]),
    [final] ).

cnf(i_0_12718,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk181_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | X4 = X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3) != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_12719,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | X4 = X2
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3) != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_12720,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk407_5(X3,X4,X5,X2,X1)) = X4
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = X3
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_12721,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk406_5(X4,X3,X5,X1,X2))
    | X5 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
    | hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_12722,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5) = c_HOL_OThe(X2,c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5)),
    inference(split_conjunct,[status(thm)],[i_0_7253]),
    [final] ).

cnf(i_0_12723,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk262_3(X3,X2,X1)),esk263_3(X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7254]),
    [final] ).

cnf(i_0_12724,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7255]),
    [final] ).

cnf(i_0_12725,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_4(X1,X2,X3,X4)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7185]),
    [final] ).

cnf(i_0_12726,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_4(X1,X2,X3,X4)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7186]),
    [final] ).

cnf(i_0_12727,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk305_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_12728,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7256]),
    [final] ).

cnf(i_0_12729,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk222_4(X2,X3,X1,X4)),X4))
    | c_Fun_Oinj__on(X1,X3,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7257]),
    [final] ).

cnf(i_0_12730,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7050]),
    [final] ).

cnf(i_0_12731,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7258,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12732,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X1,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7167]),
    [final] ).

cnf(i_0_12733,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk195_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X1,X2)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_12734,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk487_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))
    | X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7259]),
    [final] ).

cnf(i_0_12735,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7260,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12736,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk521_2(X2,X1)),esk520_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7244]),
    [final] ).

cnf(i_0_12737,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk507_2(X2,X1)),esk509_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6950]),
    [final] ).

cnf(i_0_12738,plain,
    ( c_Nitpick_Orefl_H(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk264_2(X2,X1)),esk264_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7261]),
    [final] ).

cnf(i_0_12739,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk203_3(X2,X1,X3)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7262]),
    [final] ).

cnf(i_0_12740,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk173_3(X2,X1,X3)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7263]),
    [final] ).

cnf(i_0_12741,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk407_5(X3,X4,X5,X2,X1)) = X4
    | X4 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_12742,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk406_5(X4,X3,X5,X1,X2))
    | X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_12743,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7264]),
    [final] ).

cnf(i_0_12744,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6891]),
    [final] ).

cnf(i_0_12745,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7265,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12746,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7)) = hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7)
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7266]),
    [final] ).

cnf(i_0_12747,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X7,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OPair(X6,X7),X4),X5))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7267]),
    [final] ).

cnf(i_0_12748,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk488_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))
    | hBOOL(hAPP(X2,X3))
    | X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_7268]),
    [final] ).

cnf(i_0_12749,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7269]),
    [final] ).

cnf(i_0_12750,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),X3),
    inference(split_conjunct,[status(thm)],[i_0_7270]),
    [final] ).

cnf(i_0_12751,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7271,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12752,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7272,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12753,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7273]),
    [final] ).

cnf(i_0_12754,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_7274,c_0_6712]),
    [final] ).

cnf(i_0_12755,plain,
    ( hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X6,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7275]),
    [final] ).

cnf(i_0_12756,plain,
    ( hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X6,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7276]),
    [final] ).

cnf(i_0_12757,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk464_5(X4,X3,X1,X5,X2))
    | hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(c_List_Ofilter(X2,X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_12758,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk467_5(X1,X4,X5,X3,X2))
    | hAPP(c_List_Ofilter(X2,X3),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_12759,plain,
    ( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(rw,[status(thm)],[i_0_7277,c_0_7122]),
    [final] ).

cnf(i_0_12760,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X5),hAPP(hAPP(c_List_Oappend(X2),X5),X1))),c_List_Olexord(X2,X6)))
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7278]),
    [final] ).

cnf(i_0_12761,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk379_4(X2,X3,X1,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6984]),
    [final] ).

cnf(i_0_12762,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk378_4(X2,X3,X1,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6983]),
    [final] ).

cnf(i_0_12763,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_7279]),
    [final] ).

cnf(i_0_12764,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk490_3(X1,X2,X3)),esk491_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7116]),
    [final] ).

cnf(i_0_12765,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk404_3(X1,X2,X3)),esk405_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6946]),
    [final] ).

cnf(i_0_12766,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk272_3(X1,X2,X3)),esk273_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7103]),
    [final] ).

cnf(i_0_12767,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk269_3(X1,X2,X3)),esk270_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5324]),
    [final] ).

cnf(i_0_12768,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk267_3(X1,X2,X3)),esk268_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5321]),
    [final] ).

cnf(i_0_12769,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk276_3(X1,X2,X3)),esk277_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7280]),
    [final] ).

cnf(i_0_12770,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7281]),
    [final] ).

cnf(i_0_12771,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7282]),
    [final] ).

cnf(i_0_12772,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7283]),
    [final] ).

cnf(i_0_12773,plain,
    ( hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)))),X2) = c_List_Osublist(X1,X2,X3)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7284]),
    [final] ).

cnf(i_0_12774,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_COMBC(X1,X2,X1),X3)),X4),hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X5))),
    inference(rw,[status(thm)],[i_0_7285,c_0_6186]),
    [final] ).

cnf(i_0_12775,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk346_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,X1)))) ),
    inference(rw,[status(thm)],[i_0_7286,c_0_6104]),
    [final] ).

cnf(i_0_12776,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)))
    | esk454_2(X1,X2) != esk453_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk452_2(X1,X2))) ),
    inference(rw,[status(thm)],[i_0_7287,c_0_6143]),
    [final] ).

cnf(i_0_12777,plain,
    ( hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),esk528_3(X1,X3,X2))) != esk528_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7288]),
    [final] ).

cnf(i_0_12778,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Int_Oint),X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))
    | ~ c_Nat__Transfer_Ois__nat(hAPP(X1,esk166_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7240]),
    [final] ).

cnf(i_0_12779,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Int_Oint),X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))
    | ~ c_Nat__Transfer_Ois__nat(hAPP(X1,esk167_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7241]),
    [final] ).

cnf(i_0_12780,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk494_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__ex1(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_12781,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk486_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__ex1(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_12782,plain,
    ( hAPP(c_Set_Oimage(X1,X1,X3),X2) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X1,X3),X2)),X2))
    | ~ c_Fun_Oinj__on(X1,X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7291]),
    [final] ).

cnf(i_0_12783,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7292]),
    [final] ).

cnf(i_0_12784,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7276]),
    [final] ).

cnf(i_0_12785,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12786,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_12787,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5) = X5
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7293]),
    [final] ).

cnf(i_0_12788,plain,
    ( hAPP(c_List_Oset(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7294]),
    [final] ).

cnf(i_0_12789,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk320_4(X2,X3,X4,X1)),X3))
    | c_Equiv__Relations_Ocongruent(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6239]),
    [final] ).

cnf(i_0_12790,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))
    | c_List_OtakeWhile(X2,X1,X3) = hAPP(hAPP(c_List_Otake(X2),X4),X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12791,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12792,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7295]),
    [final] ).

cnf(i_0_12793,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_7296,c_0_6293]),
    [final] ).

cnf(i_0_12794,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7297,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12795,plain,
    ( hAPP(hAPP(X3,X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,X6),X4),X7),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Big__Operators_Ocomm__monoid__big(X5,X1,X6,X7,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7298]),
    [final] ).

cnf(i_0_12796,plain,
    ( hAPP(hAPP(X5,X7),X6) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X7),X4),X6)
    | ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7299]),
    [final] ).

cnf(i_0_12797,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | c_List_OtakeWhile(X2,X4,X3) = hAPP(hAPP(c_List_Otake(X2),X1),X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12798,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4) = hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7300]),
    [final] ).

cnf(i_0_12799,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk426_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))
    | hBOOL(hAPP(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7001]),
    [final] ).

cnf(i_0_12800,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
    | hAPP(hAPP(c_List_Onth(X1),X2),esk403_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk403_4(X3,X2,X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7188]),
    [final] ).

cnf(i_0_12801,plain,
    ( X4 = X5
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
    | ~ c_Relation_Ototal__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_12802,plain,
    hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6) = hAPP(c_Set_Ovimage(X1,X3,X5),hAPP(c_Set_Ovimage(X3,X2,X4),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7301]),
    [final] ).

cnf(i_0_12803,plain,
    hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6) = hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7302]),
    [final] ).

cnf(i_0_12804,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk345_3(X3,X2,X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7303]),
    [final] ).

cnf(i_0_12805,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(X6,hAPP(c_Product__Type_Ofst(X2,X3),hAPP(X5,X7))),hAPP(c_Product__Type_Osnd(X2,X3),hAPP(X5,X7))),
    inference(split_conjunct,[status(thm)],[i_0_7304]),
    [final] ).

cnf(i_0_12806,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7305]),
    [final] ).

cnf(i_0_12807,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7239]),
    [final] ).

cnf(i_0_12808,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk517_4(X2,X3,X4,X1)),X3))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Wellfounded_Omax__extp(X1,X4,X3,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_12809,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk286_4(X2,X3,X4,X1)),X3))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Wellfounded_Omax__extp(X1,X4,X3,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_12810,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk515_4(X2,X3,X4,X1)),X4))
    | c_Wellfounded_Omax__extp(X1,X2,X4,X3)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6996]),
    [final] ).

cnf(i_0_12811,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7306]),
    [final] ).

cnf(i_0_12812,plain,
    c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_7307]),
    [final] ).

cnf(i_0_12813,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12814,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk461_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))
    | c_List_OtakeWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2)) = hAPP(hAPP(c_List_Oappend(X1),X4),c_List_OtakeWhile(X1,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7308]),
    [final] ).

cnf(i_0_12815,plain,
    ( c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))
    | ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7309]),
    [final] ).

cnf(i_0_12816,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk128_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | hAPP(X2,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_12817,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X3,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7311]),
    [final] ).

cnf(i_0_12818,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X1,X2,X3,X4)),X1))
    | X4 = X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3) != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_12819,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk180_4(X1,X2,X3,X4)),X1))
    | X4 = X2
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3) != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_12820,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7312]),
    [final] ).

cnf(i_0_12821,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12822,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_12823,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_12824,plain,
    ( esk277_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(X1,esk277_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk276_3(X1,X2,X3),esk277_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7280]),
    [final] ).

cnf(i_0_12825,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(X3,X6),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7313]),
    [final] ).

cnf(i_0_12826,plain,
    c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),c_List_OtakeWhile(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7314]),
    [final] ).

cnf(i_0_12827,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk190_4(X2,X3,X4,X1)),esk189_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7104]),
    [final] ).

cnf(i_0_12828,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7315]),
    [final] ).

cnf(i_0_12829,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7316]),
    [final] ).

cnf(i_0_12830,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7317]),
    [final] ).

cnf(i_0_12831,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7045]),
    [final] ).

cnf(i_0_12832,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk130_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | hAPP(X2,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_12833,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3)))
    | ~ c_Relation_Orefl__on(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7319]),
    [final] ).

cnf(i_0_12834,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7315]),
    [final] ).

cnf(i_0_12835,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7317]),
    [final] ).

cnf(i_0_12836,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7202]),
    [final] ).

cnf(i_0_12837,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(split_conjunct,[status(thm)],[i_0_7320]),
    [final] ).

cnf(i_0_12838,plain,
    ( c_Fun_Oinj__on(X1,X5,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X3),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X2,X5,X6,hAPP(c_Set_Oimage(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7321]),
    [final] ).

cnf(i_0_12839,plain,
    ( c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),X6)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))
    | ~ c_Fun_Oinj__on(X4,X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7191]),
    [final] ).

cnf(i_0_12840,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))
    | c_List_OtakeWhile(X2,X1,X3) = hAPP(hAPP(c_List_Otake(X2),X4),X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X1,X3,X2,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12841,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_12842,plain,
    c_Enum_Oproduct(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X5) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Omap(X2,tc_prod(X1,X2)),hAPP(c_Product__Type_OPair(X1,X2),X3)),X5)),c_Enum_Oproduct(X1,X2,X4,X5)),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_12843,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X4))) ),
    inference(rw,[status(thm)],[i_0_7323,c_0_7324]),
    [final] ).

cnf(i_0_12844,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | c_List_OtakeWhile(X2,X4,X3) = hAPP(hAPP(c_List_Otake(X2),X1),X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk447_4(X4,X3,X2,X1)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6994]),
    [final] ).

cnf(i_0_12845,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7325]),
    [final] ).

cnf(i_0_12846,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12847,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12848,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7326]),
    [final] ).

cnf(i_0_12849,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6355]),
    [final] ).

cnf(i_0_12850,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7327]),
    [final] ).

cnf(i_0_12851,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7328]),
    [final] ).

cnf(i_0_12852,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otake(X1)),X4)),X2),
    inference(split_conjunct,[status(thm)],[i_0_7329]),
    [final] ).

cnf(i_0_12853,plain,
    hAPP(c_Relation_OImage(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),hAPP(c_Relation_OImage(X1,X2,X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7330]),
    [final] ).

cnf(i_0_12854,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5) = hAPP(hAPP(c_Product__Type_Oscomp(X3,X2,X3,tc_prod(X2,X3)),hAPP(X4,X5)),c_Random_Oiterate(X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_12855,plain,
    ( hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7305]),
    [final] ).

cnf(i_0_12856,plain,
    ( hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7332]),
    [final] ).

cnf(i_0_12857,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7333]),
    [final] ).

cnf(i_0_12858,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7334]),
    [final] ).

cnf(i_0_12859,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7335]),
    [final] ).

cnf(i_0_12860,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7336]),
    [final] ).

cnf(i_0_12861,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7337]),
    [final] ).

cnf(i_0_12862,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7338]),
    [final] ).

cnf(i_0_12863,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7339]),
    [final] ).

cnf(i_0_12864,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X4)) = hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7340,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_12865,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)),
    inference(split_conjunct,[status(thm)],[i_0_7341]),
    [final] ).

cnf(i_0_12866,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)),
    inference(split_conjunct,[status(thm)],[i_0_7342]),
    [final] ).

cnf(i_0_12867,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7343]),
    [final] ).

cnf(i_0_12868,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_7059]),
    [final] ).

cnf(i_0_12869,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(X2,hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7344]),
    [final] ).

cnf(i_0_12870,plain,
    ( hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7345]),
    [final] ).

cnf(i_0_12871,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin),
    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_7346,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12872,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin),
    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_7347,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12873,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_7348]),
    [final] ).

cnf(i_0_12874,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_7349]),
    [final] ).

cnf(i_0_12875,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7350]),
    [final] ).

cnf(i_0_12876,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7351]),
    [final] ).

cnf(i_0_12877,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk21_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7352]),
    [final] ).

cnf(i_0_12878,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk20_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7352]),
    [final] ).

cnf(i_0_12879,plain,
    ( c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7353]),
    [final] ).

cnf(i_0_12880,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ c_Equiv__Relations_Oequiv(X1,X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7354]),
    [final] ).

cnf(i_0_12881,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),X4) = hAPP(hAPP(c_List_Oappend(X1),X3),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | X2 != hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)
    | X4 != hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_12882,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7333]),
    [final] ).

cnf(i_0_12883,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7334]),
    [final] ).

cnf(i_0_12884,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7355]),
    [final] ).

cnf(i_0_12885,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk121_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Rings_Ocomm__semiring__1(X4)
    | ~ class_Rings_Ono__zero__divisors(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7356]),
    [final] ).

cnf(i_0_12886,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk377_4(X4,X1,X3,X2)),esk376_4(X4,X1,X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(c_Relation_Oconverse(X3,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6541]),
    [final] ).

cnf(i_0_12887,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7357]),
    [final] ).

cnf(i_0_12888,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))
    | c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X2),X3),X5)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7358]),
    [final] ).

cnf(i_0_12889,plain,
    ( hBOOL(hAPP(X1,esk197_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk195_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X1,X2)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_12890,plain,
    ( c_Relation_Ototal__on(X1,X2,X3)
    | ~ c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
    inference(rw,[status(thm)],[i_0_7359,c_0_6097]),
    [final] ).

cnf(i_0_12891,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk200_4(X2,X3,X4,X1)),esk199_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7125]),
    [final] ).

cnf(i_0_12892,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk192_4(X2,X3,X4,X1)),esk191_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7126]),
    [final] ).

cnf(i_0_12893,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_7054]),
    [final] ).

cnf(i_0_12894,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk108_4(X2,X3,X4,X1)),X3))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7360]),
    [final] ).

cnf(i_0_12895,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk98_4(X2,X3,X4,X1)),X3))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7361]),
    [final] ).

cnf(i_0_12896,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk109_4(X2,X3,X1,X4)),X3))
    | c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7362]),
    [final] ).

cnf(i_0_12897,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X1,X4)),X3))
    | c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7363]),
    [final] ).

cnf(i_0_12898,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk248_4(X2,X3,X1,X4))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7364]),
    [final] ).

cnf(i_0_12899,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7365]),
    [final] ).

cnf(i_0_12900,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7366]),
    [final] ).

cnf(i_0_12901,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7367]),
    [final] ).

cnf(i_0_12902,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7368]),
    [final] ).

cnf(i_0_12903,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk451_4(X2,X1,X3,X4)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olinorder__class_Osorted(X1,X2)
    | X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_12904,plain,
    ( hAPP(X1,esk365_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk364_4(X2,X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_12905,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
    | ~ c_Typedef_Otype__definition(X6,X4,X7,X1,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7370]),
    [final] ).

cnf(i_0_12906,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7371]),
    [final] ).

cnf(i_0_12907,plain,
    ( hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),X4)
    | X1 != X2 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7372,c_0_6712]),c_0_6712]),
    [final] ).

cnf(i_0_12908,plain,
    hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OField(X1),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7373]),
    [final] ).

cnf(i_0_12909,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7374]),
    [final] ).

cnf(i_0_12910,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk184_4(X2,X3,X4,X1)),esk183_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7138]),
    [final] ).

cnf(i_0_12911,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7375,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12912,plain,
    c_Nitpick_Opair__box_Opair__box__size(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(X4,X6))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_7376]),
    [final] ).

cnf(i_0_12913,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk229_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk230_3(X2,X3,X1)),esk231_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_12914,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7066]),
    [final] ).

cnf(i_0_12915,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7338]),
    [final] ).

cnf(i_0_12916,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7378]),
    [final] ).

cnf(i_0_12917,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),hAPP(X2,X3))),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7379]),
    [final] ).

cnf(i_0_12918,plain,
    ( c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7380]),
    [final] ).

cnf(i_0_12919,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_7381]),
    [final] ).

cnf(i_0_12920,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7382,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12921,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7383]),
    [final] ).

cnf(i_0_12922,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7384]),
    [final] ).

cnf(i_0_12923,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[conj_4]),
    [final] ).

cnf(i_0_12924,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7385]),
    [final] ).

cnf(i_0_12925,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7386]),
    [final] ).

cnf(i_0_12926,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk248_4(X2,X3,X4,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7364]),
    [final] ).

cnf(i_0_12927,plain,
    ( hAPP(X4,X2) = X5
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7387]),
    [final] ).

cnf(i_0_12928,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7388,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12929,plain,
    ( c_Fun_Oinj__on(X1,X3,X5,X6)
    | ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7389]),
    [final] ).

cnf(i_0_12930,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_12931,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_12932,plain,
    ( X1 = hAPP(X2,esk73_4(X1,X2,X3,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7009]),
    [final] ).

cnf(i_0_12933,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),
    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_7390,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_12934,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7391]),
    [final] ).

cnf(i_0_12935,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X3),
    inference(split_conjunct,[status(thm)],[i_0_7392]),
    [final] ).

cnf(i_0_12936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7393,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12937,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7394,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12938,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7395,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12939,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7396,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12940,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7397,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12941,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7398,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12942,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7399,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12943,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7400,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12944,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5) != X6
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7401]),
    [final] ).

cnf(i_0_12945,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)
    | ~ class_Rings_Oring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7402]),
    [final] ).

cnf(i_0_12946,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk231_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk229_3(X2,X3,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_12947,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk230_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk229_3(X2,X3,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_12948,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    | hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X2,tc_HOL_Obool)),X4),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5),c_Relation_OImage(X2,X1,X3)),X6))
    | ~ c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7403]),
    [final] ).

cnf(i_0_12949,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3)) = hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_7404]),
    [final] ).

cnf(i_0_12950,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
    inference(rw,[status(thm)],[i_0_7405,c_0_6097]),
    [final] ).

cnf(i_0_12951,plain,
    ( hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),hAPP(c_Set_Oimage(X1,X2,X3),X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7406]),
    [final] ).

cnf(i_0_12952,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X1,X5),X2)),hAPP(c_Set_Ovimage(X4,X1,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7407]),
    [final] ).

cnf(i_0_12953,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7408]),
    [final] ).

cnf(i_0_12954,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X5) = hAPP(X5,X6)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X4,tc_HOL_Obool),X3,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7409]),
    [final] ).

cnf(i_0_12955,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7410]),
    [final] ).

cnf(i_0_12956,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7411]),
    [final] ).

cnf(i_0_12957,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(X7,X8,X9,X1),X2),X3) = hAPP(hAPP(c_Fun_Ocomp(X10,X8,X11,X4),X5),X6)
    | hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7412]),
    [final] ).

cnf(i_0_12958,plain,
    ( hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),X4)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7413,c_0_6293]),c_0_6293]),
    [final] ).

cnf(i_0_12959,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk471_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7232]),
    [final] ).

cnf(i_0_12960,plain,
    ( hAPP(c_Fun_Ocomp(X2,X1,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X3) = c_Fun_Oid(X1)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7414]),
    [final] ).

cnf(i_0_12961,plain,
    ( hAPP(c_Fun_Ocomp(X2,X1,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X3) = c_Fun_Oid(X1)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7146]),
    [final] ).

cnf(i_0_12962,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7415]),
    [final] ).

cnf(i_0_12963,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X4,X2) = hAPP(hAPP(X5,X3),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7416]),
    [final] ).

cnf(i_0_12964,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7417]),
    [final] ).

cnf(i_0_12965,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7418]),
    [final] ).

cnf(i_0_12966,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7069]),
    [final] ).

cnf(i_0_12967,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
    | c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_12968,plain,
    ( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
    | ~ c_Wellfounded_Owf(X1,hAPP(X2,esk293_4(X3,X2,X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7419]),
    [final] ).

cnf(i_0_12969,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7420]),
    [final] ).

cnf(i_0_12970,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7421]),
    [final] ).

cnf(i_0_12971,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7422]),
    [final] ).

cnf(i_0_12972,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7423,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_12973,plain,
    ( hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7424]),
    [final] ).

cnf(i_0_12974,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
    inference(rw,[status(thm)],[i_0_7425,c_0_6104]),
    [final] ).

cnf(i_0_12975,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7426]),
    [final] ).

cnf(i_0_12976,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7427]),
    [final] ).

cnf(i_0_12977,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7152]),
    [final] ).

cnf(i_0_12978,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7153]),
    [final] ).

cnf(i_0_12979,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7428]),
    [final] ).

cnf(i_0_12980,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk202_4(X2,X3,X4,X1)),esk201_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7185]),
    [final] ).

cnf(i_0_12981,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk194_4(X2,X3,X4,X1)),esk193_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7186]),
    [final] ).

cnf(i_0_12982,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7429,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_12983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6500]),
    [final] ).

cnf(i_0_12984,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7430]),
    [final] ).

cnf(i_0_12985,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7431]),
    [final] ).

cnf(i_0_12986,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7432]),
    [final] ).

cnf(i_0_12987,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7433]),
    [final] ).

cnf(i_0_12988,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7434]),
    [final] ).

cnf(i_0_12989,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7435]),
    [final] ).

cnf(i_0_12990,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(X5,X3),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7436]),
    [final] ).

cnf(i_0_12991,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7437]),
    [final] ).

cnf(i_0_12992,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7438]),
    [final] ).

cnf(i_0_12993,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7439]),
    [final] ).

cnf(i_0_12994,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7440]),
    [final] ).

cnf(i_0_12995,plain,
    ( hBOOL(hAPP(X1,esk546_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X2,esk545_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X2,X5))
    | ~ c_Equiv__Relations_Oequivp(X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6999]),
    [final] ).

cnf(i_0_12996,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7441]),
    [final] ).

cnf(i_0_12997,plain,
    ( hAPP(X3,hAPP(X4,X6)) = X6
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7442]),
    [final] ).

cnf(i_0_12998,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7443]),
    [final] ).

cnf(i_0_12999,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13000,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_13001,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13002,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_13003,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk252_3(X2,X1,X3)),X3)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7444]),
    [final] ).

cnf(i_0_13004,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7445]),
    [final] ).

cnf(i_0_13005,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7338]),
    [final] ).

cnf(i_0_13006,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7446]),
    [final] ).

cnf(i_0_13007,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7447]),
    [final] ).

cnf(i_0_13008,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4) != X5
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7448]),
    [final] ).

cnf(i_0_13009,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7449]),
    [final] ).

cnf(i_0_13010,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),X3))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7450]),
    [final] ).

cnf(i_0_13011,plain,
    hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7451,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_13012,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7452]),
    [final] ).

cnf(i_0_13013,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7453]),
    [final] ).

cnf(i_0_13014,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7454]),
    [final] ).

cnf(i_0_13015,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7455]),
    [final] ).

cnf(i_0_13016,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7456]),
    [final] ).

cnf(i_0_13017,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7457]),
    [final] ).

cnf(i_0_13018,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7458]),
    [final] ).

cnf(i_0_13019,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7459]),
    [final] ).

cnf(i_0_13020,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7460]),
    [final] ).

cnf(i_0_13021,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7461]),
    [final] ).

cnf(i_0_13022,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7462,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13023,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7463,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13024,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13025,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13026,plain,
    ( hBOOL(hAPP(X3,esk198_2(X3,X2)))
    | hBOOL(hAPP(X3,esk195_2(X3,X2)))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X3,X2)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_13027,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7464]),
    [final] ).

cnf(i_0_13028,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X5
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7465]),
    [final] ).

cnf(i_0_13029,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_7466]),
    [final] ).

cnf(i_0_13030,plain,
    ( hAPP(X4,X5) = hAPP(X4,X6)
    | ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7467]),
    [final] ).

cnf(i_0_13031,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7468]),
    [final] ).

cnf(i_0_13032,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7469,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13033,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_7470,c_0_6104]),
    [final] ).

cnf(i_0_13034,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | hAPP(hAPP(c_List_Oappend(X1),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),X5)
    | hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2
    | hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_13035,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7303]),
    [final] ).

cnf(i_0_13036,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7471]),
    [final] ).

cnf(i_0_13037,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7472]),
    [final] ).

cnf(i_0_13038,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7179]),
    [final] ).

cnf(i_0_13039,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat))))),
    inference(split_conjunct,[status(thm)],[i_0_7473]),
    [final] ).

cnf(i_0_13040,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_13041,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_13042,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7474]),
    [final] ).

cnf(i_0_13043,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7475]),
    [final] ).

cnf(i_0_13044,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7476]),
    [final] ).

cnf(i_0_13045,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7477]),
    [final] ).

cnf(i_0_13046,plain,
    ( hAPP(c_Set_Oimage(X2,X1,X4),X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7478]),
    [final] ).

cnf(i_0_13047,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7479]),
    [final] ).

cnf(i_0_13048,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2))))
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7371]),
    [final] ).

cnf(i_0_13049,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13050,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13051,plain,
    ( hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7482]),
    [final] ).

cnf(i_0_13052,plain,
    ( hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7483]),
    [final] ).

cnf(i_0_13053,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5),X6) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X5),hAPP(c_Product__Type_Ofst(X1,X2),X6))),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),hAPP(c_Product__Type_Osnd(X1,X2),X6))),
    inference(split_conjunct,[status(thm)],[i_0_7484]),
    [final] ).

cnf(i_0_13054,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7216]),
    [final] ).

cnf(i_0_13055,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7217]),
    [final] ).

cnf(i_0_13056,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7485,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13057,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7486,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13058,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7487,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13059,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7488,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13060,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7489,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13061,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X3))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))) ),
    inference(rw,[status(thm)],[i_0_7490,c_0_6732]),
    [final] ).

cnf(i_0_13062,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_7491]),
    [final] ).

cnf(i_0_13063,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_7492]),
    [final] ).

cnf(i_0_13064,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X2),X5),X6)),X7) = hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X3),X5),hAPP(hAPP(c_Relation_Orel__comp(X4,X2,X3),X6),X7)),
    inference(split_conjunct,[status(thm)],[i_0_7493]),
    [final] ).

cnf(i_0_13065,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_13066,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_13067,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7494]),
    [final] ).

cnf(i_0_13068,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7495]),
    [final] ).

cnf(i_0_13069,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7496]),
    [final] ).

cnf(i_0_13070,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),X4) = X5
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7422]),
    [final] ).

cnf(i_0_13071,plain,
    hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7497]),
    [final] ).

cnf(i_0_13072,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13073,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13074,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7498]),
    [final] ).

cnf(i_0_13075,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13076,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13077,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X1,X3,X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7499]),
    [final] ).

cnf(i_0_13078,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X3,X1,X5,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7499]),
    [final] ).

cnf(i_0_13079,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7500]),
    [final] ).

cnf(i_0_13080,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7501]),
    [final] ).

cnf(i_0_13081,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X2)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X3)),hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_7502]),
    [final] ).

cnf(i_0_13082,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7503]),
    [final] ).

cnf(i_0_13083,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_7504,c_0_6097]),
    [final] ).

cnf(i_0_13084,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7505]),
    [final] ).

cnf(i_0_13085,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7506]),
    [final] ).

cnf(i_0_13086,plain,
    ( X3 = esk73_4(X1,X2,X4,X5)
    | X1 != hAPP(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7009]),
    [final] ).

cnf(i_0_13087,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7391]),
    [final] ).

cnf(i_0_13088,plain,
    ( ~ c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(rw,[status(thm)],[i_0_7507,c_0_6189]),
    [final] ).

cnf(i_0_13089,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7508]),
    [final] ).

cnf(i_0_13090,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin),
    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_7509,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_13091,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(hAPP(X3,X4),X2) = X5
    | ~ c_Big__Operators_Ocomm__monoid__big(X6,X1,X7,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7298]),
    [final] ).

cnf(i_0_13092,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))
    | hAPP(hAPP(X5,X7),X6) = X4
    | ~ c_Big__Operators_Ocomm__monoid__big(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7510]),
    [final] ).

cnf(i_0_13093,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7511]),
    [final] ).

cnf(i_0_13094,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),hAPP(X5,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7512]),
    [final] ).

cnf(i_0_13095,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7513]),
    [final] ).

cnf(i_0_13096,plain,
    hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Relation_OImage(X1,X2,X3)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7514]),
    [final] ).

cnf(i_0_13097,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_Ovimage(X1,X2,X3)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7515]),
    [final] ).

cnf(i_0_13098,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_Ovimage(X1,X2,X3)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7516]),
    [final] ).

cnf(i_0_13099,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_Oimage(X1,X2,X3)),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7517]),
    [final] ).

cnf(i_0_13100,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7518]),
    [final] ).

cnf(i_0_13101,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7519]),
    [final] ).

cnf(i_0_13102,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_7520]),
    [final] ).

cnf(i_0_13103,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7521,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13104,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk490_3(X1,X2,X3)),esk491_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7116]),
    [final] ).

cnf(i_0_13105,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk404_3(X1,X2,X3)),esk405_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6946]),
    [final] ).

cnf(i_0_13106,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk276_3(X1,X2,X3)),esk277_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7280]),
    [final] ).

cnf(i_0_13107,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk272_3(X1,X2,X3)),esk273_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7103]),
    [final] ).

cnf(i_0_13108,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk269_3(X1,X2,X3)),esk270_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5324]),
    [final] ).

cnf(i_0_13109,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk267_3(X1,X2,X3)),esk268_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5321]),
    [final] ).

cnf(i_0_13110,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
    | ~ c_List_Olist__all2(X1,X3,X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6306]),
    [final] ).

cnf(i_0_13111,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
    | ~ c_List_Olist__all2(X1,X3,X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6572]),
    [final] ).

cnf(i_0_13112,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)
    | ~ c_List_Olist__all2(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7522]),
    [final] ).

cnf(i_0_13113,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7523]),
    [final] ).

cnf(i_0_13114,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7524]),
    [final] ).

cnf(i_0_13115,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(X1,esk210_3(X2,X1,X3)),esk211_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7525]),
    [final] ).

cnf(i_0_13116,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X2),X3)))
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7526]),
    [final] ).

cnf(i_0_13117,plain,
    ( c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7527]),
    [final] ).

cnf(i_0_13118,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,tc_HOL_Obool),X1,X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
    inference(split_conjunct,[status(thm)],[i_0_7528]),
    [final] ).

cnf(i_0_13119,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7529]),
    [final] ).

cnf(i_0_13120,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7530]),
    [final] ).

cnf(i_0_13121,plain,
    ( hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7531]),
    [final] ).

cnf(i_0_13122,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3))
    | X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7525]),
    [final] ).

cnf(i_0_13123,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(X1,esk212_3(X2,X1,X3)),esk213_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7532]),
    [final] ).

cnf(i_0_13124,plain,
    hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2) = hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X1)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2),
    inference(split_conjunct,[status(thm)],[i_0_7533]),
    [final] ).

cnf(i_0_13125,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_7534]),
    [final] ).

cnf(i_0_13126,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_7535]),
    [final] ).

cnf(i_0_13127,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Fun_Ocomp(X1,X2,X2,X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)) != c_Fun_Oid(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7536]),
    [final] ).

cnf(i_0_13128,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7537]),
    [final] ).

cnf(i_0_13129,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Typedef_Otype__definition(X4,X5,X1,X6,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_7538]),
    [final] ).

cnf(i_0_13130,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7539]),
    [final] ).

cnf(i_0_13131,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7540]),
    [final] ).

cnf(i_0_13132,plain,
    ( hAPP(X4,hAPP(X3,X6)) = X6
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7541]),
    [final] ).

cnf(i_0_13133,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7542]),
    [final] ).

cnf(i_0_13134,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7532]),
    [final] ).

cnf(i_0_13135,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7543,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13136,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7544]),
    [final] ).

cnf(i_0_13137,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7545]),
    [final] ).

cnf(i_0_13138,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_7546,c_0_6104]),
    [final] ).

cnf(i_0_13139,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk182_4(X2,X3,X4,X1)),esk181_4(X2,X3,X4,X1))
    | X1 = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_13140,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk180_4(X2,X3,X4,X1)),esk179_4(X2,X3,X4,X1))
    | X1 = X3
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_13141,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_13142,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_13143,plain,
    ( c_List_OtakeWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = hAPP(hAPP(c_List_Oappend(X4),X3),c_List_OtakeWhile(X4,X1,X2))
    | ~ hBOOL(hAPP(X1,esk461_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7308]),
    [final] ).

cnf(i_0_13144,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7547]),
    [final] ).

cnf(i_0_13145,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | hBOOL(hAPP(X1,esk195_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X1,X2)),X2))))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_13146,plain,
    ( hAPP(X3,X4) = X5
    | c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7548]),
    [final] ).

cnf(i_0_13147,plain,
    ( X4 = c_List_Olist_ONil(X2)
    | ~ c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7549]),
    [final] ).

cnf(i_0_13148,plain,
    ( X4 = c_List_Olist_ONil(X1)
    | ~ c_List_Olist__all2(X1,X2,X3,X4,c_List_Olist_ONil(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_13149,plain,
    ( X2 = X3
    | ~ c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7551]),
    [final] ).

cnf(i_0_13150,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6841]),
    [final] ).

cnf(i_0_13151,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7552]),
    [final] ).

cnf(i_0_13152,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6649]),
    [final] ).

cnf(i_0_13153,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7553]),
    [final] ).

cnf(i_0_13154,plain,
    ( c_Fun_Obij__betw(X1,X3,esk537_4(X4,X3,X2,X1),X2,X4)
    | hAPP(c_Finite__Set_Ocard(X1),X2) != hAPP(c_Finite__Set_Ocard(X3),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7464]),
    [final] ).

cnf(i_0_13155,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X2),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7554]),
    [final] ).

cnf(i_0_13156,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7555]),
    [final] ).

cnf(i_0_13157,plain,
    ( X2 = X3
    | ~ c_List_Olist__all2(X1,X1,c_fequal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7556]),
    [final] ).

cnf(i_0_13158,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_13159,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13160,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_13161,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13162,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7401]),
    [final] ).

cnf(i_0_13163,plain,
    ( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7402]),
    [final] ).

cnf(i_0_13164,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7557]),
    [final] ).

cnf(i_0_13165,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7558]),
    [final] ).

cnf(i_0_13166,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7559,c_0_6143]),c_0_6143]),
    [final] ).

cnf(i_0_13167,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X4),X2)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7560]),
    [final] ).

cnf(i_0_13168,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X4),X2)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7561]),
    [final] ).

cnf(i_0_13169,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7562]),
    [final] ).

cnf(i_0_13170,plain,
    ( hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7563]),
    [final] ).

cnf(i_0_13171,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7564,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13172,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_ONil(X2)),X1)),c_List_Olexord(X2,X5)))
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7107]),
    [final] ).

cnf(i_0_13173,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7565]),
    [final] ).

cnf(i_0_13174,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk396_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X2))))
    | X3 = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7279]),
    [final] ).

cnf(i_0_13175,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7566]),
    [final] ).

cnf(i_0_13176,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7567]),
    [final] ).

cnf(i_0_13177,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13178,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7569]),
    [final] ).

cnf(i_0_13179,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId__on(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_7570]),
    [final] ).

cnf(i_0_13180,plain,
    ( c_List_Olinorder__class_Osorted(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk451_4(X3,X1,X4,X2)))
    | X3 != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)
    | ~ c_List_Olinorder__class_Osorted(X1,X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_13181,plain,
    ( c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1))),c_List_Olist_ONil(X1)),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7571]),
    [final] ).

cnf(i_0_13182,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13183,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13184,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13185,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13186,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7420]),
    [final] ).

cnf(i_0_13187,plain,
    ( c_Equiv__Relations_Ocongruent(X4,X2,X3,X1)
    | hAPP(X1,esk565_4(X2,X1,X3,X4)) != hAPP(X1,esk566_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6558]),
    [final] ).

cnf(i_0_13188,plain,
    hAPP(c_Relation_ORange(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7572]),
    [final] ).

cnf(i_0_13189,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7573]),
    [final] ).

cnf(i_0_13190,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
    | ~ c_Relation_Orefl__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6686]),
    [final] ).

cnf(i_0_13191,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7574]),
    [final] ).

cnf(i_0_13192,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5)) = hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7575]),
    [final] ).

cnf(i_0_13193,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5)) = hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7576]),
    [final] ).

cnf(i_0_13194,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7305]),
    [final] ).

cnf(i_0_13195,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X5))
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7305]),
    [final] ).

cnf(i_0_13196,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7577]),
    [final] ).

cnf(i_0_13197,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7578]),
    [final] ).

cnf(i_0_13198,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7579,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_13199,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_7580]),
    [final] ).

cnf(i_0_13200,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7581]),
    [final] ).

cnf(i_0_13201,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7582]),
    [final] ).

cnf(i_0_13202,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7583]),
    [final] ).

cnf(i_0_13203,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7583]),
    [final] ).

cnf(i_0_13204,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7584]),
    [final] ).

cnf(i_0_13205,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7585]),
    [final] ).

cnf(i_0_13206,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5330]),
    [final] ).

cnf(i_0_13207,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7334]),
    [final] ).

cnf(i_0_13208,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7586]),
    [final] ).

cnf(i_0_13209,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk228_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7587]),
    [final] ).

cnf(i_0_13210,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk227_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7587]),
    [final] ).

cnf(i_0_13211,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Osemigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7588]),
    [final] ).

cnf(i_0_13212,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7589]),
    [final] ).

cnf(i_0_13213,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7590,c_0_6097]),c_0_6104]),
    [final] ).

cnf(i_0_13214,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist__update(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7591]),
    [final] ).

cnf(i_0_13215,plain,
    ( X4 = X5
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7592]),
    [final] ).

cnf(i_0_13216,plain,
    ( hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X3)),hAPP(c_Code__Numeral_Oof__nat,X1)) = hAPP(hAPP(c_List_Onth(X2),X3),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7593]),
    [final] ).

cnf(i_0_13217,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3) = X5
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7448]),
    [final] ).

cnf(i_0_13218,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7449]),
    [final] ).

cnf(i_0_13219,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13220,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13221,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13222,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13223,plain,
    ( X1 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7596]),
    [final] ).

cnf(i_0_13224,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7597]),
    [final] ).

cnf(i_0_13225,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13226,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7597]),
    [final] ).

cnf(i_0_13227,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13228,plain,
    c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6))) = hAPP(hAPP(X4,X5),X6),
    inference(rw,[status(thm)],[i_0_7599,c_0_7600]),
    [final] ).

cnf(i_0_13229,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk70_4(X4,X3,X5,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_13230,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk70_4(X4,X5,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6852]),
    [final] ).

cnf(i_0_13231,plain,
    c_List_Oset__Cons(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2),
    inference(split_conjunct,[status(thm)],[i_0_7601]),
    [final] ).

cnf(i_0_13232,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk28_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_13233,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X4),X5)),X6)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7602]),
    [final] ).

cnf(i_0_13234,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X4),X5)),X6)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7603]),
    [final] ).

cnf(i_0_13235,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
    | X1 != hAPP(c_Set_Oimage(tc_Nat_Onat,X2,X3),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7604]),
    [final] ).

cnf(i_0_13236,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
    | X1 != hAPP(c_Set_Oimage(tc_Nat_Onat,X2,X3),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7605]),
    [final] ).

cnf(i_0_13237,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_7422]),
    [final] ).

cnf(i_0_13238,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X1),X3))),c_List_Olist_ONil(X2))) = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7606]),
    [final] ).

cnf(i_0_13239,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4),
    inference(split_conjunct,[status(thm)],[i_0_7607]),
    [final] ).

cnf(i_0_13240,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X3)))),
    inference(split_conjunct,[status(thm)],[i_0_7608]),
    [final] ).

cnf(i_0_13241,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_13242,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_13243,plain,
    ( hBOOL(hAPP(X1,esk28_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_13244,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7609,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13245,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk223_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7610]),
    [final] ).

cnf(i_0_13246,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7611]),
    [final] ).

cnf(i_0_13247,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7612]),
    [final] ).

cnf(i_0_13248,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_13249,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_13250,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13251,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13252,plain,
    ( ~ c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3))
    | ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7613]),
    [final] ).

cnf(i_0_13253,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X2)),X1),
    inference(split_conjunct,[status(thm)],[i_0_7614]),
    [final] ).

cnf(i_0_13254,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(rw,[status(thm)],[i_0_7615,c_0_7324]),
    [final] ).

cnf(i_0_13255,plain,
    ( c_Wellfounded_OwfP(X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X1))
    | hAPP(X1,esk322_3(X2,X1,X3)) != hAPP(X1,esk323_3(X2,X1,X3))
    | ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk321_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6943]),
    [final] ).

cnf(i_0_13256,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7616]),
    [final] ).

cnf(i_0_13257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7617]),
    [final] ).

cnf(i_0_13258,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7618]),
    [final] ).

cnf(i_0_13259,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7619]),
    [final] ).

cnf(i_0_13260,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7620]),
    [final] ).

cnf(i_0_13261,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk230_3(X2,X3,X1)),esk231_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(X1),esk229_3(X2,X3,X1)) != X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_13262,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1))),hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7621,c_0_6732]),c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_13263,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13264,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7622]),
    [final] ).

cnf(i_0_13265,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13266,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7622]),
    [final] ).

cnf(i_0_13267,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X2)),X1),
    inference(split_conjunct,[status(thm)],[i_0_7623]),
    [final] ).

cnf(i_0_13268,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7624]),
    [final] ).

cnf(i_0_13269,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),X7)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X7)),
    inference(split_conjunct,[status(thm)],[i_0_7625]),
    [final] ).

cnf(i_0_13270,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7626]),
    [final] ).

cnf(i_0_13271,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7627]),
    [final] ).

cnf(i_0_13272,plain,
    ( hAPP(c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3)),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7628]),
    [final] ).

cnf(i_0_13273,plain,
    c_Nitpick_Opair__box_Opair__box__rec(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_7629]),
    [final] ).

cnf(i_0_13274,plain,
    c_Nitpick_Opair__box_Opair__box__case(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_7630]),
    [final] ).

cnf(i_0_13275,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7631]),
    [final] ).

cnf(i_0_13276,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),c_List_OtakeWhile(X1,X3,X4)),X5) = c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7632]),
    [final] ).

cnf(i_0_13277,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7633,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13278,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7634,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13279,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk363_2(X2,X1)),esk363_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
    inference(rw,[status(thm)],[i_0_7635,c_0_6097]),
    [final] ).

cnf(i_0_13280,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin),
    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_7636,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_13281,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7637]),
    [final] ).

cnf(i_0_13282,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7582]),
    [final] ).

cnf(i_0_13283,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))))
    | X1 != X2 ),
    inference(rw,[status(thm)],[i_0_7638,c_0_6097]),
    [final] ).

cnf(i_0_13284,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
    inference(rw,[status(thm)],[i_0_7639,c_0_6097]),
    [final] ).

cnf(i_0_13285,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_7640]),
    [final] ).

cnf(i_0_13286,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7641]),
    [final] ).

cnf(i_0_13287,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7642]),
    [final] ).

cnf(i_0_13288,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7643]),
    [final] ).

cnf(i_0_13289,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7644]),
    [final] ).

cnf(i_0_13290,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_13291,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7646]),
    [final] ).

cnf(i_0_13292,plain,
    ( hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X4) = hAPP(hAPP(c_List_Oappend(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4)),hAPP(hAPP(c_List_Otake(X3),X2),hAPP(hAPP(c_List_Odrop(X3),X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7647]),
    [final] ).

cnf(i_0_13293,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk132_3(X2,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7648]),
    [final] ).

cnf(i_0_13294,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
    inference(rw,[status(thm)],[i_0_7649,c_0_6143]),
    [final] ).

cnf(i_0_13295,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X2)))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7526]),
    [final] ).

cnf(i_0_13296,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),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)],[i_0_7650,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_13297,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X1),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13298,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,X6)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6386]),
    [final] ).

cnf(i_0_13299,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X6)),hAPP(X4,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7652]),
    [final] ).

cnf(i_0_13300,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),c_List_Olast(X2,X1))),X1) = c_List_Obutlast(X2,X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7653]),
    [final] ).

cnf(i_0_13301,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7654]),
    [final] ).

cnf(i_0_13302,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7655]),
    [final] ).

cnf(i_0_13303,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk231_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hAPP(c_Finite__Set_Ocard(X1),esk229_3(X2,X3,X1)) != X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_13304,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk230_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
    | hAPP(c_Finite__Set_Ocard(X1),esk229_3(X2,X3,X1)) != X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_13305,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7656]),
    [final] ).

cnf(i_0_13306,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13307,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13308,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7657]),
    [final] ).

cnf(i_0_13309,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk520_2(X2,X1)),esk521_2(X2,X1))),X2))
    | c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7244]),
    [final] ).

cnf(i_0_13310,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk519_2(X2,X1)),esk518_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7087]),
    [final] ).

cnf(i_0_13311,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk518_2(X2,X1)),esk519_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7087]),
    [final] ).

cnf(i_0_13312,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk508_2(X2,X1)),esk509_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6950]),
    [final] ).

cnf(i_0_13313,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk507_2(X2,X1)),esk508_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6950]),
    [final] ).

cnf(i_0_13314,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk271_2(X2,X1)),esk271_2(X2,X1))),X2))
    | c_Relation_Oirrefl(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7658]),
    [final] ).

cnf(i_0_13315,plain,
    ( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7659]),
    [final] ).

cnf(i_0_13316,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk156_3(X1,X2,X3))),X2))
    | hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_13317,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13318,plain,
    ( hAPP(X4,hAPP(X5,X9)) = hAPP(X7,hAPP(X8,X9))
    | hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X6,X2,X3,X7),X8) ),
    inference(split_conjunct,[status(thm)],[i_0_7662]),
    [final] ).

cnf(i_0_13319,plain,
    ( hAPP(X4,hAPP(X5,X9)) = hAPP(X7,hAPP(X8,X9))
    | hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X6,X2,X3,X7),X8) ),
    inference(split_conjunct,[status(thm)],[i_0_7663]),
    [final] ).

cnf(i_0_13320,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X4)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7664]),
    [final] ).

cnf(i_0_13321,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13322,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13323,plain,
    ( hAPP(X4,hAPP(X5,X7)) = hAPP(X6,X7)
    | hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X2,X2,X3,c_Fun_Oid(X2)),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7665]),
    [final] ).

cnf(i_0_13324,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X4))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4)))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7666]),
    [final] ).

cnf(i_0_13325,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7069]),
    [final] ).

cnf(i_0_13326,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_13327,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7667]),
    [final] ).

cnf(i_0_13328,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))
    | ~ c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7668]),
    [final] ).

cnf(i_0_13329,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))
    | hAPP(hAPP(c_List_Oappend(X2),X3),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_13330,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2)) = hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk229_3(X1,X2,X3)),X2))
    | esk230_3(X1,X2,X3) != esk231_3(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_13331,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7669]),
    [final] ).

cnf(i_0_13332,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7670]),
    [final] ).

cnf(i_0_13333,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7671]),
    [final] ).

cnf(i_0_13334,plain,
    ( ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7672]),
    [final] ).

cnf(i_0_13335,plain,
    ( ~ c_Relation_Oirrefl(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7658]),
    [final] ).

cnf(i_0_13336,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7673]),
    [final] ).

cnf(i_0_13337,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7674]),
    [final] ).

cnf(i_0_13338,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13339,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13340,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13341,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13342,plain,
    c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),
    inference(rw,[status(thm)],[i_0_7675,c_0_6097]),
    [final] ).

cnf(i_0_13343,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),hAPP(hAPP(c_COMBB(X1,X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1),X2)),X4)),X5)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7676]),
    [final] ).

cnf(i_0_13344,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7677]),
    [final] ).

cnf(i_0_13345,plain,
    hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBB(X3,X2,X1),X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7678]),
    [final] ).

cnf(i_0_13346,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7430]),
    [final] ).

cnf(i_0_13347,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7431]),
    [final] ).

cnf(i_0_13348,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7432]),
    [final] ).

cnf(i_0_13349,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk156_3(X1,X2,X3))),X2))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_13350,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk444_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk445_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7679]),
    [final] ).

cnf(i_0_13351,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk440_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk439_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13352,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6505]),
    [final] ).

cnf(i_0_13353,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7681]),
    [final] ).

cnf(i_0_13354,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7682]),
    [final] ).

cnf(i_0_13355,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7683]),
    [final] ).

cnf(i_0_13356,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2),X6) = hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X2),X6)),X1),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7684]),
    [final] ).

cnf(i_0_13357,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_7685]),
    [final] ).

cnf(i_0_13358,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X2,X1,X3))),esk572_3(X2,X1,X3))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13359,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7687]),
    [final] ).

cnf(i_0_13360,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7688,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13361,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7689,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13362,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7690,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13363,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7691,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13364,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,esk488_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7268]),
    [final] ).

cnf(i_0_13365,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7692]),
    [final] ).

cnf(i_0_13366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7693]),
    [final] ).

cnf(i_0_13367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7694]),
    [final] ).

cnf(i_0_13368,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X4,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7695]),
    [final] ).

cnf(i_0_13369,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk575_3(X2,X1,X3))),esk576_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13370,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7697]),
    [final] ).

cnf(i_0_13371,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Set_Oinsert(X1),X2)),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7698]),
    [final] ).

cnf(i_0_13372,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk233_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_3(X1,X2,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_13373,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk225_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk224_3(X1,X2,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_13374,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_7699]),
    [final] ).

cnf(i_0_13375,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_OtakeWhile(X2,X4,X5)) = c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X4),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7700]),
    [final] ).

cnf(i_0_13376,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_7701,c_0_6071]),
    [final] ).

cnf(i_0_13377,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Ohb__bind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7702]),
    [final] ).

cnf(i_0_13378,plain,
    ( c_Fun_Oinj__on(X1,tc_fun(X4,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,X2),X1),c_COMBK(X2,X4)),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7703]),
    [final] ).

cnf(i_0_13379,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7704]),
    [final] ).

cnf(i_0_13380,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7705]),
    [final] ).

cnf(i_0_13381,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7706]),
    [final] ).

cnf(i_0_13382,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7707]),
    [final] ).

cnf(i_0_13383,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1) = hAPP(c_Lazy__Sequence_Obind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3)),X5),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7708]),
    [final] ).

cnf(i_0_13384,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X5))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13385,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13386,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(X2,X4)),hAPP(hAPP(c_List_Ozip(X2,X4),X3),X5)),X1) = hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X4),X5),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7709]),
    [final] ).

cnf(i_0_13387,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_7710]),
    [final] ).

cnf(i_0_13388,plain,
    ( hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)
    | hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_7711,c_0_6293]),
    [final] ).

cnf(i_0_13389,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7712]),
    [final] ).

cnf(i_0_13390,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13391,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13392,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X2))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(rw,[status(thm)],[i_0_7713,c_0_6186]),
    [final] ).

cnf(i_0_13393,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7452]),
    [final] ).

cnf(i_0_13394,plain,
    hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X5) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7714]),
    [final] ).

cnf(i_0_13395,plain,
    ( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)))),X1) = hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
    inference(rw,[status(thm)],[i_0_7715,c_0_6189]),
    [final] ).

cnf(i_0_13396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,esk156_3(X2,X1,X3)))))
    | hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_13397,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_7716]),
    [final] ).

cnf(i_0_13398,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))) = c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7717]),
    [final] ).

cnf(i_0_13399,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk575_3(X2,X1,X3))),esk576_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13400,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X2,X1,X3))),esk572_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13401,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7718]),
    [final] ).

cnf(i_0_13402,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X4)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)),X4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7719,c_0_6732]),c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_13403,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk210_3(X1,X3,X2))),esk211_3(X1,X3,X2))
    | hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7525]),
    [final] ).

cnf(i_0_13404,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13405,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7306]),
    [final] ).

cnf(i_0_13406,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7306]),
    [final] ).

cnf(i_0_13407,plain,
    ( hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),X3),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(rw,[status(thm)],[i_0_7720,c_0_6186]),
    [final] ).

cnf(i_0_13408,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk569_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7721]),
    [final] ).

cnf(i_0_13409,plain,
    ( hBOOL(hAPP(X1,esk197_2(X1,X2)))
    | hBOOL(hAPP(X1,esk195_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk195_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk196_2(X1,X2)),X2))))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7208]),
    [final] ).

cnf(i_0_13410,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_7722]),
    [final] ).

cnf(i_0_13411,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X8),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X7),X5)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5)
    | X6 != hAPP(c_Set_Oimage(X2,X3,X4),X5)
    | X7 != hAPP(c_Fun_Ocomp(X3,X1,X2,X8),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7723]),
    [final] ).

cnf(i_0_13412,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk212_3(X1,X3,X2))),esk213_3(X1,X3,X2))
    | hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7532]),
    [final] ).

cnf(i_0_13413,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7724]),
    [final] ).

cnf(i_0_13414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_7725]),
    [final] ).

cnf(i_0_13415,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X3,X5))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7726]),
    [final] ).

cnf(i_0_13416,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7727]),
    [final] ).

cnf(i_0_13417,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7728]),
    [final] ).

cnf(i_0_13418,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7729]),
    [final] ).

cnf(i_0_13419,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X1,X2,X3,esk222_4(X3,X2,X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7257]),
    [final] ).

cnf(i_0_13420,plain,
    c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),c_Lazy__Sequence_Olazy__sequence_OEmpty(X2))) = X3,
    inference(rw,[status(thm)],[i_0_7730,c_0_7600]),
    [final] ).

cnf(i_0_13421,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7731]),
    [final] ).

cnf(i_0_13422,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7731]),
    [final] ).

cnf(i_0_13423,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,esk156_3(X2,X1,X3)))))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_13424,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X3)),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13425,plain,
    ( hAPP(X2,X3) = hAPP(X2,X4)
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),X6))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7733]),
    [final] ).

cnf(i_0_13426,plain,
    ( hBOOL(hAPP(X1,esk293_4(X2,X3,X4,X1)))
    | c_Wellfounded_Owf(tc_prod(X2,X4),c_Recdef_Osame__fst(X2,X4,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7419]),
    [final] ).

cnf(i_0_13427,plain,
    ( hBOOL(hAPP(X4,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_13428,plain,
    ( hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = X4
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7288]),
    [final] ).

cnf(i_0_13429,plain,
    ( hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = X4
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7734]),
    [final] ).

cnf(i_0_13430,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,X5)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6964]),
    [final] ).

cnf(i_0_13431,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7735]),
    [final] ).

cnf(i_0_13432,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
    inference(split_conjunct,[status(thm)],[i_0_7736]),
    [final] ).

cnf(i_0_13433,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
    inference(split_conjunct,[status(thm)],[i_0_7737]),
    [final] ).

cnf(i_0_13434,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7738]),
    [final] ).

cnf(i_0_13435,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7739]),
    [final] ).

cnf(i_0_13436,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_7740]),
    [final] ).

cnf(i_0_13437,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),c_List_Orotate1(X1)),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7741,c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_13438,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7511]),
    [final] ).

cnf(i_0_13439,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7742]),
    [final] ).

cnf(i_0_13440,plain,
    ( c_Fun_Oinj__on(X1,X1,X3,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X1,X1,X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13441,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7744]),
    [final] ).

cnf(i_0_13442,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7745]),
    [final] ).

cnf(i_0_13443,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7746]),
    [final] ).

cnf(i_0_13444,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X5),X4)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7443]),
    [final] ).

cnf(i_0_13445,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_13446,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7095]),
    [final] ).

cnf(i_0_13447,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7747]),
    [final] ).

cnf(i_0_13448,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7747]),
    [final] ).

cnf(i_0_13449,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7748]),
    [final] ).

cnf(i_0_13450,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7748]),
    [final] ).

cnf(i_0_13451,plain,
    ( c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Ototal__on(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_7749,c_0_6097]),
    [final] ).

cnf(i_0_13452,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oaccp(X1,X3)),c_Wellfounded_Oaccp(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7750]),
    [final] ).

cnf(i_0_13453,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_13454,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6)) = hAPP(X4,X5)
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7751]),
    [final] ).

cnf(i_0_13455,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7752]),
    [final] ).

cnf(i_0_13456,plain,
    ( X2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7753]),
    [final] ).

cnf(i_0_13457,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
    | ~ class_Groups_Oab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7754]),
    [final] ).

cnf(i_0_13458,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7755,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13459,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7756]),
    [final] ).

cnf(i_0_13460,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7757,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13461,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7758,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13462,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7759,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13463,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7760,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13464,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than)) ),
    inference(split_conjunct,[status(thm)],[i_0_7761]),
    [final] ).

cnf(i_0_13465,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
    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_7762,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6224]),c_0_6224]),c_0_6224]),
    [final] ).

cnf(i_0_13466,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)) = hAPP(c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7763]),
    [final] ).

cnf(i_0_13467,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)),hAPP(X5,X2))
    | hAPP(X5,X2) = c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Fields_Ofield(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7764]),
    [final] ).

cnf(i_0_13468,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_7765,c_0_6104]),
    [final] ).

cnf(i_0_13469,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk188_3(X1,X2,X3)),X1))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_13470,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_3(X1,X2,X3)),X1))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7646]),
    [final] ).

cnf(i_0_13471,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7712]),
    [final] ).

cnf(i_0_13472,plain,
    ( X4 = X5
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7766]),
    [final] ).

cnf(i_0_13473,plain,
    ( X4 = X5
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7767]),
    [final] ).

cnf(i_0_13474,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_13475,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk15_3(X2,X3,X1)),esk16_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7248]),
    [final] ).

cnf(i_0_13476,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7769]),
    [final] ).

cnf(i_0_13477,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,X1,esk538_2(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7770]),
    [final] ).

cnf(i_0_13478,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
    inference(rw,[status(thm)],[i_0_7771,c_0_6097]),
    [final] ).

cnf(i_0_13479,plain,
    ( hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))
    | ~ c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7772]),
    [final] ).

cnf(i_0_13480,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7773]),
    [final] ).

cnf(i_0_13481,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7774]),
    [final] ).

cnf(i_0_13482,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7775]),
    [final] ).

cnf(i_0_13483,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7776]),
    [final] ).

cnf(i_0_13484,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7777]),
    [final] ).

cnf(i_0_13485,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7778]),
    [final] ).

cnf(i_0_13486,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7779]),
    [final] ).

cnf(i_0_13487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7780]),
    [final] ).

cnf(i_0_13488,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7781]),
    [final] ).

cnf(i_0_13489,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)) = X3,
    inference(rw,[status(thm)],[i_0_7782,c_0_6293]),
    [final] ).

cnf(i_0_13490,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)),hAPP(X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Oab__group__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7783]),
    [final] ).

cnf(i_0_13491,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(X5,X4))
    | ~ class_Rings_Oring(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7784]),
    [final] ).

cnf(i_0_13492,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7785]),
    [final] ).

cnf(i_0_13493,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Oabs__class_Oabs(X1)),X2))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7786]),
    [final] ).

cnf(i_0_13494,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)),
    inference(rw,[status(thm)],[i_0_7787,c_0_6143]),
    [final] ).

cnf(i_0_13495,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,c_Groups_Otimes__class_Otimes(X4)),X1),c_Groups_Oone__class_Oone(X4)),X2) = c_Groups_Oone__class_Oone(X4)
    | hAPP(X1,esk250_4(X1,X2,X3,X4)) != c_Groups_Oone__class_Oone(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))
    | ~ class_Groups_Ocomm__monoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7231]),
    [final] ).

cnf(i_0_13496,plain,
    ( hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_13497,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,X1,esk540_2(X2,X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7788]),
    [final] ).

cnf(i_0_13498,plain,
    ( c_Fun_Obij__betw(X1,tc_Nat_Onat,esk541_2(X2,X1),X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7789]),
    [final] ).

cnf(i_0_13499,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_7790]),
    [final] ).

cnf(i_0_13500,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7791]),
    [final] ).

cnf(i_0_13501,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))
    | ~ class_Groups_Oab__group__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7792]),
    [final] ).

cnf(i_0_13502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Rings_Olinordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7793]),
    [final] ).

cnf(i_0_13503,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7794]),
    [final] ).

cnf(i_0_13504,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7795]),
    [final] ).

cnf(i_0_13505,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7796]),
    [final] ).

cnf(i_0_13506,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7797]),
    [final] ).

cnf(i_0_13507,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7798]),
    [final] ).

cnf(i_0_13508,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7799]),
    [final] ).

cnf(i_0_13509,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7800]),
    [final] ).

cnf(i_0_13510,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7801]),
    [final] ).

cnf(i_0_13511,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)),
    inference(rw,[status(thm)],[i_0_7802,c_0_6143]),
    [final] ).

cnf(i_0_13512,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7803]),
    [final] ).

cnf(i_0_13513,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_13514,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk42_3(X2,X3,X1)),X2))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7804]),
    [final] ).

cnf(i_0_13515,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk40_3(X2,X3,X1)),X2))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7805]),
    [final] ).

cnf(i_0_13516,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk42_3(X2,X3,X1)),X3))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7804]),
    [final] ).

cnf(i_0_13517,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk40_3(X2,X3,X1)),X3))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7805]),
    [final] ).

cnf(i_0_13518,plain,
    ( hBOOL(hAPP(hAPP(X4,X6),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6509]),
    [final] ).

cnf(i_0_13519,plain,
    ( hBOOL(hAPP(hAPP(X4,X6),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7806]),
    [final] ).

cnf(i_0_13520,plain,
    ( hBOOL(hAPP(hAPP(X4,X6),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7807]),
    [final] ).

cnf(i_0_13521,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7808]),
    [final] ).

cnf(i_0_13522,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7809]),
    [final] ).

cnf(i_0_13523,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7810]),
    [final] ).

cnf(i_0_13524,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7811]),
    [final] ).

cnf(i_0_13525,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Product__Type_Ofst(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X2,X1),X3))),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7812]),
    [final] ).

cnf(i_0_13526,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(c_Finite__Set_Ocard(X2),X4),
    inference(split_conjunct,[status(thm)],[i_0_7813]),
    [final] ).

cnf(i_0_13527,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13528,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13529,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7814,c_0_6097]),
    [final] ).

cnf(i_0_13530,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7815]),
    [final] ).

cnf(i_0_13531,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_Set_Ovimage(X4,X5,X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7387]),
    [final] ).

cnf(i_0_13532,plain,
    c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),X3),
    inference(split_conjunct,[status(thm)],[i_0_7816]),
    [final] ).

cnf(i_0_13533,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk234_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7817]),
    [final] ).

cnf(i_0_13534,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk131_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7818]),
    [final] ).

cnf(i_0_13535,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7819]),
    [final] ).

cnf(i_0_13536,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7820]),
    [final] ).

cnf(i_0_13537,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7821]),
    [final] ).

cnf(i_0_13538,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_7822]),
    [final] ).

cnf(i_0_13539,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7823]),
    [final] ).

cnf(i_0_13540,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_7824]),
    [final] ).

cnf(i_0_13541,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_13542,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5331]),
    [final] ).

cnf(i_0_13543,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X3)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),c_List_Oremove1(X2,X3,X4))))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7825]),
    [final] ).

cnf(i_0_13544,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7826]),
    [final] ).

cnf(i_0_13545,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7827]),
    [final] ).

cnf(i_0_13546,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7828]),
    [final] ).

cnf(i_0_13547,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7829]),
    [final] ).

cnf(i_0_13548,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7830]),
    [final] ).

cnf(i_0_13549,plain,
    ( X1 = hAPP(X2,esk4_4(X3,X2,X4,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Set_Oimage(X4,X5,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7143]),
    [final] ).

cnf(i_0_13550,plain,
    c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_7831]),
    [final] ).

cnf(i_0_13551,plain,
    ( hAPP(c_Fun_Ocomp(X1,X2,X2,X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)) = c_Fun_Oid(X2)
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7536]),
    [final] ).

cnf(i_0_13552,plain,
    hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X4),X5) = c_Lazy__Sequence_Ohb__bind(X1,X2,hAPP(X3,X5),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7832]),
    [final] ).

cnf(i_0_13553,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X6),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X4 != hAPP(c_Set_Oimage(X1,X5,X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6583]),
    [final] ).

cnf(i_0_13554,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),hAPP(c_Nat_OSuc,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7833]),
    [final] ).

cnf(i_0_13555,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_7834]),
    [final] ).

cnf(i_0_13556,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1)) ),
    inference(rw,[status(thm)],[i_0_7835,c_0_6186]),
    [final] ).

cnf(i_0_13557,plain,
    ( c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7836,c_0_6097]),
    [final] ).

cnf(i_0_13558,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7837,c_0_6097]),
    [final] ).

cnf(i_0_13559,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7838]),
    [final] ).

cnf(i_0_13560,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X4),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7839]),
    [final] ).

cnf(i_0_13561,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X5),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7840]),
    [final] ).

cnf(i_0_13562,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7840]),
    [final] ).

cnf(i_0_13563,plain,
    ( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7841]),
    [final] ).

cnf(i_0_13564,plain,
    ( hBOOL(hAPP(X1,esk494_4(X2,X1,X3,X4)))
    | c_List_Olist__ex1(X3,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_13565,plain,
    ( hBOOL(hAPP(X1,esk486_4(X2,X1,X3,X4)))
    | c_List_Olist__ex1(X3,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_13566,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_7842,c_0_6097]),
    [final] ).

cnf(i_0_13567,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_7843,c_0_6097]),
    [final] ).

cnf(i_0_13568,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_13569,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_13570,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13571,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))
    | hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1) != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
    inference(rw,[status(thm)],[i_0_7844,c_0_6293]),
    [final] ).

cnf(i_0_13572,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X3)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7845]),
    [final] ).

cnf(i_0_13573,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X2,X1,X3)),X2))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13574,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) = X5
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | hAPP(hAPP(c_List_Oappend(X1),X3),X4) != hAPP(hAPP(c_List_Oappend(X1),X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_13575,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13576,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5)) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),c_List_Oremdups(X1,X5))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7846]),
    [final] ).

cnf(i_0_13577,plain,
    c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),c_Predicate_Oconversep(X1,X2,X3)),c_Predicate_Oconversep(X1,X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_7847]),
    [final] ).

cnf(i_0_13578,plain,
    c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),c_Predicate_Oconversep(X1,X2,X3)),c_Predicate_Oconversep(X1,X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_7848]),
    [final] ).

cnf(i_0_13579,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7849]),
    [final] ).

cnf(i_0_13580,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7850]),
    [final] ).

cnf(i_0_13581,plain,
    c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
    inference(rw,[status(thm)],[i_0_7851,c_0_6097]),
    [final] ).

cnf(i_0_13582,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_13583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_13584,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7854]),
    [final] ).

cnf(i_0_13585,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X3),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7855]),
    [final] ).

cnf(i_0_13586,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X3),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7856]),
    [final] ).

cnf(i_0_13587,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X2,X1,X3)),X2))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13588,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7857]),
    [final] ).

cnf(i_0_13589,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7858]),
    [final] ).

cnf(i_0_13590,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7859]),
    [final] ).

cnf(i_0_13591,plain,
    ( c_Fun_Oinj__on(X1,X2,esk75_4(X3,X2,X4,X1),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6636]),
    [final] ).

cnf(i_0_13592,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7860]),
    [final] ).

cnf(i_0_13593,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7861]),
    [final] ).

cnf(i_0_13594,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7862,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13595,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_7863]),
    [final] ).

cnf(i_0_13596,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7864]),
    [final] ).

cnf(i_0_13597,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_7865]),
    [final] ).

cnf(i_0_13598,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_13599,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_13600,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7866]),
    [final] ).

cnf(i_0_13601,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7867]),
    [final] ).

cnf(i_0_13602,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))),hAPP(c_List_Oset(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7868]),
    [final] ).

cnf(i_0_13603,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),hAPP(c_List_Oset(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_7869]),
    [final] ).

cnf(i_0_13604,plain,
    ( c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7870]),
    [final] ).

cnf(i_0_13605,plain,
    hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_7871]),
    [final] ).

cnf(i_0_13606,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk223_3(X2,X3,X1)),X3))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7610]),
    [final] ).

cnf(i_0_13607,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7872,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13608,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_13609,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_13610,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5)) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7873]),
    [final] ).

cnf(i_0_13611,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7874]),
    [final] ).

cnf(i_0_13612,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7712]),
    [final] ).

cnf(i_0_13613,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7875]),
    [final] ).

cnf(i_0_13614,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7876]),
    [final] ).

cnf(i_0_13615,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk392_3(X1,X3,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7877]),
    [final] ).

cnf(i_0_13616,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7878]),
    [final] ).

cnf(i_0_13617,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Relation_ODomain(X3,X3),X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7508]),
    [final] ).

cnf(i_0_13618,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7879,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13619,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7880,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13620,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_13621,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_13622,plain,
    ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7597]),
    [final] ).

cnf(i_0_13623,plain,
    ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X5,X1,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13624,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))
    | ~ c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(rw,[status(thm)],[i_0_7881,c_0_6104]),
    [final] ).

cnf(i_0_13625,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13627,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4),X3),X5)),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),X6))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6455]),
    [final] ).

cnf(i_0_13628,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk436_3(X2,X3,X1)),esk437_3(X2,X3,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_13629,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7883]),
    [final] ).

cnf(i_0_13630,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X2,X1,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13631,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X2,X1,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13632,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13633,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13634,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X2)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7884]),
    [final] ).

cnf(i_0_13635,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7885]),
    [final] ).

cnf(i_0_13636,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk211_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7525]),
    [final] ).

cnf(i_0_13637,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4)),X5),X6) = X4,
    inference(split_conjunct,[status(thm)],[i_0_7886]),
    [final] ).

cnf(i_0_13638,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13639,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13640,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7887]),
    [final] ).

cnf(i_0_13641,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7888]),
    [final] ).

cnf(i_0_13642,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk213_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7532]),
    [final] ).

cnf(i_0_13643,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk188_3(X2,X1,X3)),esk187_3(X2,X1,X3))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3) = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_13644,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk186_3(X2,X1,X3)),esk185_3(X2,X1,X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3) = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7646]),
    [final] ).

cnf(i_0_13645,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7889]),
    [final] ).

cnf(i_0_13646,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7890]),
    [final] ).

cnf(i_0_13647,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7891]),
    [final] ).

cnf(i_0_13648,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13649,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13650,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7892]),
    [final] ).

cnf(i_0_13651,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7893]),
    [final] ).

cnf(i_0_13652,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7894]),
    [final] ).

cnf(i_0_13653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13654,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13655,plain,
    ( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk243_2(X2,X1)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk242_2(X2,X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7604]),
    [final] ).

cnf(i_0_13656,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X3),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7838]),
    [final] ).

cnf(i_0_13657,plain,
    ( hAPP(hAPP(c_List_Onth(X2),c_List_OtakeWhile(X2,X3,X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7895]),
    [final] ).

cnf(i_0_13658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7523]),
    [final] ).

cnf(i_0_13659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7524]),
    [final] ).

cnf(i_0_13660,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk316_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk315_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_13661,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Int_Oint),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7896]),
    [final] ).

cnf(i_0_13662,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7897]),
    [final] ).

cnf(i_0_13663,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7668]),
    [final] ).

cnf(i_0_13664,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_7898,c_0_6732]),
    [final] ).

cnf(i_0_13665,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_7899,c_0_6143]),
    [final] ).

cnf(i_0_13666,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_7900,c_0_6143]),
    [final] ).

cnf(i_0_13667,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7901]),
    [final] ).

cnf(i_0_13668,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7902]),
    [final] ).

cnf(i_0_13669,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_7903]),
    [final] ).

cnf(i_0_13670,plain,
    hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4) = hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_7904]),
    [final] ).

cnf(i_0_13671,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Int_Oint),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7905]),
    [final] ).

cnf(i_0_13672,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7906]),
    [final] ).

cnf(i_0_13673,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7854]),
    [final] ).

cnf(i_0_13674,plain,
    c_Fun_Oinj__on(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_7907]),
    [final] ).

cnf(i_0_13675,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7908]),
    [final] ).

cnf(i_0_13676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7909]),
    [final] ).

cnf(i_0_13677,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X3,X5),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7910]),
    [final] ).

cnf(i_0_13678,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7911,c_0_6189]),c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_13679,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_7912]),
    [final] ).

cnf(i_0_13680,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7913]),
    [final] ).

cnf(i_0_13681,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5332]),
    [final] ).

cnf(i_0_13682,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X2),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7526]),
    [final] ).

cnf(i_0_13683,plain,
    ( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7914]),
    [final] ).

cnf(i_0_13684,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1))),hAPP(X4,hAPP(c_Nat_OSuc,X1)))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7915]),
    [final] ).

cnf(i_0_13685,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk227_3(X2,X3,X1)),esk228_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7587]),
    [final] ).

cnf(i_0_13686,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7916]),
    [final] ).

cnf(i_0_13687,plain,
    ( hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X3),X4),X6)) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)),hAPP(hAPP(c_List_Ozip(X1,X3),X5),X6))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7917]),
    [final] ).

cnf(i_0_13688,plain,
    c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = c_List_Olist_Olist__size(X3,hAPP(c_Fun_Ocomp(X1,tc_Nat_Onat,X3,X2),X4),X5),
    inference(split_conjunct,[status(thm)],[i_0_7918]),
    [final] ).

cnf(i_0_13689,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Relation_Orefl__on(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6192]),
    [final] ).

cnf(i_0_13690,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Relation_Orefl__on(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6686]),
    [final] ).

cnf(i_0_13691,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3))
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7919]),
    [final] ).

cnf(i_0_13692,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7920]),
    [final] ).

cnf(i_0_13693,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7921]),
    [final] ).

cnf(i_0_13694,plain,
    ( hBOOL(hAPP(hAPP(X4,X5),X6))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X3,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7922]),
    [final] ).

cnf(i_0_13695,plain,
    ( hBOOL(hAPP(hAPP(X6,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7923]),
    [final] ).

cnf(i_0_13696,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_13697,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7673]),
    [final] ).

cnf(i_0_13698,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7924]),
    [final] ).

cnf(i_0_13699,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7925]),
    [final] ).

cnf(i_0_13700,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7926]),
    [final] ).

cnf(i_0_13701,plain,
    ( hBOOL(hAPP(X2,X4))
    | hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3) != c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(rw,[status(thm)],[i_0_7927,c_0_6293]),
    [final] ).

cnf(i_0_13702,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),esk489_3(X3,X2,X1))))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7928]),
    [final] ).

cnf(i_0_13703,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7622]),
    [final] ).

cnf(i_0_13704,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(hAPP(X3,X4),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7929]),
    [final] ).

cnf(i_0_13705,plain,
    ( X1 = c_List_Olist_ONil(tc_List_Olist(X2))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2))),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7930]),
    [final] ).

cnf(i_0_13706,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7931]),
    [final] ).

cnf(i_0_13707,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7932]),
    [final] ).

cnf(i_0_13708,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7933]),
    [final] ).

cnf(i_0_13709,plain,
    hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X4)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7934]),
    [final] ).

cnf(i_0_13710,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7935]),
    [final] ).

cnf(i_0_13711,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7936]),
    [final] ).

cnf(i_0_13712,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7937]),
    [final] ).

cnf(i_0_13713,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7938]),
    [final] ).

cnf(i_0_13714,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7939]),
    [final] ).

cnf(i_0_13715,plain,
    ( hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
    | hBOOL(hAPP(X3,X4))
    | X1 != hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
    inference(rw,[status(thm)],[i_0_7940,c_0_6293]),
    [final] ).

cnf(i_0_13716,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7941]),
    [final] ).

cnf(i_0_13717,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X3)),c_Enum_Oproduct(X1,X3,X2,X4)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7942]),
    [final] ).

cnf(i_0_13718,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7943]),
    [final] ).

cnf(i_0_13719,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7583]),
    [final] ).

cnf(i_0_13720,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13721,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13722,plain,
    ( hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3) = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(rw,[status(thm)],[i_0_7944,c_0_6712]),
    [final] ).

cnf(i_0_13723,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
    | hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7945]),
    [final] ).

cnf(i_0_13724,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7582]),
    [final] ).

cnf(i_0_13725,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7946]),
    [final] ).

cnf(i_0_13726,plain,
    ( hBOOL(hAPP(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
    | ~ hBOOL(hAPP(X2,hAPP(c_Int_ORep__Integ,esk313_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7947]),
    [final] ).

cnf(i_0_13727,plain,
    ( c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(rw,[status(thm)],[i_0_7948,c_0_6189]),
    [final] ).

cnf(i_0_13728,plain,
    ( hAPP(X1,esk20_4(X2,X1,X3,X4)) = hAPP(X1,esk21_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7352]),
    [final] ).

cnf(i_0_13729,plain,
    ( hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X5)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7591]),
    [final] ).

cnf(i_0_13730,plain,
    ( hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X5)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7949]),
    [final] ).

cnf(i_0_13731,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(split_conjunct,[status(thm)],[fact_type__definition__Integ]),
    [final] ).

cnf(i_0_13732,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7950]),
    [final] ).

cnf(i_0_13733,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7951]),
    [final] ).

cnf(i_0_13734,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7952]),
    [final] ).

cnf(i_0_13735,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7953]),
    [final] ).

cnf(i_0_13736,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7954]),
    [final] ).

cnf(i_0_13737,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7955]),
    [final] ).

cnf(i_0_13738,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7956]),
    [final] ).

cnf(i_0_13739,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7957]),
    [final] ).

cnf(i_0_13740,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Relation_OImage(X1,X1,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7958]),
    [final] ).

cnf(i_0_13741,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_7959]),
    [final] ).

cnf(i_0_13742,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_7960]),
    [final] ).

cnf(i_0_13743,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk571_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13744,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X2,X3,X1))),esk572_3(X2,X3,X1))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13745,plain,
    c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X3,
    inference(split_conjunct,[status(thm)],[i_0_7961]),
    [final] ).

cnf(i_0_13746,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X4))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7962]),
    [final] ).

cnf(i_0_13747,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7963]),
    [final] ).

cnf(i_0_13748,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7964]),
    [final] ).

cnf(i_0_13749,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7965]),
    [final] ).

cnf(i_0_13750,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6585]),
    [final] ).

cnf(i_0_13751,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7966]),
    [final] ).

cnf(i_0_13752,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X3 = X5
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7967]),
    [final] ).

cnf(i_0_13753,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X4 = X6
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_13754,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7969]),
    [final] ).

cnf(i_0_13755,plain,
    ( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk570_3(X2,X4,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Ozero__class_Ozero(X1))))
    | ~ hBOOL(hAPP(X4,X3))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7721]),
    [final] ).

cnf(i_0_13756,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7970,c_0_6293]),
    [final] ).

cnf(i_0_13757,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7971]),
    [final] ).

cnf(i_0_13758,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7972]),
    [final] ).

cnf(i_0_13759,plain,
    ( c_Relation_Osingle__valued(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
    | ~ c_Relation_Osingle__valued(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7973]),
    [final] ).

cnf(i_0_13760,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk576_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13761,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk575_3(X2,X3,X1))),esk576_3(X2,X3,X1))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13762,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk480_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7974]),
    [final] ).

cnf(i_0_13763,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk477_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7975]),
    [final] ).

cnf(i_0_13764,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin),
    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_7976,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_13765,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7977]),
    [final] ).

cnf(i_0_13766,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7978]),
    [final] ).

cnf(i_0_13767,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7979]),
    [final] ).

cnf(i_0_13768,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7980]),
    [final] ).

cnf(i_0_13769,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7981]),
    [final] ).

cnf(i_0_13770,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7982]),
    [final] ).

cnf(i_0_13771,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7983]),
    [final] ).

cnf(i_0_13772,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7984]),
    [final] ).

cnf(i_0_13773,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7985]),
    [final] ).

cnf(i_0_13774,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13775,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_type__definition__code__numeral]),
    [final] ).

cnf(i_0_13776,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3),
    inference(split_conjunct,[status(thm)],[i_0_7986]),
    [final] ).

cnf(i_0_13777,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7987]),
    [final] ).

cnf(i_0_13778,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7988]),
    [final] ).

cnf(i_0_13779,plain,
    ( hAPP(c_List_Ofilter(X2,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),X4)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),hAPP(c_List_Ofilter(X2,X5),X4))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
    | ~ hBOOL(hAPP(X5,X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7989]),
    [final] ).

cnf(i_0_13780,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7864]),
    [final] ).

cnf(i_0_13781,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_7990,c_0_6071]),
    [final] ).

cnf(i_0_13782,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7991,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13783,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7992]),
    [final] ).

cnf(i_0_13784,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_13785,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7993]),
    [final] ).

cnf(i_0_13786,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7994]),
    [final] ).

cnf(i_0_13787,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7995]),
    [final] ).

cnf(i_0_13788,plain,
    ( hBOOL(hAPP(X1,esk69_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_13789,plain,
    ( hBOOL(hAPP(X1,esk69_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6850]),
    [final] ).

cnf(i_0_13790,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7718]),
    [final] ).

cnf(i_0_13791,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_7996]),
    [final] ).

cnf(i_0_13792,plain,
    ( hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X2))),hAPP(c_List_Ofilter(X3,X1),X4)) = hAPP(c_List_Ofilter(X3,X1),X4)
    | hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_7997,c_0_6712]),
    [final] ).

cnf(i_0_13793,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),hAPP(hAPP(c_List_Oappend(tc_Int_Oint),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7998,c_0_7999]),c_0_8000]),c_0_8000]),
    [final] ).

cnf(i_0_13794,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8001]),
    [final] ).

cnf(i_0_13795,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7548]),
    [final] ).

cnf(i_0_13796,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk136_3(X2,X3,X1)),esk137_3(X2,X3,X1)))
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_13797,plain,
    ( hAPP(X1,esk233_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_3(X2,X1,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_13798,plain,
    ( hAPP(X1,esk225_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk224_3(X2,X1,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_13799,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6)) = hAPP(X4,X5)
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8003]),
    [final] ).

cnf(i_0_13800,plain,
    ( hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),c_List_Olist_ONil(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8004]),
    [final] ).

cnf(i_0_13801,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8005]),
    [final] ).

cnf(i_0_13802,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8006]),
    [final] ).

cnf(i_0_13803,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(X1,X2),tc_fun(X1,X2)),X3),c_Fun_Ocomp(X2,X2,X1,X4)) = c_Fun_Ocomp(X2,X2,X1,hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8007]),
    [final] ).

cnf(i_0_13804,plain,
    hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X4),X5) = hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X5)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8008]),
    [final] ).

cnf(i_0_13805,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8009]),
    [final] ).

cnf(i_0_13806,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8010]),
    [final] ).

cnf(i_0_13807,plain,
    ( X4 = X5
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8011]),
    [final] ).

cnf(i_0_13808,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2) = c_List_Olist_ONil(X1)
    | hBOOL(hAPP(hAPP(c_member(X1),esk442_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_8012,c_0_6293]),
    [final] ).

cnf(i_0_13809,plain,
    ( c_List_Olist__all2(X3,X2,X4,c_List_Olist_ONil(X3),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7549]),
    [final] ).

cnf(i_0_13810,plain,
    ( c_List_Olist__all2(X2,X3,X4,X1,c_List_Olist_ONil(X3))
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_13811,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7890]),
    [final] ).

cnf(i_0_13812,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8013]),
    [final] ).

cnf(i_0_13813,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13814,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7889]),
    [final] ).

cnf(i_0_13815,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13816,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7893]),
    [final] ).

cnf(i_0_13817,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8014]),
    [final] ).

cnf(i_0_13818,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13819,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7892]),
    [final] ).

cnf(i_0_13820,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13821,plain,
    ( c_Fun_Obij__betw(X3,X3,c_Fun_Oid(X3),X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7551]),
    [final] ).

cnf(i_0_13822,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8015]),
    [final] ).

cnf(i_0_13823,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8016]),
    [final] ).

cnf(i_0_13824,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7568]),
    [final] ).

cnf(i_0_13825,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk396_3(X1,X2,X3)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7279]),
    [final] ).

cnf(i_0_13826,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8017]),
    [final] ).

cnf(i_0_13827,plain,
    ( c_Fun_Oinj__on(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8018]),
    [final] ).

cnf(i_0_13828,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(split_conjunct,[status(thm)],[i_0_8019]),
    [final] ).

cnf(i_0_13829,plain,
    hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8020]),
    [final] ).

cnf(i_0_13830,plain,
    hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8021]),
    [final] ).

cnf(i_0_13831,plain,
    ( c_List_Olist__all2(X3,X3,c_fequal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7556]),
    [final] ).

cnf(i_0_13832,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7854]),
    [final] ).

cnf(i_0_13833,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk576_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13834,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk571_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13835,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk575_3(X2,X3,X1))),esk576_3(X2,X3,X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13836,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X2,X3,X1))),esk572_3(X2,X3,X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13837,plain,
    ( c_List_Oremove1(X1,X3,X2) = hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X3))),X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_8022,c_0_6712]),
    [final] ).

cnf(i_0_13838,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8023]),
    [final] ).

cnf(i_0_13839,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8024]),
    [final] ).

cnf(i_0_13840,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8025]),
    [final] ).

cnf(i_0_13841,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8026]),
    [final] ).

cnf(i_0_13842,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_13843,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_13844,plain,
    ( hBOOL(hAPP(X1,esk203_3(X2,X1,X3)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7262]),
    [final] ).

cnf(i_0_13845,plain,
    ( hBOOL(hAPP(X1,esk173_3(X2,X1,X3)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7263]),
    [final] ).

cnf(i_0_13846,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8027]),
    [final] ).

cnf(i_0_13847,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5) = hAPP(X5,X4),
    inference(split_conjunct,[status(thm)],[i_0_8028]),
    [final] ).

cnf(i_0_13848,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X2,X1,X3)))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13849,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8029,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_13850,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk391_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7877]),
    [final] ).

cnf(i_0_13851,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8030]),
    [final] ).

cnf(i_0_13852,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8031]),
    [final] ).

cnf(i_0_13853,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8032]),
    [final] ).

cnf(i_0_13854,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8033,c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_13855,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))) = hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8034,c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_13856,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13857,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(X1,esk128_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
    | hAPP(X1,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_13858,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_8035]),
    [final] ).

cnf(i_0_13859,plain,
    ( hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8036]),
    [final] ).

cnf(i_0_13860,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6)) = hAPP(hAPP(c_List_Olist_OCons(X5),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8037]),
    [final] ).

cnf(i_0_13861,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_13862,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_13863,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13864,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),c_List_Oset(X1)),c_Enum_Osublists(X1,X2))))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8038]),
    [final] ).

cnf(i_0_13865,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8039]),
    [final] ).

cnf(i_0_13866,plain,
    hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X3)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X2)),hAPP(c_Set_OPow(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_8040]),
    [final] ).

cnf(i_0_13867,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,X3),X4)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8041]),
    [final] ).

cnf(i_0_13868,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7939]),
    [final] ).

cnf(i_0_13869,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7939]),
    [final] ).

cnf(i_0_13870,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8042]),
    [final] ).

cnf(i_0_13871,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_13872,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8043]),
    [final] ).

cnf(i_0_13873,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13874,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X1),X2))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8044]),
    [final] ).

cnf(i_0_13875,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8045]),
    [final] ).

cnf(i_0_13876,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8046]),
    [final] ).

cnf(i_0_13877,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8047]),
    [final] ).

cnf(i_0_13878,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8046]),
    [final] ).

cnf(i_0_13879,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8047]),
    [final] ).

cnf(i_0_13880,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7993]),
    [final] ).

cnf(i_0_13881,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8048]),
    [final] ).

cnf(i_0_13882,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7994]),
    [final] ).

cnf(i_0_13883,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8049]),
    [final] ).

cnf(i_0_13884,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7864]),
    [final] ).

cnf(i_0_13885,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_8050]),
    [final] ).

cnf(i_0_13886,plain,
    ( c_List_Oupto(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8051]),
    [final] ).

cnf(i_0_13887,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X5)
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6656]),
    [final] ).

cnf(i_0_13888,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_13889,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8052]),
    [final] ).

cnf(i_0_13890,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13891,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8053]),
    [final] ).

cnf(i_0_13892,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8054,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13893,plain,
    ( c_Partial__Function_Oflat__lub(X1,X3,X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7187]),
    [final] ).

cnf(i_0_13894,plain,
    ( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8055]),
    [final] ).

cnf(i_0_13895,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_8056]),
    [final] ).

cnf(i_0_13896,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7018]),
    [final] ).

cnf(i_0_13897,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7019]),
    [final] ).

cnf(i_0_13898,plain,
    hAPP(c_Set_OPow(X1),X2) = hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8057]),
    [final] ).

cnf(i_0_13899,plain,
    hAPP(c_List_Orev(X1),X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_8058]),
    [final] ).

cnf(i_0_13900,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13901,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(X1,esk130_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
    | hAPP(X1,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_13902,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X2),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8059]),
    [final] ).

cnf(i_0_13903,plain,
    ( hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1)) = X3
    | X1 != c_List_Olist_ONil(X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1)) ),
    inference(rw,[status(thm)],[i_0_8060,c_0_6186]),
    [final] ).

cnf(i_0_13904,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8061]),
    [final] ).

cnf(i_0_13905,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8062]),
    [final] ).

cnf(i_0_13906,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8063,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13907,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Oantisym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8064]),
    [final] ).

cnf(i_0_13908,plain,
    ( c_Wellfounded_Oacyclic(X1,X3)
    | ~ c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8065]),
    [final] ).

cnf(i_0_13909,plain,
    ( c_Wellfounded_Owf(X1,X3)
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8066]),
    [final] ).

cnf(i_0_13910,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8067]),
    [final] ).

cnf(i_0_13911,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7163]),
    [final] ).

cnf(i_0_13912,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7164]),
    [final] ).

cnf(i_0_13913,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2)) = hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))
    | esk230_3(X1,X2,X3) != esk231_3(X1,X2,X3)
    | hAPP(c_Finite__Set_Ocard(X3),esk229_3(X1,X2,X3)) != X1
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7377]),
    [final] ).

cnf(i_0_13914,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8068]),
    [final] ).

cnf(i_0_13915,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8069]),
    [final] ).

cnf(i_0_13916,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8070]),
    [final] ).

cnf(i_0_13917,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8071]),
    [final] ).

cnf(i_0_13918,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_OtakeWhile(X1,X4,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8072]),
    [final] ).

cnf(i_0_13919,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8073]),
    [final] ).

cnf(i_0_13920,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8074]),
    [final] ).

cnf(i_0_13921,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8075]),
    [final] ).

cnf(i_0_13922,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_List_Oset(X1),X3))),
    inference(split_conjunct,[status(thm)],[i_0_8076]),
    [final] ).

cnf(i_0_13923,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X2,X1,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13924,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X2,X1,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13925,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8077]),
    [final] ).

cnf(i_0_13926,plain,
    ( X2 = X4
    | X3 = X5
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8078]),
    [final] ).

cnf(i_0_13927,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[i_0_8079,c_0_6189]),
    [final] ).

cnf(i_0_13928,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8080]),
    [final] ).

cnf(i_0_13929,plain,
    ( c_Divides_OnegDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5331]),
    [final] ).

cnf(i_0_13930,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk211_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7525]),
    [final] ).

cnf(i_0_13931,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8081]),
    [final] ).

cnf(i_0_13932,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(rw,[status(thm)],[i_0_8082,c_0_6071]),
    [final] ).

cnf(i_0_13933,plain,
    ( hBOOL(hAPP(X1,esk495_4(X2,X3,X1,X4)))
    | c_FunDef_OTHE__default(X3,X2,X1) = c_HOL_OThe(X3,X1)
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8083]),
    [final] ).

cnf(i_0_13934,plain,
    c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk300_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6547]),
    [final] ).

cnf(i_0_13935,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_8084]),
    [final] ).

cnf(i_0_13936,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_8085]),
    [final] ).

cnf(i_0_13937,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8086]),
    [final] ).

cnf(i_0_13938,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13939,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13940,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13941,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13942,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13943,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13944,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_13945,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_13946,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Odrop(X1)),X4),X2),
    inference(split_conjunct,[status(thm)],[i_0_8087]),
    [final] ).

cnf(i_0_13947,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8088]),
    [final] ).

cnf(i_0_13948,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8089]),
    [final] ).

cnf(i_0_13949,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3)))
    | hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1) = hAPP(c_Random_Opick(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8090]),
    [final] ).

cnf(i_0_13950,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8091,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13951,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8092,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13952,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8093,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13953,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8094,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_13954,plain,
    ( c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3)
    | c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7613]),
    [final] ).

cnf(i_0_13955,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8095]),
    [final] ).

cnf(i_0_13956,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8096]),
    [final] ).

cnf(i_0_13957,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6780]),
    [final] ).

cnf(i_0_13958,plain,
    hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8097]),
    [final] ).

cnf(i_0_13959,plain,
    hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_ORange(X1,X2),X3)),hAPP(c_Relation_ORange(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8098]),
    [final] ).

cnf(i_0_13960,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6)) = hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),X5),hAPP(X3,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8099]),
    [final] ).

cnf(i_0_13961,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk213_3(X2,X3,X1)))
    | hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7532]),
    [final] ).

cnf(i_0_13962,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8100]),
    [final] ).

cnf(i_0_13963,plain,
    ( X1 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8101]),
    [final] ).

cnf(i_0_13964,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8102]),
    [final] ).

cnf(i_0_13965,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X3),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8103]),
    [final] ).

cnf(i_0_13966,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8104]),
    [final] ).

cnf(i_0_13967,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8042]),
    [final] ).

cnf(i_0_13968,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk372_3(X2,X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8105]),
    [final] ).

cnf(i_0_13969,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8106]),
    [final] ).

cnf(i_0_13970,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk281_3(X2,X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8107]),
    [final] ).

cnf(i_0_13971,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8108]),
    [final] ).

cnf(i_0_13972,plain,
    ( hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8109]),
    [final] ).

cnf(i_0_13973,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_13974,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_13975,plain,
    ( hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8110]),
    [final] ).

cnf(i_0_13976,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X5) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_8111]),
    [final] ).

cnf(i_0_13977,plain,
    ( c_Wellfounded_OwfP(X1,X3)
    | ~ c_Wellfounded_OwfP(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8112]),
    [final] ).

cnf(i_0_13978,plain,
    ( X2 = X3
    | hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8113]),
    [final] ).

cnf(i_0_13979,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8114]),
    [final] ).

cnf(i_0_13980,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8115]),
    [final] ).

cnf(i_0_13981,plain,
    ( c_List_Olinorder__class_Osort__key(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olinorder__class_Osort__key(X2,X1,X3,X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8116]),
    [final] ).

cnf(i_0_13982,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X3,X4,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7666]),
    [final] ).

cnf(i_0_13983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8117]),
    [final] ).

cnf(i_0_13984,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_13985,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8118]),
    [final] ).

cnf(i_0_13986,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_13987,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8119]),
    [final] ).

cnf(i_0_13988,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8120]),
    [final] ).

cnf(i_0_13989,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7798]),
    [final] ).

cnf(i_0_13990,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8121]),
    [final] ).

cnf(i_0_13991,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8122]),
    [final] ).

cnf(i_0_13992,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8123]),
    [final] ).

cnf(i_0_13993,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8124]),
    [final] ).

cnf(i_0_13994,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8125]),
    [final] ).

cnf(i_0_13995,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7801]),
    [final] ).

cnf(i_0_13996,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8126]),
    [final] ).

cnf(i_0_13997,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_13998,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_13999,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14000,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Ois__nat(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8130]),
    [final] ).

cnf(i_0_14001,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk39_3(X2,X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8131]),
    [final] ).

cnf(i_0_14002,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_5478]),
    [final] ).

cnf(i_0_14003,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8132]),
    [final] ).

cnf(i_0_14004,plain,
    ( c_List_Olist__all(X2,X1,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk481_3(X3,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8133]),
    [final] ).

cnf(i_0_14005,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7818]),
    [final] ).

cnf(i_0_14006,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8134]),
    [final] ).

cnf(i_0_14007,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8135]),
    [final] ).

cnf(i_0_14008,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
    inference(split_conjunct,[status(thm)],[i_0_8136]),
    [final] ).

cnf(i_0_14009,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_8137]),
    [final] ).

cnf(i_0_14010,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8138,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14011,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8139,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14012,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8115]),
    [final] ).

cnf(i_0_14013,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8114]),
    [final] ).

cnf(i_0_14014,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8140]),
    [final] ).

cnf(i_0_14015,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8141,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14016,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8142,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14017,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8143]),
    [final] ).

cnf(i_0_14018,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8144]),
    [final] ).

cnf(i_0_14019,plain,
    ( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8145]),
    [final] ).

cnf(i_0_14020,plain,
    hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(rw,[status(thm)],[i_0_8146,c_0_6712]),
    [final] ).

cnf(i_0_14021,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_List_Olist_ONil(tc_List_Olist(X2))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2))),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7930]),
    [final] ).

cnf(i_0_14022,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8147]),
    [final] ).

cnf(i_0_14023,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(X3,X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_8148]),
    [final] ).

cnf(i_0_14024,plain,
    ( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X6) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(X3,X5) != X6
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8149]),
    [final] ).

cnf(i_0_14025,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8150]),
    [final] ).

cnf(i_0_14026,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_14027,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_14028,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14029,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14030,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14031,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14032,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6838]),
    [final] ).

cnf(i_0_14033,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6838]),
    [final] ).

cnf(i_0_14034,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7725]),
    [final] ).

cnf(i_0_14035,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8151]),
    [final] ).

cnf(i_0_14036,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7808]),
    [final] ).

cnf(i_0_14037,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14038,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7810]),
    [final] ).

cnf(i_0_14039,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14040,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7852]),
    [final] ).

cnf(i_0_14041,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8154]),
    [final] ).

cnf(i_0_14042,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7853]),
    [final] ).

cnf(i_0_14043,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8155]),
    [final] ).

cnf(i_0_14044,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7820]),
    [final] ).

cnf(i_0_14045,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8156]),
    [final] ).

cnf(i_0_14046,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8157]),
    [final] ).

cnf(i_0_14047,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7821]),
    [final] ).

cnf(i_0_14048,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8158]),
    [final] ).

cnf(i_0_14049,plain,
    ( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | hAPP(hAPP(c_List_Oappend(X2),X1),X4) != hAPP(hAPP(c_List_Oappend(X2),X3),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_14050,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7849]),
    [final] ).

cnf(i_0_14051,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7850]),
    [final] ).

cnf(i_0_14052,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)
    | hAPP(X5,X2) = c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Fields_Ofield(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7764]),
    [final] ).

cnf(i_0_14053,plain,
    ( hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_8159,c_0_6293]),
    [final] ).

cnf(i_0_14054,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk335_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7177]),
    [final] ).

cnf(i_0_14055,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk334_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7178]),
    [final] ).

cnf(i_0_14056,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk284_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7179]),
    [final] ).

cnf(i_0_14057,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8160]),
    [final] ).

cnf(i_0_14058,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8161]),
    [final] ).

cnf(i_0_14059,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8042]),
    [final] ).

cnf(i_0_14060,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_14061,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14062,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14063,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8162]),
    [final] ).

cnf(i_0_14064,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8163,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14065,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6512]),
    [final] ).

cnf(i_0_14066,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7656]),
    [final] ).

cnf(i_0_14067,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8164]),
    [final] ).

cnf(i_0_14068,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8165]),
    [final] ).

cnf(i_0_14069,plain,
    ( hBOOL(hAPP(X1,esk487_4(X1,X2,X3,X4)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7259]),
    [final] ).

cnf(i_0_14070,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X2),X1),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)),X3)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8166]),
    [final] ).

cnf(i_0_14071,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8167]),
    [final] ).

cnf(i_0_14072,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8168]),
    [final] ).

cnf(i_0_14073,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))
    | ~ c_Nitpick_Orefl_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7261]),
    [final] ).

cnf(i_0_14074,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8169]),
    [final] ).

cnf(i_0_14075,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8170]),
    [final] ).

cnf(i_0_14076,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8171]),
    [final] ).

cnf(i_0_14077,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8172]),
    [final] ).

cnf(i_0_14078,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X5)))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8173]),
    [final] ).

cnf(i_0_14079,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X5)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8174]),
    [final] ).

cnf(i_0_14080,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X5)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8175]),
    [final] ).

cnf(i_0_14081,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8176]),
    [final] ).

cnf(i_0_14082,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8177]),
    [final] ).

cnf(i_0_14083,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Groups_Oab__group__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7783]),
    [final] ).

cnf(i_0_14084,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8178]),
    [final] ).

cnf(i_0_14085,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8179]),
    [final] ).

cnf(i_0_14086,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8180]),
    [final] ).

cnf(i_0_14087,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8181]),
    [final] ).

cnf(i_0_14088,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8182]),
    [final] ).

cnf(i_0_14089,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8183]),
    [final] ).

cnf(i_0_14090,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8184]),
    [final] ).

cnf(i_0_14091,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X1,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8185]),
    [final] ).

cnf(i_0_14092,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(X5,X3)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8186]),
    [final] ).

cnf(i_0_14093,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)))),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8187]),
    [final] ).

cnf(i_0_14094,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8188]),
    [final] ).

cnf(i_0_14095,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6596]),
    [final] ).

cnf(i_0_14096,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8189]),
    [final] ).

cnf(i_0_14097,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk219_3(X2,X3,X1)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8190]),
    [final] ).

cnf(i_0_14098,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8043]),
    [final] ).

cnf(i_0_14099,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_14100,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(X3,X6),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4))
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8191]),
    [final] ).

cnf(i_0_14101,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2)))
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8192]),
    [final] ).

cnf(i_0_14102,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8193]),
    [final] ).

cnf(i_0_14103,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8194]),
    [final] ).

cnf(i_0_14104,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_8195]),
    [final] ).

cnf(i_0_14105,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | hAPP(X1,esk108_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7360]),
    [final] ).

cnf(i_0_14106,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | hAPP(X1,esk98_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7361]),
    [final] ).

cnf(i_0_14107,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)
    | hAPP(X1,esk109_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7362]),
    [final] ).

cnf(i_0_14108,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)
    | hAPP(X1,esk99_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7363]),
    [final] ).

cnf(i_0_14109,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8196]),
    [final] ).

cnf(i_0_14110,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8197]),
    [final] ).

cnf(i_0_14111,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk216_3(X2,X1,X3))),esk217_3(X2,X1,X3))
    | hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_14112,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk234_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7817]),
    [final] ).

cnf(i_0_14113,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk131_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7818]),
    [final] ).

cnf(i_0_14114,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk393_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8199]),
    [final] ).

cnf(i_0_14115,plain,
    c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),c_List_Olist_Olist__size(X1,X2,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8200]),
    [final] ).

cnf(i_0_14116,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X1),X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7838]),
    [final] ).

cnf(i_0_14117,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7622]),
    [final] ).

cnf(i_0_14118,plain,
    c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2)),X3)) = c_Random_Oselect__weight(X1,X3),
    inference(split_conjunct,[status(thm)],[i_0_8201]),
    [final] ).

cnf(i_0_14119,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7761]),
    [final] ).

cnf(i_0_14120,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8202]),
    [final] ).

cnf(i_0_14121,plain,
    ( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)) = c_List_Otranspose(X1,X2)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8203]),
    [final] ).

cnf(i_0_14122,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2))))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7259]),
    [final] ).

cnf(i_0_14123,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7268]),
    [final] ).

cnf(i_0_14124,plain,
    hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))) = X4,
    inference(rw,[status(thm)],[i_0_8204,c_0_6186]),
    [final] ).

cnf(i_0_14125,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8081]),
    [final] ).

cnf(i_0_14126,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8205]),
    [final] ).

cnf(i_0_14127,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),X3),X4)) = c_List_Omaps(X2,X1,X3,X4),
    inference(rw,[status(thm)],[i_0_8206,c_0_6143]),
    [final] ).

cnf(i_0_14128,plain,
    c_List_Omaps(X1,X2,X3,X4) = hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),X3),X4)),
    inference(rw,[status(thm)],[i_0_8207,c_0_6143]),
    [final] ).

cnf(i_0_14129,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8208]),
    [final] ).

cnf(i_0_14130,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8209]),
    [final] ).

cnf(i_0_14131,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)) = hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X1),hAPP(c_Relation_Oconverse(X3,X2),X5)),hAPP(c_Relation_Oconverse(X1,X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8210]),
    [final] ).

cnf(i_0_14132,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8211]),
    [final] ).

cnf(i_0_14133,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk221_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8095]),
    [final] ).

cnf(i_0_14134,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8212]),
    [final] ).

cnf(i_0_14135,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8213]),
    [final] ).

cnf(i_0_14136,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk154_3(X2,X1,X3))),esk155_3(X2,X1,X3))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_14137,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8215]),
    [final] ).

cnf(i_0_14138,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8216]),
    [final] ).

cnf(i_0_14139,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3) = hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8217,c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_14140,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk20_4(X1,X2,X3,X4) != esk21_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7352]),
    [final] ).

cnf(i_0_14141,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8218]),
    [final] ).

cnf(i_0_14142,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk571_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14143,plain,
    ( hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8090]),
    [final] ).

cnf(i_0_14144,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)
    | X1 != X3
    | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) != X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8219,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_14145,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_8220]),
    [final] ).

cnf(i_0_14146,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X2,X3,X1)),X2))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14147,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk576_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14148,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8046]),
    [final] ).

cnf(i_0_14149,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8221]),
    [final] ).

cnf(i_0_14150,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))
    | ~ hBOOL(hAPP(X5,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7259]),
    [final] ).

cnf(i_0_14151,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))),hAPP(X4,X1))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8222]),
    [final] ).

cnf(i_0_14152,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X2,X3,X1)),X2))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14153,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))))
    | ~ hBOOL(hAPP(X6,X5))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8223]),
    [final] ).

cnf(i_0_14154,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))))
    | ~ hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X6,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8223]),
    [final] ).

cnf(i_0_14155,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,X1)),X4),X5),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8224]),
    [final] ).

cnf(i_0_14156,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,X1)),X4),X5),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8225]),
    [final] ).

cnf(i_0_14157,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8226]),
    [final] ).

cnf(i_0_14158,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8226]),
    [final] ).

cnf(i_0_14159,plain,
    ( hBOOL(hAPP(X2,X4))
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8227]),
    [final] ).

cnf(i_0_14160,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk216_3(X2,X1,X3))),esk217_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_14161,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_8228]),
    [final] ).

cnf(i_0_14162,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8229]),
    [final] ).

cnf(i_0_14163,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8230]),
    [final] ).

cnf(i_0_14164,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk17_3(X2,X3,X1)),esk18_3(X2,X3,X1)))
    | hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6765]),
    [final] ).

cnf(i_0_14165,plain,
    ( c_Divides_OposDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5333]),
    [final] ).

cnf(i_0_14166,plain,
    ( hBOOL(hAPP(X5,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7268]),
    [final] ).

cnf(i_0_14167,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X4),X3))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8086]),
    [final] ).

cnf(i_0_14168,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8231]),
    [final] ).

cnf(i_0_14169,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8231]),
    [final] ).

cnf(i_0_14170,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8232]),
    [final] ).

cnf(i_0_14171,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8232]),
    [final] ).

cnf(i_0_14172,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8233]),
    [final] ).

cnf(i_0_14173,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8234]),
    [final] ).

cnf(i_0_14174,plain,
    ( c_Wellfounded_OwfP(X1,X2)
    | ~ c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8235]),
    [final] ).

cnf(i_0_14175,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8236]),
    [final] ).

cnf(i_0_14176,plain,
    ( hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X2))),X2) = c_List_Olist_ONil(X3)
    | ~ hBOOL(hAPP(X1,esk442_3(X2,X1,X3))) ),
    inference(rw,[status(thm)],[i_0_8237,c_0_6293]),
    [final] ).

cnf(i_0_14177,plain,
    ( X3 = X5
    | hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)) != hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8238]),
    [final] ).

cnf(i_0_14178,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8239]),
    [final] ).

cnf(i_0_14179,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk328_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk328_2(X2,X1))))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8240]),
    [final] ).

cnf(i_0_14180,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8241]),
    [final] ).

cnf(i_0_14181,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8242]),
    [final] ).

cnf(i_0_14182,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8072]),
    [final] ).

cnf(i_0_14183,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8243]),
    [final] ).

cnf(i_0_14184,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8244]),
    [final] ).

cnf(i_0_14185,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8245]),
    [final] ).

cnf(i_0_14186,plain,
    ( c_Nitpick_Onorm__frac(X2,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6772]),
    [final] ).

cnf(i_0_14187,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk281_3(X3,X1,X2)),esk281_3(X3,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X1),c_Relation_OId__on(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8107]),
    [final] ).

cnf(i_0_14188,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8246]),
    [final] ).

cnf(i_0_14189,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X5)) = hAPP(X3,X5)
    | ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8247]),
    [final] ).

cnf(i_0_14190,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5333]),
    [final] ).

cnf(i_0_14191,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8248,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6224]),
    [final] ).

cnf(i_0_14192,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))),X3)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8249]),
    [final] ).

cnf(i_0_14193,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
    inference(rw,[status(thm)],[i_0_8250,c_0_6104]),
    [final] ).

cnf(i_0_14194,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14195,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8251,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_14196,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8252,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_14197,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7480]),
    [final] ).

cnf(i_0_14198,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7481]),
    [final] ).

cnf(i_0_14199,plain,
    hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8253]),
    [final] ).

cnf(i_0_14200,plain,
    hAPP(c_List_Oset(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4)) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_List_Oset(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_List_Oset(X2),X4))),
    inference(split_conjunct,[status(thm)],[i_0_8254]),
    [final] ).

cnf(i_0_14201,plain,
    ( hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5) = X3
    | hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3) != X4
    | hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3) != X5
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8255]),
    [final] ).

cnf(i_0_14202,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk154_3(X2,X1,X3))),esk155_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_14203,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7874]),
    [final] ).

cnf(i_0_14204,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8256]),
    [final] ).

cnf(i_0_14205,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8256]),
    [final] ).

cnf(i_0_14206,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8257]),
    [final] ).

cnf(i_0_14207,plain,
    ( hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8258]),
    [final] ).

cnf(i_0_14208,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14209,plain,
    hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(c_List_Orotate1(X1),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8259,c_0_6732]),c_0_6732]),
    [final] ).

cnf(i_0_14210,plain,
    ( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_List_Olistrelp(X4,X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8260]),
    [final] ).

cnf(i_0_14211,plain,
    ( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_List_Olistrelp(X4,X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8261]),
    [final] ).

cnf(i_0_14212,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14213,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8262,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14214,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk576_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14215,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk571_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14216,plain,
    ( X1 = hAPP(c_Int_ORep__Integ,esk314_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)) ),
    inference(split_conjunct,[status(thm)],[i_0_8263]),
    [final] ).

cnf(i_0_14217,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk253_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8264]),
    [final] ).

cnf(i_0_14218,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk419_3(X2,X3,X1)),c_List_Olists(X1,X2)))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8265]),
    [final] ).

cnf(i_0_14219,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk392_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))
    | hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7877]),
    [final] ).

cnf(i_0_14220,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8266]),
    [final] ).

cnf(i_0_14221,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14222,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X2,X3,X1)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14223,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X2,X3,X1)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14224,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk391_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7877]),
    [final] ).

cnf(i_0_14225,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8267]),
    [final] ).

cnf(i_0_14226,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8268]),
    [final] ).

cnf(i_0_14227,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8269]),
    [final] ).

cnf(i_0_14228,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8270]),
    [final] ).

cnf(i_0_14229,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8266]),
    [final] ).

cnf(i_0_14230,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14231,plain,
    ( c_Fun_Oinj__on(X1,X2,esk24_4(X3,X2,X1,X4),X4)
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X2,X1,X5),X3) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_6647]),
    [final] ).

cnf(i_0_14232,plain,
    ( c_List_Olistrelp(X1,X2,X3,X4)
    | ~ c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8260]),
    [final] ).

cnf(i_0_14233,plain,
    ( hBOOL(hAPP(X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
    | ~ epred2_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14234,plain,
    ( hBOOL(hAPP(X5,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
    | ~ epred1_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8271]),
    [final] ).

cnf(i_0_14236,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8272]),
    [final] ).

cnf(i_0_14237,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8273]),
    [final] ).

cnf(i_0_14238,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8274]),
    [final] ).

cnf(i_0_14239,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk246_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8275]),
    [final] ).

cnf(i_0_14240,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8276]),
    [final] ).

cnf(i_0_14241,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8277]),
    [final] ).

cnf(i_0_14242,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7804]),
    [final] ).

cnf(i_0_14243,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7805]),
    [final] ).

cnf(i_0_14244,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8278]),
    [final] ).

cnf(i_0_14245,plain,
    ( hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8279]),
    [final] ).

cnf(i_0_14246,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8280]),
    [final] ).

cnf(i_0_14247,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8281]),
    [final] ).

cnf(i_0_14248,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7993]),
    [final] ).

cnf(i_0_14249,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8282]),
    [final] ).

cnf(i_0_14250,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7950]),
    [final] ).

cnf(i_0_14251,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8283]),
    [final] ).

cnf(i_0_14252,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8114]),
    [final] ).

cnf(i_0_14253,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8284]),
    [final] ).

cnf(i_0_14254,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8115]),
    [final] ).

cnf(i_0_14255,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7953]),
    [final] ).

cnf(i_0_14256,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8285]),
    [final] ).

cnf(i_0_14257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8286]),
    [final] ).

cnf(i_0_14258,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8287]),
    [final] ).

cnf(i_0_14259,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7955]),
    [final] ).

cnf(i_0_14260,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14261,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8288]),
    [final] ).

cnf(i_0_14262,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8289]),
    [final] ).

cnf(i_0_14263,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8290]),
    [final] ).

cnf(i_0_14264,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8291]),
    [final] ).

cnf(i_0_14265,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8292]),
    [final] ).

cnf(i_0_14266,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8293]),
    [final] ).

cnf(i_0_14267,plain,
    ( c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6772]),
    [final] ).

cnf(i_0_14268,plain,
    ( c_Nitpick_Onorm__frac(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6772]),
    [final] ).

cnf(i_0_14269,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk91_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8294]),
    [final] ).

cnf(i_0_14270,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk43_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8295]),
    [final] ).

cnf(i_0_14271,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk41_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8296]),
    [final] ).

cnf(i_0_14272,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X3)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_14273,plain,
    c_List_Omaps(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(X3,X4)),c_List_Omaps(X1,X2,X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_8297]),
    [final] ).

cnf(i_0_14274,plain,
    ( hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = c_List_Olist_ONil(X1)
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk427_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8298,c_0_6143]),
    [final] ).

cnf(i_0_14275,plain,
    ( c_List_Olist_ONil(X1) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk428_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8299,c_0_6143]),
    [final] ).

cnf(i_0_14276,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8300]),
    [final] ).

cnf(i_0_14277,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8301]),
    [final] ).

cnf(i_0_14278,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14279,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8302]),
    [final] ).

cnf(i_0_14280,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4)))) = hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4)),
    inference(rw,[status(thm)],[i_0_8303,c_0_8304]),
    [final] ).

cnf(i_0_14281,plain,
    ( hBOOL(hAPP(X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
    | ~ epred2_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14282,plain,
    ( hBOOL(hAPP(X5,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
    | ~ epred1_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14283,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(c_List_Oset(X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8305]),
    [final] ).

cnf(i_0_14284,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8306]),
    [final] ).

cnf(i_0_14285,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8307]),
    [final] ).

cnf(i_0_14286,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8308]),
    [final] ).

cnf(i_0_14287,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8309]),
    [final] ).

cnf(i_0_14288,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_14289,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8311]),
    [final] ).

cnf(i_0_14290,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8312]),
    [final] ).

cnf(i_0_14291,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk394_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8313]),
    [final] ).

cnf(i_0_14292,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14293,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8314]),
    [final] ).

cnf(i_0_14294,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8315]),
    [final] ).

cnf(i_0_14295,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8316]),
    [final] ).

cnf(i_0_14296,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8317]),
    [final] ).

cnf(i_0_14297,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8318]),
    [final] ).

cnf(i_0_14298,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8319]),
    [final] ).

cnf(i_0_14299,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6)) = hAPP(hAPP(c_List_Olist_OCons(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8037]),
    [final] ).

cnf(i_0_14300,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8320]),
    [final] ).

cnf(i_0_14301,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8321]),
    [final] ).

cnf(i_0_14302,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8322]),
    [final] ).

cnf(i_0_14303,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8323]),
    [final] ).

cnf(i_0_14304,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8324]),
    [final] ).

cnf(i_0_14305,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8325]),
    [final] ).

cnf(i_0_14306,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3) = X3,
    inference(rw,[status(thm)],[i_0_8326,c_0_6097]),
    [final] ).

cnf(i_0_14307,plain,
    ( hAPP(X4,X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7416]),
    [final] ).

cnf(i_0_14308,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8327]),
    [final] ).

cnf(i_0_14309,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8328]),
    [final] ).

cnf(i_0_14310,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_14311,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8127]),
    [final] ).

cnf(i_0_14312,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8329]),
    [final] ).

cnf(i_0_14313,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8330]),
    [final] ).

cnf(i_0_14314,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8331]),
    [final] ).

cnf(i_0_14315,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8332]),
    [final] ).

cnf(i_0_14316,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8333]),
    [final] ).

cnf(i_0_14317,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14318,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14319,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8334]),
    [final] ).

cnf(i_0_14320,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8335]),
    [final] ).

cnf(i_0_14321,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8334]),
    [final] ).

cnf(i_0_14322,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8336]),
    [final] ).

cnf(i_0_14323,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14324,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14325,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8337]),
    [final] ).

cnf(i_0_14326,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_8338]),
    [final] ).

cnf(i_0_14327,plain,
    c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X4,X5)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,hAPP(X3,X4),c_Lazy__Sequence_Omap(X1,X2,X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_8339]),
    [final] ).

cnf(i_0_14328,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk577_3(X2,X1,X3))),esk578_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14329,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk573_3(X2,X1,X3))),esk574_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14330,plain,
    c_List_Otranspose(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),c_List_Otranspose(X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_8340]),
    [final] ).

cnf(i_0_14331,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8341,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14332,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8342,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14333,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8343]),
    [final] ).

cnf(i_0_14334,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8344]),
    [final] ).

cnf(i_0_14335,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8345]),
    [final] ).

cnf(i_0_14336,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8345]),
    [final] ).

cnf(i_0_14337,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8346]),
    [final] ).

cnf(i_0_14338,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8347]),
    [final] ).

cnf(i_0_14339,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8346]),
    [final] ).

cnf(i_0_14340,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8347]),
    [final] ).

cnf(i_0_14341,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8348]),
    [final] ).

cnf(i_0_14342,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8349]),
    [final] ).

cnf(i_0_14343,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8348]),
    [final] ).

cnf(i_0_14344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8349]),
    [final] ).

cnf(i_0_14345,plain,
    ( X3 = X4
    | hAPP(hAPP(c_List_Onth(X1),X2),X3) != hAPP(hAPP(c_List_Onth(X1),X2),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8350]),
    [final] ).

cnf(i_0_14346,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | hAPP(hAPP(c_List_Onth(X1),X2),X3) != hAPP(hAPP(c_List_Onth(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_14347,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8352]),
    [final] ).

cnf(i_0_14348,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk246_2(X1,X2)),X2))
    | c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8275]),
    [final] ).

cnf(i_0_14349,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8353]),
    [final] ).

cnf(i_0_14350,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8354]),
    [final] ).

cnf(i_0_14351,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ c_Fun_Oinj__on(X1,X3,X4,hAPP(c_List_Oset(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8352]),
    [final] ).

cnf(i_0_14352,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk575_3(X1,X2,X3))),esk576_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14353,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14354,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8355]),
    [final] ).

cnf(i_0_14355,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8356,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14356,plain,
    ( X2 = X4
    | hBOOL(hAPP(hAPP(c_List_Oset(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8357,c_0_8358]),c_0_8358]),
    [final] ).

cnf(i_0_14357,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X6),X5)),X4)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8359]),
    [final] ).

cnf(i_0_14358,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = X5
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6654]),
    [final] ).

cnf(i_0_14359,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = X5
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6655]),
    [final] ).

cnf(i_0_14360,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk221_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8095]),
    [final] ).

cnf(i_0_14361,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8360]),
    [final] ).

cnf(i_0_14362,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8361]),
    [final] ).

cnf(i_0_14363,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8362]),
    [final] ).

cnf(i_0_14364,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8363]),
    [final] ).

cnf(i_0_14365,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk43_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8295]),
    [final] ).

cnf(i_0_14366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk91_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8294]),
    [final] ).

cnf(i_0_14367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk41_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8296]),
    [final] ).

cnf(i_0_14368,plain,
    ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8364]),
    [final] ).

cnf(i_0_14369,plain,
    ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8085]),
    [final] ).

cnf(i_0_14370,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(rw,[status(thm)],[i_0_8365,c_0_6732]),
    [final] ).

cnf(i_0_14371,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5334]),
    [final] ).

cnf(i_0_14372,plain,
    ( c_List_Olinorder__class_Osorted(X1,X3)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8366]),
    [final] ).

cnf(i_0_14373,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)
    | ~ hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_14374,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X3)))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8367]),
    [final] ).

cnf(i_0_14375,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8368]),
    [final] ).

cnf(i_0_14376,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8369]),
    [final] ).

cnf(i_0_14377,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(c_List_Orev(X2),X3)),X1) = hAPP(hAPP(c_List_Onth(X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_OSuc,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8370]),
    [final] ).

cnf(i_0_14378,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X1),X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8161]),
    [final] ).

cnf(i_0_14379,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8371]),
    [final] ).

cnf(i_0_14380,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8372]),
    [final] ).

cnf(i_0_14381,plain,
    hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3),X5) = hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X5),
    inference(split_conjunct,[status(thm)],[i_0_8373]),
    [final] ).

cnf(i_0_14382,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8374]),
    [final] ).

cnf(i_0_14383,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8375]),
    [final] ).

cnf(i_0_14384,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8376]),
    [final] ).

cnf(i_0_14385,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8377]),
    [final] ).

cnf(i_0_14386,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8378]),
    [final] ).

cnf(i_0_14387,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Rings_Osemiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8379]),
    [final] ).

cnf(i_0_14388,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8380]),
    [final] ).

cnf(i_0_14389,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Rings_Osemiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8381]),
    [final] ).

cnf(i_0_14390,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8382]),
    [final] ).

cnf(i_0_14391,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8383]),
    [final] ).

cnf(i_0_14392,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14393,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14394,plain,
    c_List_Olist_Olist__size(X1,X2,X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8384]),
    [final] ).

cnf(i_0_14395,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(X1,X2) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8059]),
    [final] ).

cnf(i_0_14396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(X6,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_14397,plain,
    ( hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8385]),
    [final] ).

cnf(i_0_14398,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3))))
    | X2 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8067]),
    [final] ).

cnf(i_0_14399,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_14400,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8202]),
    [final] ).

cnf(i_0_14401,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))),X3)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8386]),
    [final] ).

cnf(i_0_14402,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8387]),
    [final] ).

cnf(i_0_14403,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_8388]),
    [final] ).

cnf(i_0_14404,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8389]),
    [final] ).

cnf(i_0_14405,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8390]),
    [final] ).

cnf(i_0_14406,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7383]),
    [final] ).

cnf(i_0_14407,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7384]),
    [final] ).

cnf(i_0_14408,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8391]),
    [final] ).

cnf(i_0_14409,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8392]),
    [final] ).

cnf(i_0_14410,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8393]),
    [final] ).

cnf(i_0_14411,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8394]),
    [final] ).

cnf(i_0_14412,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7972]),
    [final] ).

cnf(i_0_14413,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7971]),
    [final] ).

cnf(i_0_14414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8395]),
    [final] ).

cnf(i_0_14415,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7978]),
    [final] ).

cnf(i_0_14416,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8396]),
    [final] ).

cnf(i_0_14417,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7980]),
    [final] ).

cnf(i_0_14418,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8397]),
    [final] ).

cnf(i_0_14419,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7981]),
    [final] ).

cnf(i_0_14420,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8398]),
    [final] ).

cnf(i_0_14421,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7983]),
    [final] ).

cnf(i_0_14422,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8399]),
    [final] ).

cnf(i_0_14423,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8400]),
    [final] ).

cnf(i_0_14424,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8401]),
    [final] ).

cnf(i_0_14425,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8211]),
    [final] ).

cnf(i_0_14426,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8402]),
    [final] ).

cnf(i_0_14427,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8403]),
    [final] ).

cnf(i_0_14428,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8404]),
    [final] ).

cnf(i_0_14429,plain,
    c_Divides_Opdivmod(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8405]),
    [final] ).

cnf(i_0_14430,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8406]),
    [final] ).

cnf(i_0_14431,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14432,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14433,plain,
    hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4) = c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8407]),
    [final] ).

cnf(i_0_14434,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_8408]),
    [final] ).

cnf(i_0_14435,plain,
    hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Relation_OField(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8409]),
    [final] ).

cnf(i_0_14436,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8244]),
    [final] ).

cnf(i_0_14437,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8245]),
    [final] ).

cnf(i_0_14438,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8410]),
    [final] ).

cnf(i_0_14439,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8288]),
    [final] ).

cnf(i_0_14440,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8411]),
    [final] ).

cnf(i_0_14441,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8412]),
    [final] ).

cnf(i_0_14442,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8413]),
    [final] ).

cnf(i_0_14443,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X1,X5),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8414]),
    [final] ).

cnf(i_0_14444,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8415]),
    [final] ).

cnf(i_0_14445,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8416]),
    [final] ).

cnf(i_0_14446,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8417]),
    [final] ).

cnf(i_0_14447,plain,
    ( hBOOL(hAPP(X4,hAPP(X3,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8418]),
    [final] ).

cnf(i_0_14448,plain,
    ( epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk571_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14449,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk111_3(X2,X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8419]),
    [final] ).

cnf(i_0_14450,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk111_3(X2,X3,X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8419]),
    [final] ).

cnf(i_0_14451,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8420]),
    [final] ).

cnf(i_0_14452,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8421]),
    [final] ).

cnf(i_0_14453,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8422]),
    [final] ).

cnf(i_0_14454,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8423]),
    [final] ).

cnf(i_0_14455,plain,
    ( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(X2,X4),X5),X3)),X1) = hAPP(X5,hAPP(hAPP(c_List_Onth(X2),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8424]),
    [final] ).

cnf(i_0_14456,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nitpick_Onat__gcd(X2,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8425]),
    [final] ).

cnf(i_0_14457,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8426]),
    [final] ).

cnf(i_0_14458,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_14459,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8427]),
    [final] ).

cnf(i_0_14460,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8428]),
    [final] ).

cnf(i_0_14461,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X5,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)
    | ~ hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_14462,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk479_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk480_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7974]),
    [final] ).

cnf(i_0_14463,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk477_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk478_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7975]),
    [final] ).

cnf(i_0_14464,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X1),esk474_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk475_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8429]),
    [final] ).

cnf(i_0_14465,plain,
    c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8430]),
    [final] ).

cnf(i_0_14466,plain,
    c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8431]),
    [final] ).

cnf(i_0_14467,plain,
    ( epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk576_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14468,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8432]),
    [final] ).

cnf(i_0_14469,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_8433]),
    [final] ).

cnf(i_0_14470,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8295]),
    [final] ).

cnf(i_0_14471,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8294]),
    [final] ).

cnf(i_0_14472,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8296]),
    [final] ).

cnf(i_0_14473,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = c_List_Oremove1(X1,X3,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8434]),
    [final] ).

cnf(i_0_14474,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8362]),
    [final] ).

cnf(i_0_14475,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8362]),
    [final] ).

cnf(i_0_14476,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8435]),
    [final] ).

cnf(i_0_14477,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_14478,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_14479,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk418_3(X2,X3,X1)),X2))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8265]),
    [final] ).

cnf(i_0_14480,plain,
    ( hAPP(c_List_Ofilter(X2,X3),c_List_Olinorder__class_Osort__key(X2,X1,X4,X5)) = c_List_Olinorder__class_Osort__key(X2,X1,X4,hAPP(c_List_Ofilter(X2,X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8436]),
    [final] ).

cnf(i_0_14481,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8437]),
    [final] ).

cnf(i_0_14482,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8438]),
    [final] ).

cnf(i_0_14483,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8439]),
    [final] ).

cnf(i_0_14484,plain,
    ( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7436]),
    [final] ).

cnf(i_0_14485,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8440]),
    [final] ).

cnf(i_0_14486,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8441]),
    [final] ).

cnf(i_0_14487,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8442]),
    [final] ).

cnf(i_0_14488,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8443]),
    [final] ).

cnf(i_0_14489,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_8444]),
    [final] ).

cnf(i_0_14490,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8445]),
    [final] ).

cnf(i_0_14491,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5341]),
    [final] ).

cnf(i_0_14492,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8446]),
    [final] ).

cnf(i_0_14493,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_14494,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8448]),
    [final] ).

cnf(i_0_14495,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8345]),
    [final] ).

cnf(i_0_14496,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8449]),
    [final] ).

cnf(i_0_14497,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8450]),
    [final] ).

cnf(i_0_14498,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8347]),
    [final] ).

cnf(i_0_14499,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8348]),
    [final] ).

cnf(i_0_14500,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8451]),
    [final] ).

cnf(i_0_14501,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8452]),
    [final] ).

cnf(i_0_14502,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8453]),
    [final] ).

cnf(i_0_14503,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8454]),
    [final] ).

cnf(i_0_14504,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_8455]),
    [final] ).

cnf(i_0_14505,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_8456]),
    [final] ).

cnf(i_0_14506,plain,
    ( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_8457,c_0_6732]),
    [final] ).

cnf(i_0_14507,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8458]),
    [final] ).

cnf(i_0_14508,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8459]),
    [final] ).

cnf(i_0_14509,plain,
    ( c_Finite__Set_Ofun__left__comm(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8460]),
    [final] ).

cnf(i_0_14510,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8461]),
    [final] ).

cnf(i_0_14511,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8462]),
    [final] ).

cnf(i_0_14512,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8463]),
    [final] ).

cnf(i_0_14513,plain,
    ( X4 = X5
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8464]),
    [final] ).

cnf(i_0_14514,plain,
    ( hAPP(X4,hAPP(X5,X7)) = hAPP(X6,X7)
    | hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_8465]),
    [final] ).

cnf(i_0_14515,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_8466]),
    [final] ).

cnf(i_0_14516,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8027]),
    [final] ).

cnf(i_0_14517,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | c_List_Oupto(X1,X2) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8051]),
    [final] ).

cnf(i_0_14518,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk369_3(X2,X1,X3)),esk367_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk367_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7075]),
    [final] ).

cnf(i_0_14519,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7437]),
    [final] ).

cnf(i_0_14520,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7438]),
    [final] ).

cnf(i_0_14521,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7439]),
    [final] ).

cnf(i_0_14522,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X2) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7440]),
    [final] ).

cnf(i_0_14523,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)) = hAPP(hAPP(c_List_Odrop(X2),X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8467]),
    [final] ).

cnf(i_0_14524,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8188]),
    [final] ).

cnf(i_0_14525,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_8468]),
    [final] ).

cnf(i_0_14526,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8469]),
    [final] ).

cnf(i_0_14527,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8470]),
    [final] ).

cnf(i_0_14528,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8471]),
    [final] ).

cnf(i_0_14529,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8472]),
    [final] ).

cnf(i_0_14530,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8473]),
    [final] ).

cnf(i_0_14531,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8474]),
    [final] ).

cnf(i_0_14532,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7925]),
    [final] ).

cnf(i_0_14533,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8475]),
    [final] ).

cnf(i_0_14534,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8476]),
    [final] ).

cnf(i_0_14535,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7925]),
    [final] ).

cnf(i_0_14536,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8475]),
    [final] ).

cnf(i_0_14537,plain,
    ( c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8477]),
    [final] ).

cnf(i_0_14538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8478]),
    [final] ).

cnf(i_0_14539,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8479]),
    [final] ).

cnf(i_0_14540,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8480]),
    [final] ).

cnf(i_0_14541,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8481]),
    [final] ).

cnf(i_0_14542,plain,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8482]),
    [final] ).

cnf(i_0_14543,plain,
    ( hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8483]),
    [final] ).

cnf(i_0_14544,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8484]),
    [final] ).

cnf(i_0_14545,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8485]),
    [final] ).

cnf(i_0_14546,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8486]),
    [final] ).

cnf(i_0_14547,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))),X2)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8487]),
    [final] ).

cnf(i_0_14548,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8488]),
    [final] ).

cnf(i_0_14549,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8489]),
    [final] ).

cnf(i_0_14550,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X3,X4,X1),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8414]),
    [final] ).

cnf(i_0_14551,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8490]),
    [final] ).

cnf(i_0_14552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),X1),X3))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8491]),
    [final] ).

cnf(i_0_14553,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7410]),
    [final] ).

cnf(i_0_14554,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7411]),
    [final] ).

cnf(i_0_14555,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8492]),
    [final] ).

cnf(i_0_14556,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8493]),
    [final] ).

cnf(i_0_14557,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8494]),
    [final] ).

cnf(i_0_14558,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8202]),
    [final] ).

cnf(i_0_14559,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X2,X3)))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8495]),
    [final] ).

cnf(i_0_14560,plain,
    hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(c_Fun_Ocomp(X1,X1,X1,X3),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8496]),
    [final] ).

cnf(i_0_14561,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8497]),
    [final] ).

cnf(i_0_14562,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8498]),
    [final] ).

cnf(i_0_14563,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk576_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14564,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk571_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8499]),
    [final] ).

cnf(i_0_14566,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8500]),
    [final] ).

cnf(i_0_14567,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8501]),
    [final] ).

cnf(i_0_14568,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[i_0_8502,c_0_6071]),
    [final] ).

cnf(i_0_14569,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8503,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14570,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8194]),
    [final] ).

cnf(i_0_14571,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8194]),
    [final] ).

cnf(i_0_14572,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8504]),
    [final] ).

cnf(i_0_14573,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oorder(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6442]),
    [final] ).

cnf(i_0_14574,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8505]),
    [final] ).

cnf(i_0_14575,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8211]),
    [final] ).

cnf(i_0_14576,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8437]),
    [final] ).

cnf(i_0_14577,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8506]),
    [final] ).

cnf(i_0_14578,plain,
    hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8507]),
    [final] ).

cnf(i_0_14579,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8508]),
    [final] ).

cnf(i_0_14580,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8509]),
    [final] ).

cnf(i_0_14581,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8510]),
    [final] ).

cnf(i_0_14582,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8205]),
    [final] ).

cnf(i_0_14583,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk393_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8199]),
    [final] ).

cnf(i_0_14584,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_8511]),
    [final] ).

cnf(i_0_14585,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_8512]),
    [final] ).

cnf(i_0_14586,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8513]),
    [final] ).

cnf(i_0_14587,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X2,X3,X1)))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14588,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8514]),
    [final] ).

cnf(i_0_14589,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8515]),
    [final] ).

cnf(i_0_14590,plain,
    ( X1 = X2
    | X1 = X3
    | hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14591,plain,
    ( X1 = X2
    | X1 = X3
    | hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14592,plain,
    ( X1 = X2
    | X3 = X2
    | hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14593,plain,
    ( X1 = X2
    | X3 = X2
    | hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14594,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8086]),
    [final] ).

cnf(i_0_14595,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8517]),
    [final] ).

cnf(i_0_14596,plain,
    ( hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | hAPP(hAPP(c_List_Oappend(X1),X3),X4) != hAPP(hAPP(c_List_Oappend(X1),X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_14597,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8518]),
    [final] ).

cnf(i_0_14598,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8519]),
    [final] ).

cnf(i_0_14599,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8519]),
    [final] ).

cnf(i_0_14600,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8520]),
    [final] ).

cnf(i_0_14601,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8521]),
    [final] ).

cnf(i_0_14602,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk217_3(X1,X2,X3)),X1))
    | hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_14603,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X2,X3,X1)))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14604,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8522]),
    [final] ).

cnf(i_0_14605,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8192]),
    [final] ).

cnf(i_0_14606,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk571_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14607,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8523]),
    [final] ).

cnf(i_0_14608,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8524]),
    [final] ).

cnf(i_0_14609,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_8525]),
    [final] ).

cnf(i_0_14610,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8526,c_0_6071]),
    [final] ).

cnf(i_0_14611,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8527,c_0_6071]),
    [final] ).

cnf(i_0_14612,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8528,c_0_6071]),
    [final] ).

cnf(i_0_14613,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8529,c_0_6071]),
    [final] ).

cnf(i_0_14614,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))) ),
    inference(rw,[status(thm)],[i_0_8530,c_0_6071]),
    [final] ).

cnf(i_0_14615,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[i_0_8531,c_0_6071]),
    [final] ).

cnf(i_0_14616,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8532]),
    [final] ).

cnf(i_0_14617,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3),
    inference(split_conjunct,[status(thm)],[i_0_8533]),
    [final] ).

cnf(i_0_14618,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6793]),
    [final] ).

cnf(i_0_14619,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk220_3(X2,X3,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8534]),
    [final] ).

cnf(i_0_14620,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8535]),
    [final] ).

cnf(i_0_14621,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2) = X2,
    inference(rw,[status(thm)],[i_0_8536,c_0_6097]),
    [final] ).

cnf(i_0_14622,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8537]),
    [final] ).

cnf(i_0_14623,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8538]),
    [final] ).

cnf(i_0_14624,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk576_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14625,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_8260]),
    [final] ).

cnf(i_0_14626,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8539]),
    [final] ).

cnf(i_0_14627,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8540]),
    [final] ).

cnf(i_0_14628,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Ois__nat(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8130]),
    [final] ).

cnf(i_0_14629,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk38_3(X2,X3,X1)),X3))
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8541]),
    [final] ).

cnf(i_0_14630,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk39_3(X2,X3,X1)),X3))
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8131]),
    [final] ).

cnf(i_0_14631,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X1),X4),X5)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8542]),
    [final] ).

cnf(i_0_14632,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk226_2(X2,X1)),X2))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8543]),
    [final] ).

cnf(i_0_14633,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8544]),
    [final] ).

cnf(i_0_14634,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8545]),
    [final] ).

cnf(i_0_14635,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8546]),
    [final] ).

cnf(i_0_14636,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_3(X1,X2,X3)),X1))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_14637,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)) ),
    inference(rw,[status(thm)],[i_0_8547,c_0_6224]),
    [final] ).

cnf(i_0_14638,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8548,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_14639,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8549]),
    [final] ).

cnf(i_0_14640,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8236]),
    [final] ).

cnf(i_0_14641,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8550]),
    [final] ).

cnf(i_0_14642,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8243]),
    [final] ).

cnf(i_0_14643,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8551]),
    [final] ).

cnf(i_0_14644,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8552]),
    [final] ).

cnf(i_0_14645,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X5)))
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_8265]),
    [final] ).

cnf(i_0_14646,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8553]),
    [final] ).

cnf(i_0_14647,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8554]),
    [final] ).

cnf(i_0_14648,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8555]),
    [final] ).

cnf(i_0_14649,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14650,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14651,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14652,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14654,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14655,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14656,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14657,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14660,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14661,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk504_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)))
    | c_List_Oall__interval__int(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8559]),
    [final] ).

cnf(i_0_14662,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7474]),
    [final] ).

cnf(i_0_14663,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7475]),
    [final] ).

cnf(i_0_14664,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7476]),
    [final] ).

cnf(i_0_14665,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7477]),
    [final] ).

cnf(i_0_14666,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8132]),
    [final] ).

cnf(i_0_14667,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8560,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14668,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8561,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14669,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8562]),
    [final] ).

cnf(i_0_14670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8563]),
    [final] ).

cnf(i_0_14671,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8140]),
    [final] ).

cnf(i_0_14672,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8564,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14673,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8565,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14674,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8566]),
    [final] ).

cnf(i_0_14675,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8567]),
    [final] ).

cnf(i_0_14676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7954]),
    [final] ).

cnf(i_0_14677,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8568]),
    [final] ).

cnf(i_0_14678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7956]),
    [final] ).

cnf(i_0_14679,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8569]),
    [final] ).

cnf(i_0_14680,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8570]),
    [final] ).

cnf(i_0_14681,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8143]),
    [final] ).

cnf(i_0_14682,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8571]),
    [final] ).

cnf(i_0_14683,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8572]),
    [final] ).

cnf(i_0_14684,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8573]),
    [final] ).

cnf(i_0_14685,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8574]),
    [final] ).

cnf(i_0_14686,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8575]),
    [final] ).

cnf(i_0_14687,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8576]),
    [final] ).

cnf(i_0_14688,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8577]),
    [final] ).

cnf(i_0_14689,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk494_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_14690,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk486_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_14691,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8578]),
    [final] ).

cnf(i_0_14692,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),X2)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[i_0_8579,c_0_6072]),
    [final] ).

cnf(i_0_14693,plain,
    hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)),X5) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8580]),
    [final] ).

cnf(i_0_14694,plain,
    ( X1 = X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) != c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8581]),
    [final] ).

cnf(i_0_14695,plain,
    ( X1 = X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) != c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8581]),
    [final] ).

cnf(i_0_14696,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk437_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_14697,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk436_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_14698,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk415_2(X1,X2)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8192]),
    [final] ).

cnf(i_0_14699,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X2),hAPP(c_Set_Ovimage(X6,X4,X1),X5)))
    | hAPP(X1,X2) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8582]),
    [final] ).

cnf(i_0_14700,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X1),hAPP(c_Set_Oimage(X4,X6,X2),X5)))
    | X1 != hAPP(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8583]),
    [final] ).

cnf(i_0_14701,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X4),hAPP(c_Set_Oimage(X1,X6,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X4 != hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7143]),
    [final] ).

cnf(i_0_14702,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X4),hAPP(c_Set_Oimage(X1,X6,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X4 != hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8584]),
    [final] ).

cnf(i_0_14703,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
    | ~ hBOOL(hAPP(X1,esk261_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7254]),
    [final] ).

cnf(i_0_14704,plain,
    ( c_Random__Sequence_ORandom(X2,X3,X1,X4) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(split_conjunct,[status(thm)],[i_0_6193]),
    [final] ).

cnf(i_0_14705,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8514]),
    [final] ).

cnf(i_0_14706,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8515]),
    [final] ).

cnf(i_0_14707,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != esk128_4(X2,X3,X4,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),X3))
    | hAPP(X2,X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_14708,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
    | ~ c_Fun_Oinj__on(X4,X6,X1,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8585]),
    [final] ).

cnf(i_0_14709,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | hAPP(X3,X5) != hAPP(X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8586]),
    [final] ).

cnf(i_0_14710,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(X3,X5) != hAPP(X3,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8587]),
    [final] ).

cnf(i_0_14711,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | hAPP(X3,X5) != hAPP(X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7352]),
    [final] ).

cnf(i_0_14712,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8588]),
    [final] ).

cnf(i_0_14713,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8589]),
    [final] ).

cnf(i_0_14714,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8590]),
    [final] ).

cnf(i_0_14715,plain,
    ( c_List_Olist__ex(X2,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8591]),
    [final] ).

cnf(i_0_14716,plain,
    ( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(X2,hAPP(X3,X5)),hAPP(X3,X4)) = hAPP(X3,X4)
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8592]),
    [final] ).

cnf(i_0_14717,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk525_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk524_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk525_1(X1)),esk525_1(X1)))
    | hAPP(X1,esk524_1(X1)) != hAPP(X1,esk525_1(X1))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_14718,plain,
    ( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = X5
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8517]),
    [final] ).

cnf(i_0_14719,plain,
    ( c_Equiv__Relations_Oequiv(X1,X3,X2)
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2) != X2
    | hAPP(c_Relation_ODomain(X1,X1),X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8594]),
    [final] ).

cnf(i_0_14720,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X4)),c_List_Oreplicate(X2,X5,X6)) = c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_14721,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk217_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_14722,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8596]),
    [final] ).

cnf(i_0_14723,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8597]),
    [final] ).

cnf(i_0_14724,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8598]),
    [final] ).

cnf(i_0_14725,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6628]),
    [final] ).

cnf(i_0_14726,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X2,X3,X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14727,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X2,X3,X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14728,plain,
    ( X4 = X5
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8599]),
    [final] ).

cnf(i_0_14729,plain,
    ( X4 = X5
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8600]),
    [final] ).

cnf(i_0_14730,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)),X1) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8601]),
    [final] ).

cnf(i_0_14731,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8602]),
    [final] ).

cnf(i_0_14732,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk38_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8541]),
    [final] ).

cnf(i_0_14733,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk127_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_14734,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8603]),
    [final] ).

cnf(i_0_14735,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8604]),
    [final] ).

cnf(i_0_14736,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8605]),
    [final] ).

cnf(i_0_14737,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8606]),
    [final] ).

cnf(i_0_14738,plain,
    ( c_Nitpick_Onat__gcd(X2,X1) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8425]),
    [final] ).

cnf(i_0_14739,plain,
    c_List_Obutlast(X1,X2) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
    inference(split_conjunct,[status(thm)],[i_0_8607]),
    [final] ).

cnf(i_0_14740,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8608]),
    [final] ).

cnf(i_0_14741,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8609]),
    [final] ).

cnf(i_0_14742,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))),
    inference(split_conjunct,[status(thm)],[i_0_8610]),
    [final] ).

cnf(i_0_14743,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk472_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8611]),
    [final] ).

cnf(i_0_14744,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk438_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8612]),
    [final] ).

cnf(i_0_14745,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk435_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_14746,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8614]),
    [final] ).

cnf(i_0_14747,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7594]),
    [final] ).

cnf(i_0_14748,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7595]),
    [final] ).

cnf(i_0_14749,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8615]),
    [final] ).

cnf(i_0_14750,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14751,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8616]),
    [final] ).

cnf(i_0_14752,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8617]),
    [final] ).

cnf(i_0_14753,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8618]),
    [final] ).

cnf(i_0_14754,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8619]),
    [final] ).

cnf(i_0_14755,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8620]),
    [final] ).

cnf(i_0_14756,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8621]),
    [final] ).

cnf(i_0_14757,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14758,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8622]),
    [final] ).

cnf(i_0_14759,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14760,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8623]),
    [final] ).

cnf(i_0_14761,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8624]),
    [final] ).

cnf(i_0_14762,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk252_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7444]),
    [final] ).

cnf(i_0_14763,plain,
    ( c_Fun_Oinj__on(X1,X3,X4,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)) != hAPP(c_Finite__Set_Ocard(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8625]),
    [final] ).

cnf(i_0_14764,plain,
    ( c_Fun_Oinj__on(X2,X1,X3,X4)
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)) != hAPP(c_Finite__Set_Ocard(X2),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8626]),
    [final] ).

cnf(i_0_14765,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_8627]),
    [final] ).

cnf(i_0_14766,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_8628,c_0_6097]),
    [final] ).

cnf(i_0_14767,plain,
    ( X2 = X4
    | ~ class_Rings_Olinordered__semidom(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8629]),
    [final] ).

cnf(i_0_14768,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),esk253_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8264]),
    [final] ).

cnf(i_0_14769,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8630,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_14770,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8631,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_14771,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8632]),
    [final] ).

cnf(i_0_14772,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk219_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8190]),
    [final] ).

cnf(i_0_14773,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8633]),
    [final] ).

cnf(i_0_14774,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8634]),
    [final] ).

cnf(i_0_14775,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk389_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | X3 = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8635]),
    [final] ).

cnf(i_0_14776,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk576_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14777,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk571_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14778,plain,
    ( hAPP(hAPP(X4,X5),X6) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X5)
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8636]),
    [final] ).

cnf(i_0_14779,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8637]),
    [final] ).

cnf(i_0_14780,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8638]),
    [final] ).

cnf(i_0_14781,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8639]),
    [final] ).

cnf(i_0_14782,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk473_3(X3,X1,X2))))
    | ~ c_List_Olist__ex(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8591]),
    [final] ).

cnf(i_0_14783,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8640]),
    [final] ).

cnf(i_0_14784,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8641]),
    [final] ).

cnf(i_0_14785,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8642]),
    [final] ).

cnf(i_0_14786,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8643]),
    [final] ).

cnf(i_0_14787,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8644]),
    [final] ).

cnf(i_0_14788,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8645]),
    [final] ).

cnf(i_0_14789,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8646]),
    [final] ).

cnf(i_0_14790,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8647]),
    [final] ).

cnf(i_0_14791,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8226]),
    [final] ).

cnf(i_0_14792,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8162]),
    [final] ).

cnf(i_0_14793,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14794,plain,
    hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8648]),
    [final] ).

cnf(i_0_14795,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk503_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8649]),
    [final] ).

cnf(i_0_14796,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Otimes__class_Otimes(X3)),X4),c_Groups_Oone__class_Oone(X3)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Groups_Ocomm__monoid__mult(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8650]),
    [final] ).

cnf(i_0_14797,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8651]),
    [final] ).

cnf(i_0_14798,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Oplus__class_Oplus(X3)),X4),c_Groups_Ozero__class_Ozero(X3)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8652]),
    [final] ).

cnf(i_0_14799,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Oplus__class_Oplus(X1)),X4),c_Groups_Ozero__class_Ozero(X1)),X3)
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8653]),
    [final] ).

cnf(i_0_14800,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8645]),
    [final] ).

cnf(i_0_14801,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8646]),
    [final] ).

cnf(i_0_14802,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8654]),
    [final] ).

cnf(i_0_14803,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),c_List_Oreplicate(X1,X4,X3)) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X4,X3)),c_List_Oreplicate(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_8655]),
    [final] ).

cnf(i_0_14804,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8656]),
    [final] ).

cnf(i_0_14805,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8657]),
    [final] ).

cnf(i_0_14806,plain,
    ( hAPP(X1,esk121_4(X1,X2,X3,X4)) = c_Groups_Ozero__class_Ozero(X4)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X1),X2) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))
    | ~ class_Rings_Ocomm__semiring__1(X4)
    | ~ class_Rings_Ono__zero__divisors(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7356]),
    [final] ).

cnf(i_0_14807,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8658]),
    [final] ).

cnf(i_0_14808,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8659]),
    [final] ).

cnf(i_0_14809,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8660]),
    [final] ).

cnf(i_0_14810,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7956]),
    [final] ).

cnf(i_0_14811,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7954]),
    [final] ).

cnf(i_0_14812,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14813,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != esk130_4(X2,X3,X4,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),X3))
    | hAPP(X2,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_14814,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk172_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8661]),
    [final] ).

cnf(i_0_14815,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk129_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_14816,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8662]),
    [final] ).

cnf(i_0_14817,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk317_2(X1,X2)),c_Int_OInteg))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8663]),
    [final] ).

cnf(i_0_14818,plain,
    ( c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Predicate_Oreflp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8080]),
    [final] ).

cnf(i_0_14819,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_8664,c_0_6071]),
    [final] ).

cnf(i_0_14820,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14821,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8665]),
    [final] ).

cnf(i_0_14822,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8666]),
    [final] ).

cnf(i_0_14823,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8667]),
    [final] ).

cnf(i_0_14824,plain,
    ( hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(c_Finite__Set_Ocard(X1),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8626]),
    [final] ).

cnf(i_0_14825,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8668]),
    [final] ).

cnf(i_0_14826,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_14827,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8669]),
    [final] ).

cnf(i_0_14828,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8670]),
    [final] ).

cnf(i_0_14829,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7971]),
    [final] ).

cnf(i_0_14830,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7972]),
    [final] ).

cnf(i_0_14831,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8671]),
    [final] ).

cnf(i_0_14832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14833,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8672]),
    [final] ).

cnf(i_0_14834,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk473_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
    | ~ c_List_Olist__ex(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8591]),
    [final] ).

cnf(i_0_14835,plain,
    ( c_Relation_Osingle__valued(X1,X4,hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X4),X3),X5))
    | ~ c_Relation_Osingle__valued(X1,X2,X3)
    | ~ c_Relation_Osingle__valued(X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8673]),
    [final] ).

cnf(i_0_14836,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_8674]),
    [final] ).

cnf(i_0_14837,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14838,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8675]),
    [final] ).

cnf(i_0_14839,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8676]),
    [final] ).

cnf(i_0_14840,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X4,X5)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8677]),
    [final] ).

cnf(i_0_14841,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X4,X5)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8678]),
    [final] ).

cnf(i_0_14842,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8679]),
    [final] ).

cnf(i_0_14843,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8680]),
    [final] ).

cnf(i_0_14844,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8681]),
    [final] ).

cnf(i_0_14845,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8682]),
    [final] ).

cnf(i_0_14846,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8683]),
    [final] ).

cnf(i_0_14847,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8684]),
    [final] ).

cnf(i_0_14848,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8685]),
    [final] ).

cnf(i_0_14849,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8686]),
    [final] ).

cnf(i_0_14850,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
    | X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8078]),
    [final] ).

cnf(i_0_14851,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
    | X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8077]),
    [final] ).

cnf(i_0_14852,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8687]),
    [final] ).

cnf(i_0_14853,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_8688]),
    [final] ).

cnf(i_0_14854,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8590]),
    [final] ).

cnf(i_0_14855,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8689]),
    [final] ).

cnf(i_0_14856,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14857,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8690]),
    [final] ).

cnf(i_0_14858,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8691]),
    [final] ).

cnf(i_0_14859,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8692]),
    [final] ).

cnf(i_0_14860,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8693]),
    [final] ).

cnf(i_0_14861,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremove1(X2,X5,X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8694]),
    [final] ).

cnf(i_0_14862,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk366_3(X2,X1,X3)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7075]),
    [final] ).

cnf(i_0_14863,plain,
    hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_Relation_ODomain(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_8695]),
    [final] ).

cnf(i_0_14864,plain,
    hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_8696]),
    [final] ).

cnf(i_0_14865,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk169_2(X1,X2)),X2))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8697]),
    [final] ).

cnf(i_0_14866,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8272]),
    [final] ).

cnf(i_0_14867,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8273]),
    [final] ).

cnf(i_0_14868,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8274]),
    [final] ).

cnf(i_0_14869,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8698]),
    [final] ).

cnf(i_0_14870,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_8699]),
    [final] ).

cnf(i_0_14871,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8700]),
    [final] ).

cnf(i_0_14872,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8199]),
    [final] ).

cnf(i_0_14873,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk567_3(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)))
    | c_List_Oall__interval__nat(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8701]),
    [final] ).

cnf(i_0_14874,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8702]),
    [final] ).

cnf(i_0_14875,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8703]),
    [final] ).

cnf(i_0_14876,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14877,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8704]),
    [final] ).

cnf(i_0_14878,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8705]),
    [final] ).

cnf(i_0_14879,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8557]),
    [final] ).

cnf(i_0_14880,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14881,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8623]),
    [final] ).

cnf(i_0_14882,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8706]),
    [final] ).

cnf(i_0_14883,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8537]),
    [final] ).

cnf(i_0_14884,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8538]),
    [final] ).

cnf(i_0_14885,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))),hAPP(X2,X3))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8707]),
    [final] ).

cnf(i_0_14886,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_8708]),
    [final] ).

cnf(i_0_14887,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8709]),
    [final] ).

cnf(i_0_14888,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),esk372_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8105]),
    [final] ).

cnf(i_0_14889,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8710]),
    [final] ).

cnf(i_0_14890,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8590]),
    [final] ).

cnf(i_0_14891,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8711]),
    [final] ).

cnf(i_0_14892,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))
    | ~ c_FunDef_Oreduction__pair(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6377]),
    [final] ).

cnf(i_0_14893,plain,
    c_List_Olex(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_8712]),
    [final] ).

cnf(i_0_14894,plain,
    ( c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oremove1(X1,X2,X3)),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8713]),
    [final] ).

cnf(i_0_14895,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))) ),
    inference(rw,[status(thm)],[i_0_8714,c_0_6224]),
    [final] ).

cnf(i_0_14896,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8715]),
    [final] ).

cnf(i_0_14897,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8716]),
    [final] ).

cnf(i_0_14898,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8717]),
    [final] ).

cnf(i_0_14899,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8718]),
    [final] ).

cnf(i_0_14900,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_Random_Oselect__weight(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X1)) = c_Random_Oselect(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8719]),
    [final] ).

cnf(i_0_14901,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8720]),
    [final] ).

cnf(i_0_14902,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Oordered__ring__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8721]),
    [final] ).

cnf(i_0_14903,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin) ),
    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_8722,c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_14904,plain,
    ( c_List_Obutlast(X2,hAPP(hAPP(c_List_Otake(X2),X1),X3)) = hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8723]),
    [final] ).

cnf(i_0_14905,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk418_3(X3,X1,X2)),esk419_3(X3,X1,X2))
    | X1 = c_List_Olist_ONil(X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8265]),
    [final] ).

cnf(i_0_14906,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8724]),
    [final] ).

cnf(i_0_14907,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk90_3(X2,X3,X1)),X2))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8725]),
    [final] ).

cnf(i_0_14908,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk89_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8725]),
    [final] ).

cnf(i_0_14909,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),X1))
    | esk227_3(X1,X2,X3) != esk228_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7587]),
    [final] ).

cnf(i_0_14910,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3)) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8726]),
    [final] ).

cnf(i_0_14911,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8727]),
    [final] ).

cnf(i_0_14912,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8300]),
    [final] ).

cnf(i_0_14913,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8301]),
    [final] ).

cnf(i_0_14914,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X3)),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8728]),
    [final] ).

cnf(i_0_14915,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X3)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8729]),
    [final] ).

cnf(i_0_14916,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X3)),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8730]),
    [final] ).

cnf(i_0_14917,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8731]),
    [final] ).

cnf(i_0_14918,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
    | c_List_Olist__all(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8133]),
    [final] ).

cnf(i_0_14919,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_8732]),
    [final] ).

cnf(i_0_14920,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_8733]),
    [final] ).

cnf(i_0_14921,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk110_3(X2,X3,X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8734]),
    [final] ).

cnf(i_0_14922,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8735]),
    [final] ).

cnf(i_0_14923,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8736]),
    [final] ).

cnf(i_0_14924,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
    | X2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7753]),
    [final] ).

cnf(i_0_14925,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk450_2(X3,X1)),X2))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk449_2(X3,X1))))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_14926,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk514_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_14927,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk513_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_14928,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk493_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_14929,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk485_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_14930,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk476_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8739]),
    [final] ).

cnf(i_0_14931,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),c_Int_OInteg)),
    inference(split_conjunct,[status(thm)],[i_0_8740]),
    [final] ).

cnf(i_0_14932,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8741]),
    [final] ).

cnf(i_0_14933,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8321]),
    [final] ).

cnf(i_0_14934,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8322]),
    [final] ).

cnf(i_0_14935,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8324]),
    [final] ).

cnf(i_0_14936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8325]),
    [final] ).

cnf(i_0_14937,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8323]),
    [final] ).

cnf(i_0_14938,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk578_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14939,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk574_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14940,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk422_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8742]),
    [final] ).

cnf(i_0_14941,plain,
    ( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5342]),
    [final] ).

cnf(i_0_14942,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8743]),
    [final] ).

cnf(i_0_14943,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8744]),
    [final] ).

cnf(i_0_14944,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8745]),
    [final] ).

cnf(i_0_14945,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8746]),
    [final] ).

cnf(i_0_14946,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8747]),
    [final] ).

cnf(i_0_14947,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_8748]),
    [final] ).

cnf(i_0_14948,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1))) = c_List_Olist_ONil(X1),
    inference(rw,[status(thm)],[i_0_8749,c_0_6143]),
    [final] ).

cnf(i_0_14949,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8750]),
    [final] ).

cnf(i_0_14950,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8751]),
    [final] ).

cnf(i_0_14951,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8212]),
    [final] ).

cnf(i_0_14952,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8752]),
    [final] ).

cnf(i_0_14953,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8212]),
    [final] ).

cnf(i_0_14954,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8753]),
    [final] ).

cnf(i_0_14955,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8754]),
    [final] ).

cnf(i_0_14956,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8755]),
    [final] ).

cnf(i_0_14957,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8213]),
    [final] ).

cnf(i_0_14958,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8756]),
    [final] ).

cnf(i_0_14959,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8213]),
    [final] ).

cnf(i_0_14960,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8757]),
    [final] ).

cnf(i_0_14961,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_8758]),
    [final] ).

cnf(i_0_14962,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk79_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_14963,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk124_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8760]),
    [final] ).

cnf(i_0_14964,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Oordered__ring__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8721]),
    [final] ).

cnf(i_0_14965,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__ring__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8721]),
    [final] ).

cnf(i_0_14966,plain,
    ( hAPP(c_Quotient_OBabs(X1,X4,X3,X5),X2) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8761]),
    [final] ).

cnf(i_0_14967,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk126_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_14968,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk125_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_14969,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8764]),
    [final] ).

cnf(i_0_14970,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8765]),
    [final] ).

cnf(i_0_14971,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8766]),
    [final] ).

cnf(i_0_14972,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14973,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14974,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8414]),
    [final] ).

cnf(i_0_14975,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8767]),
    [final] ).

cnf(i_0_14976,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8164]),
    [final] ).

cnf(i_0_14977,plain,
    ( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X4)) = hAPP(X3,X4)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8768]),
    [final] ).

cnf(i_0_14978,plain,
    ( hBOOL(hAPP(hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8769,c_0_8358]),c_0_8358]),
    [final] ).

cnf(i_0_14979,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8770]),
    [final] ).

cnf(i_0_14980,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8771]),
    [final] ).

cnf(i_0_14981,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8772]),
    [final] ).

cnf(i_0_14982,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk576_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_14983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk572_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_14984,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),X3) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3),
    inference(split_conjunct,[status(thm)],[i_0_8773]),
    [final] ).

cnf(i_0_14985,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8774]),
    [final] ).

cnf(i_0_14986,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8775]),
    [final] ).

cnf(i_0_14987,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8775]),
    [final] ).

cnf(i_0_14988,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8776]),
    [final] ).

cnf(i_0_14989,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8352]),
    [final] ).

cnf(i_0_14990,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8777]),
    [final] ).

cnf(i_0_14991,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8778]),
    [final] ).

cnf(i_0_14992,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X4
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8779]),
    [final] ).

cnf(i_0_14993,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8780]),
    [final] ).

cnf(i_0_14994,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8781]),
    [final] ).

cnf(i_0_14995,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8782]),
    [final] ).

cnf(i_0_14996,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8783]),
    [final] ).

cnf(i_0_14997,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8784]),
    [final] ).

cnf(i_0_14998,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8785]),
    [final] ).

cnf(i_0_14999,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8786]),
    [final] ).

cnf(i_0_15000,plain,
    ( hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4)) = hAPP(c_Set_OPow(X2),X5)
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_8787]),
    [final] ).

cnf(i_0_15001,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8788]),
    [final] ).

cnf(i_0_15002,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = X4
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8789]),
    [final] ).

cnf(i_0_15003,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5339]),
    [final] ).

cnf(i_0_15004,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) = X3
    | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8790,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_15005,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = X3
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8791]),
    [final] ).

cnf(i_0_15006,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8478]),
    [final] ).

cnf(i_0_15007,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8792]),
    [final] ).

cnf(i_0_15008,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8792]),
    [final] ).

cnf(i_0_15009,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8479]),
    [final] ).

cnf(i_0_15010,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8793]),
    [final] ).

cnf(i_0_15011,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8794]),
    [final] ).

cnf(i_0_15012,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8794]),
    [final] ).

cnf(i_0_15013,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8249]),
    [final] ).

cnf(i_0_15014,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8795]),
    [final] ).

cnf(i_0_15015,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8796]),
    [final] ).

cnf(i_0_15016,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8492]),
    [final] ).

cnf(i_0_15017,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
    inference(rw,[status(thm)],[i_0_8797,c_0_6732]),
    [final] ).

cnf(i_0_15018,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8798]),
    [final] ).

cnf(i_0_15019,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = X3
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8799]),
    [final] ).

cnf(i_0_15020,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__ring__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8721]),
    [final] ).

cnf(i_0_15021,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk217_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_15022,plain,
    ( hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(c_Finite__Set_Ocard(X1),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8800]),
    [final] ).

cnf(i_0_15023,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk110_3(X3,X2,X1)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8734]),
    [final] ).

cnf(i_0_15024,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),X3),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_8801]),
    [final] ).

cnf(i_0_15025,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X5),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8802]),
    [final] ).

cnf(i_0_15026,plain,
    ( hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8133]),
    [final] ).

cnf(i_0_15027,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk249_3(X3,X2,X1)))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8803]),
    [final] ).

cnf(i_0_15028,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk441_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_OtakeWhile(X1,X3,X2) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8804]),
    [final] ).

cnf(i_0_15029,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8805]),
    [final] ).

cnf(i_0_15030,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8806]),
    [final] ).

cnf(i_0_15031,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk483_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olist__all(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_15032,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk484_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8808]),
    [final] ).

cnf(i_0_15033,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk482_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8809]),
    [final] ).

cnf(i_0_15034,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8810]),
    [final] ).

cnf(i_0_15035,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8811]),
    [final] ).

cnf(i_0_15036,plain,
    hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)))),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(rw,[status(thm)],[i_0_8812,c_0_6293]),
    [final] ).

cnf(i_0_15037,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X6),X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8813]),
    [final] ).

cnf(i_0_15038,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X6),X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8814]),
    [final] ).

cnf(i_0_15039,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X6),X3)
    | ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8815]),
    [final] ).

cnf(i_0_15040,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8553]),
    [final] ).

cnf(i_0_15041,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8816]),
    [final] ).

cnf(i_0_15042,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Fields_Ofield(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8817]),
    [final] ).

cnf(i_0_15043,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8818]),
    [final] ).

cnf(i_0_15044,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8819]),
    [final] ).

cnf(i_0_15045,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8820]),
    [final] ).

cnf(i_0_15046,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8821]),
    [final] ).

cnf(i_0_15047,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8822]),
    [final] ).

cnf(i_0_15048,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(c_Divides_OnegateSnd,X3)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8823]),
    [final] ).

cnf(i_0_15049,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk208_3(X2,X3,X1)),c_Groups_Oone__class_Oone(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7027]),
    [final] ).

cnf(i_0_15050,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8540]),
    [final] ).

cnf(i_0_15051,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8824]),
    [final] ).

cnf(i_0_15052,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8825]),
    [final] ).

cnf(i_0_15053,plain,
    c_List_OtakeWhile(X1,X2,X3) = hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3),
    inference(split_conjunct,[status(thm)],[i_0_8826]),
    [final] ).

cnf(i_0_15054,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk149_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8827]),
    [final] ).

cnf(i_0_15055,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_8828]),
    [final] ).

cnf(i_0_15056,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_15057,plain,
    ( X2 = X4
    | ~ class_Rings_Olinordered__semidom(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8829]),
    [final] ).

cnf(i_0_15058,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8830,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_15059,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk544_3(X2,X3,X1)),c_Quotient_ORespects(X1,X3)))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Equiv__Relations_Oequivp(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8831]),
    [final] ).

cnf(i_0_15060,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8832]),
    [final] ).

cnf(i_0_15061,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8832]),
    [final] ).

cnf(i_0_15062,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1))))
    | ~ class_Orderings_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8833]),
    [final] ).

cnf(i_0_15063,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk432_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | hAPP(c_List_Ofilter(X1,X3),X2) = c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8834]),
    [final] ).

cnf(i_0_15064,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X3),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8657]),
    [final] ).

cnf(i_0_15065,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8835]),
    [final] ).

cnf(i_0_15066,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8836]),
    [final] ).

cnf(i_0_15067,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8837]),
    [final] ).

cnf(i_0_15068,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8838]),
    [final] ).

cnf(i_0_15069,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8839]),
    [final] ).

cnf(i_0_15070,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8840]),
    [final] ).

cnf(i_0_15071,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8841]),
    [final] ).

cnf(i_0_15072,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk169_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8697]),
    [final] ).

cnf(i_0_15073,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_8842]),
    [final] ).

cnf(i_0_15074,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8843]),
    [final] ).

cnf(i_0_15075,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk154_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_15076,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk126_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15077,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk125_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_15078,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk431_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | hAPP(c_List_Ofilter(X1,X3),X2) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8844]),
    [final] ).

cnf(i_0_15079,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk472_3(X2,X3,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8611]),
    [final] ).

cnf(i_0_15080,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk438_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8612]),
    [final] ).

cnf(i_0_15081,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk435_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_15082,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8845]),
    [final] ).

cnf(i_0_15083,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4)) = hAPP(hAPP(c_List_Onth(X1),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_8846]),
    [final] ).

cnf(i_0_15084,plain,
    hAPP(c_List_Oset(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(c_List_Oset(X1),X3),
    inference(rw,[status(thm)],[i_0_8847,c_0_6732]),
    [final] ).

cnf(i_0_15085,plain,
    hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_8848]),
    [final] ).

cnf(i_0_15086,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8849]),
    [final] ).

cnf(i_0_15087,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8850]),
    [final] ).

cnf(i_0_15088,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8851]),
    [final] ).

cnf(i_0_15089,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8850]),
    [final] ).

cnf(i_0_15090,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8852]),
    [final] ).

cnf(i_0_15091,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(c_Nat_OSuc,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8853]),
    [final] ).

cnf(i_0_15092,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8854]),
    [final] ).

cnf(i_0_15093,plain,
    ( c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Predicate_Osymp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8233]),
    [final] ).

cnf(i_0_15094,plain,
    ( c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8234]),
    [final] ).

cnf(i_0_15095,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8855]),
    [final] ).

cnf(i_0_15096,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8235]),
    [final] ).

cnf(i_0_15097,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_15098,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_8856]),
    [final] ).

cnf(i_0_15099,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8857]),
    [final] ).

cnf(i_0_15100,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | c_List_Opartition(X1,X4,X5) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X6),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8858]),
    [final] ).

cnf(i_0_15101,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8859]),
    [final] ).

cnf(i_0_15102,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8860]),
    [final] ).

cnf(i_0_15103,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_15104,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk146_2(X1,X2)),X2))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8862]),
    [final] ).

cnf(i_0_15105,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8132]),
    [final] ).

cnf(i_0_15106,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8863]),
    [final] ).

cnf(i_0_15107,plain,
    hAPP(c_Lazy__Sequence_Obind(X1,X2,X3),X4) = c_Lazy__Sequence_Oflat(X2,c_Lazy__Sequence_Omap(X1,tc_Lazy__Sequence_Olazy__sequence(X2),X4,X3)),
    inference(split_conjunct,[status(thm)],[i_0_8864]),
    [final] ).

cnf(i_0_15108,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8865]),
    [final] ).

cnf(i_0_15109,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8415]),
    [final] ).

cnf(i_0_15110,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8416]),
    [final] ).

cnf(i_0_15111,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8866]),
    [final] ).

cnf(i_0_15112,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X4,X5,X2),X1),X3))
    | ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8418]),
    [final] ).

cnf(i_0_15113,plain,
    hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = hAPP(c_Relation_ODomain(X1,X1),X2),
    inference(rw,[status(thm)],[i_0_8867,c_0_6104]),
    [final] ).

cnf(i_0_15114,plain,
    hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = hAPP(c_Relation_ORange(X1,X1),X2),
    inference(rw,[status(thm)],[i_0_8868,c_0_6104]),
    [final] ).

cnf(i_0_15115,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8869]),
    [final] ).

cnf(i_0_15116,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8870]),
    [final] ).

cnf(i_0_15117,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8871]),
    [final] ).

cnf(i_0_15118,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8872]),
    [final] ).

cnf(i_0_15119,plain,
    ( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8873]),
    [final] ).

cnf(i_0_15120,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_8874]),
    [final] ).

cnf(i_0_15121,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8875]),
    [final] ).

cnf(i_0_15122,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)) = hAPP(c_Set_Oimage(X1,X4,X5),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8876]),
    [final] ).

cnf(i_0_15123,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8877,c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_15124,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8878,c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_15125,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8879]),
    [final] ).

cnf(i_0_15126,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8880]),
    [final] ).

cnf(i_0_15127,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8881]),
    [final] ).

cnf(i_0_15128,plain,
    ( c_Wellfounded_Owf(X1,X3)
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8882]),
    [final] ).

cnf(i_0_15129,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8883]),
    [final] ).

cnf(i_0_15130,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8884]),
    [final] ).

cnf(i_0_15131,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8885]),
    [final] ).

cnf(i_0_15132,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8886]),
    [final] ).

cnf(i_0_15133,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8887]),
    [final] ).

cnf(i_0_15134,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8777]),
    [final] ).

cnf(i_0_15135,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk318_1(X1)),c_Int_OInteg)),
    inference(split_conjunct,[status(thm)],[i_0_8888]),
    [final] ).

cnf(i_0_15136,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8889,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_15137,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8890,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_15138,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8891]),
    [final] ).

cnf(i_0_15139,plain,
    ( hBOOL(hAPP(X1,esk569_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
    | ~ class_Rings_Odvd(X3)
    | ~ class_Rings_Osemiring__0(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7721]),
    [final] ).

cnf(i_0_15140,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8892]),
    [final] ).

cnf(i_0_15141,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8469]),
    [final] ).

cnf(i_0_15142,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8893]),
    [final] ).

cnf(i_0_15143,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8894]),
    [final] ).

cnf(i_0_15144,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8895]),
    [final] ).

cnf(i_0_15145,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8896]),
    [final] ).

cnf(i_0_15146,plain,
    c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5))),
    inference(split_conjunct,[status(thm)],[i_0_8897]),
    [final] ).

cnf(i_0_15147,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8898]),
    [final] ).

cnf(i_0_15148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15149,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8900]),
    [final] ).

cnf(i_0_15150,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15151,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15152,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk217_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_15153,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Opartition(X1,X4,X5) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8858]),
    [final] ).

cnf(i_0_15154,plain,
    hAPP(X1,hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),X4)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),hAPP(X1,X4)),
    inference(split_conjunct,[status(thm)],[i_0_8902]),
    [final] ).

cnf(i_0_15155,plain,
    ( hBOOL(hAPP(X1,esk172_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8661]),
    [final] ).

cnf(i_0_15156,plain,
    ( hBOOL(hAPP(X2,X3))
    | hAPP(c_List_Ofilter(X4,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X5),X3),X6)) = hAPP(c_List_Ofilter(X4,X2),X6)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8903]),
    [final] ).

cnf(i_0_15157,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8904]),
    [final] ).

cnf(i_0_15158,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8905]),
    [final] ).

cnf(i_0_15159,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8906]),
    [final] ).

cnf(i_0_15160,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8907]),
    [final] ).

cnf(i_0_15161,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8908]),
    [final] ).

cnf(i_0_15162,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8909]),
    [final] ).

cnf(i_0_15163,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8910]),
    [final] ).

cnf(i_0_15164,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8911]),
    [final] ).

cnf(i_0_15165,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8912]),
    [final] ).

cnf(i_0_15166,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8913]),
    [final] ).

cnf(i_0_15167,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8914]),
    [final] ).

cnf(i_0_15168,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8915]),
    [final] ).

cnf(i_0_15169,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8916]),
    [final] ).

cnf(i_0_15170,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8917]),
    [final] ).

cnf(i_0_15171,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8918]),
    [final] ).

cnf(i_0_15172,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8919]),
    [final] ).

cnf(i_0_15173,plain,
    ( hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_List_Oset(X2),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8920]),
    [final] ).

cnf(i_0_15174,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15175,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8689]),
    [final] ).

cnf(i_0_15176,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8922]),
    [final] ).

cnf(i_0_15177,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8923]),
    [final] ).

cnf(i_0_15178,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8924]),
    [final] ).

cnf(i_0_15179,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8925]),
    [final] ).

cnf(i_0_15180,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8925]),
    [final] ).

cnf(i_0_15181,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8926]),
    [final] ).

cnf(i_0_15182,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8927]),
    [final] ).

cnf(i_0_15183,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8928]),
    [final] ).

cnf(i_0_15184,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8929]),
    [final] ).

cnf(i_0_15185,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8930]),
    [final] ).

cnf(i_0_15186,plain,
    ( hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8931]),
    [final] ).

cnf(i_0_15187,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8932]),
    [final] ).

cnf(i_0_15188,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8933]),
    [final] ).

cnf(i_0_15189,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8934]),
    [final] ).

cnf(i_0_15190,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8935]),
    [final] ).

cnf(i_0_15191,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[i_0_8936,c_0_6071]),
    [final] ).

cnf(i_0_15192,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8777]),
    [final] ).

cnf(i_0_15193,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_8937]),
    [final] ).

cnf(i_0_15194,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X3,X2))))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8266]),
    [final] ).

cnf(i_0_15195,plain,
    ( c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)) = X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8938]),
    [final] ).

cnf(i_0_15196,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk319_3(X2,X3,X1)),X2))
    | hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_15197,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_8940]),
    [final] ).

cnf(i_0_15198,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk171_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8661]),
    [final] ).

cnf(i_0_15199,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15200,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X4) = X3
    | X1 != hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
    | X4 != hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_15201,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8943]),
    [final] ).

cnf(i_0_15202,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_8944,c_0_6071]),
    [final] ).

cnf(i_0_15203,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8190]),
    [final] ).

cnf(i_0_15204,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | hAPP(hAPP(c_List_Onth(X2),X3),X1) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8313]),
    [final] ).

cnf(i_0_15205,plain,
    ( hBOOL(hAPP(X1,esk156_3(X2,X3,X1)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_15206,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8945]),
    [final] ).

cnf(i_0_15207,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_8946]),
    [final] ).

cnf(i_0_15208,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))
    | hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1)))
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7975]),
    [final] ).

cnf(i_0_15209,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X5)))
    | hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1)))
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7974]),
    [final] ).

cnf(i_0_15210,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8947,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15211,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8448]),
    [final] ).

cnf(i_0_15212,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8448]),
    [final] ).

cnf(i_0_15213,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8510]),
    [final] ).

cnf(i_0_15214,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7648]),
    [final] ).

cnf(i_0_15215,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))
    | X3 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7753]),
    [final] ).

cnf(i_0_15216,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3),
    inference(split_conjunct,[status(thm)],[i_0_8948]),
    [final] ).

cnf(i_0_15217,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
    | X4 != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_8725]),
    [final] ).

cnf(i_0_15218,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7768]),
    [final] ).

cnf(i_0_15219,plain,
    ( hBOOL(hAPP(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,hAPP(c_Code__Numeral_Onat__of,esk534_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8949]),
    [final] ).

cnf(i_0_15220,plain,
    ( hAPP(X3,X6) = hAPP(X5,X6)
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6630]),
    [final] ).

cnf(i_0_15221,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))) = X2,
    inference(rw,[status(thm)],[i_0_8950,c_0_6189]),
    [final] ).

cnf(i_0_15222,plain,
    ( X2 = X3
    | hAPP(hAPP(c_List_Onth(X1),X2),esk389_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk389_3(X1,X3,X2))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8635]),
    [final] ).

cnf(i_0_15223,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8718]),
    [final] ).

cnf(i_0_15224,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8711]),
    [final] ).

cnf(i_0_15225,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8935]),
    [final] ).

cnf(i_0_15226,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8951]),
    [final] ).

cnf(i_0_15227,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_15228,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8835]),
    [final] ).

cnf(i_0_15229,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8835]),
    [final] ).

cnf(i_0_15230,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8952]),
    [final] ).

cnf(i_0_15231,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8838]),
    [final] ).

cnf(i_0_15232,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8952]),
    [final] ).

cnf(i_0_15233,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8838]),
    [final] ).

cnf(i_0_15234,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8839]),
    [final] ).

cnf(i_0_15235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8953]),
    [final] ).

cnf(i_0_15236,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8839]),
    [final] ).

cnf(i_0_15237,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8953]),
    [final] ).

cnf(i_0_15238,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15239,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8954]),
    [final] ).

cnf(i_0_15240,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8955]),
    [final] ).

cnf(i_0_15241,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8956]),
    [final] ).

cnf(i_0_15242,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8957]),
    [final] ).

cnf(i_0_15243,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8958]),
    [final] ).

cnf(i_0_15244,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8959]),
    [final] ).

cnf(i_0_15245,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8960]),
    [final] ).

cnf(i_0_15246,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8961]),
    [final] ).

cnf(i_0_15247,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8765]),
    [final] ).

cnf(i_0_15248,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8962]),
    [final] ).

cnf(i_0_15249,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8463]),
    [final] ).

cnf(i_0_15250,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8963]),
    [final] ).

cnf(i_0_15251,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8366]),
    [final] ).

cnf(i_0_15252,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8964]),
    [final] ).

cnf(i_0_15253,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8965]),
    [final] ).

cnf(i_0_15254,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_15255,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8967]),
    [final] ).

cnf(i_0_15256,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk154_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_15257,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk170_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8697]),
    [final] ).

cnf(i_0_15258,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk571_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15259,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8968,c_0_6071]),
    [final] ).

cnf(i_0_15260,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8969,c_0_6071]),
    [final] ).

cnf(i_0_15261,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8970,c_0_6071]),
    [final] ).

cnf(i_0_15262,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8971,c_0_6071]),
    [final] ).

cnf(i_0_15263,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[i_0_8972,c_0_6071]),
    [final] ).

cnf(i_0_15264,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X3),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8973]),
    [final] ).

cnf(i_0_15265,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(c_Nat_OSuc,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8974,c_0_8975]),c_0_8975]),
    [final] ).

cnf(i_0_15266,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_8976,c_0_6104]),
    [final] ).

cnf(i_0_15267,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(rw,[status(thm)],[i_0_8977,c_0_6104]),
    [final] ).

cnf(i_0_15268,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X1)))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8403]),
    [final] ).

cnf(i_0_15269,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15270,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8978]),
    [final] ).

cnf(i_0_15271,plain,
    ( hBOOL(hAPP(hAPP(X1,esk275_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_15272,plain,
    ( hBOOL(hAPP(hAPP(X1,esk274_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_15273,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))) = X3,
    inference(rw,[status(thm)],[i_0_8981,c_0_6097]),
    [final] ).

cnf(i_0_15274,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ c_List_Oall__interval__int(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8559]),
    [final] ).

cnf(i_0_15275,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_15276,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_8983,c_0_6224]),
    [final] ).

cnf(i_0_15277,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8984]),
    [final] ).

cnf(i_0_15278,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8985]),
    [final] ).

cnf(i_0_15279,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8986]),
    [final] ).

cnf(i_0_15280,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8987]),
    [final] ).

cnf(i_0_15281,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8988]),
    [final] ).

cnf(i_0_15282,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_8989]),
    [final] ).

cnf(i_0_15283,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8990]),
    [final] ).

cnf(i_0_15284,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk348_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_15285,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk347_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_15286,plain,
    ( hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1) = c_List_Olist_ONil(X2)
    | esk427_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8991,c_0_6143]),
    [final] ).

cnf(i_0_15287,plain,
    ( c_List_Olist_ONil(X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)
    | esk428_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8992,c_0_6143]),
    [final] ).

cnf(i_0_15288,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15289,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8994]),
    [final] ).

cnf(i_0_15290,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk576_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15291,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8995]),
    [final] ).

cnf(i_0_15292,plain,
    ( hBOOL(hAPP(hAPP(X3,X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8996]),
    [final] ).

cnf(i_0_15293,plain,
    ( hBOOL(hAPP(hAPP(X3,X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8997]),
    [final] ).

cnf(i_0_15294,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8998]),
    [final] ).

cnf(i_0_15295,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8999]),
    [final] ).

cnf(i_0_15296,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5)) = hAPP(c_List_Oset(X1),X3)
    | c_List_Opartition(X1,X2,X3) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_9000]),
    [final] ).

cnf(i_0_15297,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8612]),
    [final] ).

cnf(i_0_15298,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_15299,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9001]),
    [final] ).

cnf(i_0_15300,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(split_conjunct,[status(thm)],[fact_wf__less]),
    [final] ).

cnf(i_0_15301,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9002]),
    [final] ).

cnf(i_0_15302,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
    inference(rw,[status(thm)],[i_0_9003,c_0_6104]),
    [final] ).

cnf(i_0_15303,plain,
    hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_9004]),
    [final] ).

cnf(i_0_15304,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_9005,c_0_6104]),
    [final] ).

cnf(i_0_15305,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk220_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8534]),
    [final] ).

cnf(i_0_15306,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9006]),
    [final] ).

cnf(i_0_15307,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9007]),
    [final] ).

cnf(i_0_15308,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9008]),
    [final] ).

cnf(i_0_15309,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9008]),
    [final] ).

cnf(i_0_15310,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8249]),
    [final] ).

cnf(i_0_15311,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8872]),
    [final] ).

cnf(i_0_15312,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X3),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9009]),
    [final] ).

cnf(i_0_15313,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9010]),
    [final] ).

cnf(i_0_15314,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9011]),
    [final] ).

cnf(i_0_15315,plain,
    ( c_Relation_Otrans(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9012]),
    [final] ).

cnf(i_0_15316,plain,
    ( c_Wellfounded_Owf(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Owf(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9013]),
    [final] ).

cnf(i_0_15317,plain,
    ( hBOOL(hAPP(X1,esk156_3(X2,X3,X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_15318,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(X1),
    inference(rw,[status(thm)],[i_0_9014,c_0_6143]),
    [final] ).

cnf(i_0_15319,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9015]),
    [final] ).

cnf(i_0_15320,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9016]),
    [final] ).

cnf(i_0_15321,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9017]),
    [final] ).

cnf(i_0_15322,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(X3,X1)),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9018]),
    [final] ).

cnf(i_0_15323,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9019]),
    [final] ).

cnf(i_0_15324,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9020]),
    [final] ).

cnf(i_0_15325,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9021]),
    [final] ).

cnf(i_0_15326,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9022]),
    [final] ).

cnf(i_0_15327,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8766]),
    [final] ).

cnf(i_0_15328,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),c_Set_Ovimage(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_9023]),
    [final] ).

cnf(i_0_15329,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X4),c_Set_Oimage(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_9024]),
    [final] ).

cnf(i_0_15330,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Set_OPow(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9025]),
    [final] ).

cnf(i_0_15331,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8471]),
    [final] ).

cnf(i_0_15332,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9026]),
    [final] ).

cnf(i_0_15333,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9027]),
    [final] ).

cnf(i_0_15334,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9028]),
    [final] ).

cnf(i_0_15335,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9029]),
    [final] ).

cnf(i_0_15336,plain,
    ( hAPP(c_List_Orotate1(X1),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9030]),
    [final] ).

cnf(i_0_15337,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk146_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8862]),
    [final] ).

cnf(i_0_15338,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X5,
    inference(split_conjunct,[status(thm)],[i_0_9031]),
    [final] ).

cnf(i_0_15339,plain,
    c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),
    inference(rw,[status(thm)],[i_0_9032,c_0_6104]),
    [final] ).

cnf(i_0_15340,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9033]),
    [final] ).

cnf(i_0_15341,plain,
    c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_9034]),
    [final] ).

cnf(i_0_15342,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_9035]),
    [final] ).

cnf(i_0_15343,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_9036]),
    [final] ).

cnf(i_0_15344,plain,
    ( hBOOL(hAPP(hAPP(X3,esk295_2(X4,X3)),X4))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9037]),
    [final] ).

cnf(i_0_15345,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_15346,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9039]),
    [final] ).

cnf(i_0_15347,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9040]),
    [final] ).

cnf(i_0_15348,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Obutlast(X2,X3)),X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9041]),
    [final] ).

cnf(i_0_15349,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9042]),
    [final] ).

cnf(i_0_15350,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(rw,[status(thm)],[i_0_9043,c_0_6189]),
    [final] ).

cnf(i_0_15351,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9044]),
    [final] ).

cnf(i_0_15352,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9045]),
    [final] ).

cnf(i_0_15353,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7674]),
    [final] ).

cnf(i_0_15354,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9046]),
    [final] ).

cnf(i_0_15355,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9047]),
    [final] ).

cnf(i_0_15356,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk16_3(X2,X3,X1)))
    | hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7248]),
    [final] ).

cnf(i_0_15357,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9048]),
    [final] ).

cnf(i_0_15358,plain,
    ( hBOOL(hAPP(X4,esk543_3(X4,X3,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_Equiv__Relations_Oequivp(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8831]),
    [final] ).

cnf(i_0_15359,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk148_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8827]),
    [final] ).

cnf(i_0_15360,plain,
    ( hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X3),X4)) = hAPP(c_List_Orev(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9049]),
    [final] ).

cnf(i_0_15361,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9050]),
    [final] ).

cnf(i_0_15362,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8419]),
    [final] ).

cnf(i_0_15363,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9051]),
    [final] ).

cnf(i_0_15364,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9052]),
    [final] ).

cnf(i_0_15365,plain,
    hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9053]),
    [final] ).

cnf(i_0_15366,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_9054]),
    [final] ).

cnf(i_0_15367,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_9055]),
    [final] ).

cnf(i_0_15368,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9056]),
    [final] ).

cnf(i_0_15369,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15370,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15371,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9057]),
    [final] ).

cnf(i_0_15372,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
    inference(split_conjunct,[status(thm)],[i_0_9058]),
    [final] ).

cnf(i_0_15373,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7433]),
    [final] ).

cnf(i_0_15374,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7434]),
    [final] ).

cnf(i_0_15375,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7435]),
    [final] ).

cnf(i_0_15376,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9059]),
    [final] ).

cnf(i_0_15377,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9060]),
    [final] ).

cnf(i_0_15378,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9061]),
    [final] ).

cnf(i_0_15379,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9062]),
    [final] ).

cnf(i_0_15380,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X3,X2),esk36_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9063]),
    [final] ).

cnf(i_0_15381,plain,
    ( hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5) = hAPP(c_Product__Type_OPair(X2,X3),X5)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_15382,plain,
    ( hBOOL(hAPP(X1,esk16_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7248]),
    [final] ).

cnf(i_0_15383,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9064]),
    [final] ).

cnf(i_0_15384,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9065]),
    [final] ).

cnf(i_0_15385,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9066]),
    [final] ).

cnf(i_0_15386,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9067]),
    [final] ).

cnf(i_0_15387,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9068]),
    [final] ).

cnf(i_0_15388,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9069]),
    [final] ).

cnf(i_0_15389,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9070]),
    [final] ).

cnf(i_0_15390,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9071]),
    [final] ).

cnf(i_0_15391,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9072]),
    [final] ).

cnf(i_0_15392,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9073]),
    [final] ).

cnf(i_0_15393,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk578_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15394,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk573_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15395,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8439]),
    [final] ).

cnf(i_0_15396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9074]),
    [final] ).

cnf(i_0_15397,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8805]),
    [final] ).

cnf(i_0_15398,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9075]),
    [final] ).

cnf(i_0_15399,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8806]),
    [final] ).

cnf(i_0_15400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9076]),
    [final] ).

cnf(i_0_15401,plain,
    ( hAPP(c_Set_Oimage(X1,X4,hAPP(c_COMBK(X4,X1),X5)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9077]),
    [final] ).

cnf(i_0_15402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15403,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8900]),
    [final] ).

cnf(i_0_15404,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15405,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15406,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15407,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9079]),
    [final] ).

cnf(i_0_15408,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_15409,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk275_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_15410,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk274_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_15411,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8439]),
    [final] ).

cnf(i_0_15412,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9081,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_15413,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9082]),
    [final] ).

cnf(i_0_15414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9083]),
    [final] ).

cnf(i_0_15415,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk226_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8543]),
    [final] ).

cnf(i_0_15416,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15417,plain,
    hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4)) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_9085]),
    [final] ).

cnf(i_0_15418,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk147_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8862]),
    [final] ).

cnf(i_0_15419,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9086]),
    [final] ).

cnf(i_0_15420,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8766]),
    [final] ).

cnf(i_0_15421,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9087]),
    [final] ).

cnf(i_0_15422,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9088]),
    [final] ).

cnf(i_0_15423,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9089]),
    [final] ).

cnf(i_0_15424,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9090]),
    [final] ).

cnf(i_0_15425,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9091]),
    [final] ).

cnf(i_0_15426,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9092]),
    [final] ).

cnf(i_0_15427,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9093]),
    [final] ).

cnf(i_0_15428,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_15429,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9095]),
    [final] ).

cnf(i_0_15430,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9096]),
    [final] ).

cnf(i_0_15431,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),X3) = X4
    | hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9097]),
    [final] ).

cnf(i_0_15432,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_15433,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8535]),
    [final] ).

cnf(i_0_15434,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9099]),
    [final] ).

cnf(i_0_15435,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9100]),
    [final] ).

cnf(i_0_15436,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9101]),
    [final] ).

cnf(i_0_15437,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9102]),
    [final] ).

cnf(i_0_15438,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk576_3(X1,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15439,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk571_3(X1,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15440,plain,
    ( hBOOL(hAPP(X1,esk149_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8827]),
    [final] ).

cnf(i_0_15441,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9103]),
    [final] ).

cnf(i_0_15442,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9104,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_15443,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9105]),
    [final] ).

cnf(i_0_15444,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9106]),
    [final] ).

cnf(i_0_15445,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9107]),
    [final] ).

cnf(i_0_15446,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9108]),
    [final] ).

cnf(i_0_15447,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_9109]),
    [final] ).

cnf(i_0_15448,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8490]),
    [final] ).

cnf(i_0_15449,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | esk415_2(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8192]),
    [final] ).

cnf(i_0_15450,plain,
    c_List_Oreplicate(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)),X2) = hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_9110]),
    [final] ).

cnf(i_0_15451,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | c_Sum__Type_OPlus(X2,X3,X1,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15452,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | c_Sum__Type_OPlus(X3,X2,X4,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15453,plain,
    ( hAPP(c_List_Oset(X2),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)) = hAPP(c_List_Oset(X2),X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9112]),
    [final] ).

cnf(i_0_15454,plain,
    ( hAPP(X4,X5) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7360]),
    [final] ).

cnf(i_0_15455,plain,
    ( hAPP(X4,X5) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7361]),
    [final] ).

cnf(i_0_15456,plain,
    ( hAPP(X4,X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7362]),
    [final] ).

cnf(i_0_15457,plain,
    ( hAPP(X4,X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7363]),
    [final] ).

cnf(i_0_15458,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oreplicate(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_9113]),
    [final] ).

cnf(i_0_15459,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7915]),
    [final] ).

cnf(i_0_15460,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_15461,plain,
    ( X1 = X2
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9114]),
    [final] ).

cnf(i_0_15462,plain,
    ( X1 = X2
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9114]),
    [final] ).

cnf(i_0_15463,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_15464,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9115]),
    [final] ).

cnf(i_0_15465,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_15466,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9117]),
    [final] ).

cnf(i_0_15467,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9118]),
    [final] ).

cnf(i_0_15468,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8685]),
    [final] ).

cnf(i_0_15469,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8686]),
    [final] ).

cnf(i_0_15470,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X4))),X3)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9119]),
    [final] ).

cnf(i_0_15471,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9120]),
    [final] ).

cnf(i_0_15472,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9121]),
    [final] ).

cnf(i_0_15473,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9122]),
    [final] ).

cnf(i_0_15474,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9123]),
    [final] ).

cnf(i_0_15475,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9124]),
    [final] ).

cnf(i_0_15476,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9125]),
    [final] ).

cnf(i_0_15477,plain,
    ( hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9126]),
    [final] ).

cnf(i_0_15478,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9127]),
    [final] ).

cnf(i_0_15479,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9128]),
    [final] ).

cnf(i_0_15480,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15481,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15482,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15483,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9129]),
    [final] ).

cnf(i_0_15484,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9130]),
    [final] ).

cnf(i_0_15485,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9131]),
    [final] ).

cnf(i_0_15486,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9132]),
    [final] ).

cnf(i_0_15487,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8929]),
    [final] ).

cnf(i_0_15488,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),X1),c_Product__Type_Ofst(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)) = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9133]),
    [final] ).

cnf(i_0_15489,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),X3),c_Product__Type_Osnd(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)) = X4
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9134]),
    [final] ).

cnf(i_0_15490,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9135]),
    [final] ).

cnf(i_0_15491,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9136]),
    [final] ).

cnf(i_0_15492,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9137]),
    [final] ).

cnf(i_0_15493,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9138]),
    [final] ).

cnf(i_0_15494,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8734]),
    [final] ).

cnf(i_0_15495,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9139]),
    [final] ).

cnf(i_0_15496,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9140]),
    [final] ).

cnf(i_0_15497,plain,
    ( hBOOL(hAPP(X4,X2))
    | c_List_OtakeWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5)) = c_List_OtakeWhile(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9141]),
    [final] ).

cnf(i_0_15498,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9142]),
    [final] ).

cnf(i_0_15499,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9143]),
    [final] ).

cnf(i_0_15500,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15501,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9144]),
    [final] ).

cnf(i_0_15502,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9145]),
    [final] ).

cnf(i_0_15503,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9146]),
    [final] ).

cnf(i_0_15504,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9147]),
    [final] ).

cnf(i_0_15505,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9148]),
    [final] ).

cnf(i_0_15506,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9148]),
    [final] ).

cnf(i_0_15507,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X3),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9149]),
    [final] ).

cnf(i_0_15508,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9150]),
    [final] ).

cnf(i_0_15509,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15510,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    | X1 != X2
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_15511,plain,
    ( hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9151]),
    [final] ).

cnf(i_0_15512,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9152]),
    [final] ).

cnf(i_0_15513,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9153]),
    [final] ).

cnf(i_0_15514,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9154]),
    [final] ).

cnf(i_0_15515,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9155]),
    [final] ).

cnf(i_0_15516,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9156]),
    [final] ).

cnf(i_0_15517,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9157]),
    [final] ).

cnf(i_0_15518,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9158]),
    [final] ).

cnf(i_0_15519,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8512]),
    [final] ).

cnf(i_0_15520,plain,
    ( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
    | hAPP(hAPP(c_List_Onth(X1),X2),X3) != X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9097]),
    [final] ).

cnf(i_0_15521,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9159]),
    [final] ).

cnf(i_0_15522,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9160]),
    [final] ).

cnf(i_0_15523,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9161]),
    [final] ).

cnf(i_0_15524,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9162]),
    [final] ).

cnf(i_0_15525,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8478]),
    [final] ).

cnf(i_0_15526,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8479]),
    [final] ).

cnf(i_0_15527,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9163]),
    [final] ).

cnf(i_0_15528,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9164]),
    [final] ).

cnf(i_0_15529,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9165]),
    [final] ).

cnf(i_0_15530,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9166]),
    [final] ).

cnf(i_0_15531,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9167]),
    [final] ).

cnf(i_0_15532,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9168]),
    [final] ).

cnf(i_0_15533,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9169]),
    [final] ).

cnf(i_0_15534,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9170]),
    [final] ).

cnf(i_0_15535,plain,
    hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9171]),
    [final] ).

cnf(i_0_15536,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9172]),
    [final] ).

cnf(i_0_15537,plain,
    ( hBOOL(hAPP(hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),X2))
    | X1 != X2 ),
    inference(rw,[status(thm)],[i_0_9173,c_0_8358]),
    [final] ).

cnf(i_0_15538,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9174]),
    [final] ).

cnf(i_0_15539,plain,
    ( c_Relation_Osingle__valued(X1,X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))
    | ~ c_Relation_Osingle__valued(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9175]),
    [final] ).

cnf(i_0_15540,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X1),X2),X3),X4) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9176]),
    [final] ).

cnf(i_0_15541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15542,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),esk299_2(X4,X3)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9177]),
    [final] ).

cnf(i_0_15543,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X4,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9178]),
    [final] ).

cnf(i_0_15544,plain,
    ( X4 = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X4) != hAPP(X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_9179]),
    [final] ).

cnf(i_0_15545,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8960]),
    [final] ).

cnf(i_0_15546,plain,
    c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X4)),c_List_Oreplicate(X1,X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_9180]),
    [final] ).

cnf(i_0_15547,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Oempty(X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_7708]),
    [final] ).

cnf(i_0_15548,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Ohit__bound(X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_7702]),
    [final] ).

cnf(i_0_15549,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9181]),
    [final] ).

cnf(i_0_15550,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15551,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_15552,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9182]),
    [final] ).

cnf(i_0_15553,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9183]),
    [final] ).

cnf(i_0_15554,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[i_0_9184,c_0_6224]),
    [final] ).

cnf(i_0_15555,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk204_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9185]),
    [final] ).

cnf(i_0_15556,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9186]),
    [final] ).

cnf(i_0_15557,plain,
    hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9187]),
    [final] ).

cnf(i_0_15558,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9188]),
    [final] ).

cnf(i_0_15559,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9189]),
    [final] ).

cnf(i_0_15560,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9189]),
    [final] ).

cnf(i_0_15561,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))),
    inference(rw,[status(thm)],[i_0_9190,c_0_6189]),
    [final] ).

cnf(i_0_15562,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9191]),
    [final] ).

cnf(i_0_15563,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9192]),
    [final] ).

cnf(i_0_15564,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9193]),
    [final] ).

cnf(i_0_15565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8859]),
    [final] ).

cnf(i_0_15566,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8860]),
    [final] ).

cnf(i_0_15567,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Lattices_Oboolean__algebra(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9194]),
    [final] ).

cnf(i_0_15568,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9195]),
    [final] ).

cnf(i_0_15569,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_15570,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
    inference(rw,[status(thm)],[i_0_9196,c_0_6071]),
    [final] ).

cnf(i_0_15571,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
    inference(rw,[status(thm)],[i_0_9197,c_0_6071]),
    [final] ).

cnf(i_0_15572,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
    inference(rw,[status(thm)],[i_0_9198,c_0_6071]),
    [final] ).

cnf(i_0_15573,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
    inference(rw,[status(thm)],[i_0_9199,c_0_6071]),
    [final] ).

cnf(i_0_15574,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9200]),
    [final] ).

cnf(i_0_15575,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9201]),
    [final] ).

cnf(i_0_15576,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9202]),
    [final] ).

cnf(i_0_15577,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8534]),
    [final] ).

cnf(i_0_15578,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9203]),
    [final] ).

cnf(i_0_15579,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9204]),
    [final] ).

cnf(i_0_15580,plain,
    ( c_FunDef_OTHE__default(X2,X1,X3) = c_HOL_OThe(X2,X3)
    | esk495_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8083]),
    [final] ).

cnf(i_0_15581,plain,
    ( hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9205]),
    [final] ).

cnf(i_0_15582,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk18_3(X2,X3,X1)))
    | hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6765]),
    [final] ).

cnf(i_0_15583,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X5 = X6
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_9206]),
    [final] ).

cnf(i_0_15584,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(split_conjunct,[status(thm)],[fact_int__of__def]),
    [final] ).

cnf(i_0_15585,plain,
    c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_9207]),
    [final] ).

cnf(i_0_15586,plain,
    c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_9208]),
    [final] ).

cnf(i_0_15587,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_9209]),
    [final] ).

cnf(i_0_15588,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_9210]),
    [final] ).

cnf(i_0_15589,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_9211]),
    [final] ).

cnf(i_0_15590,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8713]),
    [final] ).

cnf(i_0_15591,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8870]),
    [final] ).

cnf(i_0_15592,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8871]),
    [final] ).

cnf(i_0_15593,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9212]),
    [final] ).

cnf(i_0_15594,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9213]),
    [final] ).

cnf(i_0_15595,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9214]),
    [final] ).

cnf(i_0_15596,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9215]),
    [final] ).

cnf(i_0_15597,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9216]),
    [final] ).

cnf(i_0_15598,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8788]),
    [final] ).

cnf(i_0_15599,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9217]),
    [final] ).

cnf(i_0_15600,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3) = X4
    | hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5) != X3
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8255]),
    [final] ).

cnf(i_0_15601,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3) = X4
    | hAPP(hAPP(c_List_Ozip(X1,X2),X5),X4) != X3
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8255]),
    [final] ).

cnf(i_0_15602,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3) = X3
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9218]),
    [final] ).

cnf(i_0_15603,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9219]),
    [final] ).

cnf(i_0_15604,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8634]),
    [final] ).

cnf(i_0_15605,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(split_conjunct,[status(thm)],[fact_number__of__code__numeral__def]),
    [final] ).

cnf(i_0_15606,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9220]),
    [final] ).

cnf(i_0_15607,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9221]),
    [final] ).

cnf(i_0_15608,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9222]),
    [final] ).

cnf(i_0_15609,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9223]),
    [final] ).

cnf(i_0_15610,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
    inference(split_conjunct,[status(thm)],[i_0_9224]),
    [final] ).

cnf(i_0_15611,plain,
    ( hBOOL(hAPP(X1,esk18_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6765]),
    [final] ).

cnf(i_0_15612,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9225]),
    [final] ).

cnf(i_0_15613,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9189]),
    [final] ).

cnf(i_0_15614,plain,
    ( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Orotate1(X2)),X3) = X3
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_9226,c_0_6732]),
    [final] ).

cnf(i_0_15615,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9227]),
    [final] ).

cnf(i_0_15616,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) != c_List_Olist_ONil(X1) ),
    inference(rw,[status(thm)],[i_0_9228,c_0_6732]),
    [final] ).

cnf(i_0_15617,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9229]),
    [final] ).

cnf(i_0_15618,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9230]),
    [final] ).

cnf(i_0_15619,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8883]),
    [final] ).

cnf(i_0_15620,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8884]),
    [final] ).

cnf(i_0_15621,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8886]),
    [final] ).

cnf(i_0_15622,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8887]),
    [final] ).

cnf(i_0_15623,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ c_List_Oall__interval__nat(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8701]),
    [final] ).

cnf(i_0_15624,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9231]),
    [final] ).

cnf(i_0_15625,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9232]),
    [final] ).

cnf(i_0_15626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9233]),
    [final] ).

cnf(i_0_15627,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9234]),
    [final] ).

cnf(i_0_15628,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9235]),
    [final] ).

cnf(i_0_15629,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_List_Odrop(X1),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9236]),
    [final] ).

cnf(i_0_15630,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9237]),
    [final] ).

cnf(i_0_15631,plain,
    c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9238]),
    [final] ).

cnf(i_0_15632,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9239]),
    [final] ).

cnf(i_0_15633,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9240]),
    [final] ).

cnf(i_0_15634,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9241]),
    [final] ).

cnf(i_0_15635,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9242]),
    [final] ).

cnf(i_0_15636,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9243]),
    [final] ).

cnf(i_0_15637,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9244]),
    [final] ).

cnf(i_0_15638,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8715]),
    [final] ).

cnf(i_0_15639,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9245]),
    [final] ).

cnf(i_0_15640,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8715]),
    [final] ).

cnf(i_0_15641,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9246]),
    [final] ).

cnf(i_0_15642,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9247]),
    [final] ).

cnf(i_0_15643,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9248]),
    [final] ).

cnf(i_0_15644,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8716]),
    [final] ).

cnf(i_0_15645,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9249]),
    [final] ).

cnf(i_0_15646,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8716]),
    [final] ).

cnf(i_0_15647,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9250]),
    [final] ).

cnf(i_0_15648,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_9251,c_0_6071]),
    [final] ).

cnf(i_0_15649,plain,
    ( c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = c_List_Obutlast(X2,X3)
    | X1 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_9041]),
    [final] ).

cnf(i_0_15650,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_9252]),
    [final] ).

cnf(i_0_15651,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9046]),
    [final] ).

cnf(i_0_15652,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9047]),
    [final] ).

cnf(i_0_15653,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Otranspose(X1,X2) != c_List_Olist_ONil(tc_List_Olist(X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9253]),
    [final] ).

cnf(i_0_15654,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9254]),
    [final] ).

cnf(i_0_15655,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9255]),
    [final] ).

cnf(i_0_15656,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9256]),
    [final] ).

cnf(i_0_15657,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9257]),
    [final] ).

cnf(i_0_15658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8780]),
    [final] ).

cnf(i_0_15659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9258]),
    [final] ).

cnf(i_0_15660,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_9129]),
    [final] ).

cnf(i_0_15661,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_9259]),
    [final] ).

cnf(i_0_15662,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk576_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15663,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk572_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15664,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9260]),
    [final] ).

cnf(i_0_15665,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9261]),
    [final] ).

cnf(i_0_15666,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9262]),
    [final] ).

cnf(i_0_15667,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_15668,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9263]),
    [final] ).

cnf(i_0_15669,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9264]),
    [final] ).

cnf(i_0_15670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9265]),
    [final] ).

cnf(i_0_15671,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9265]),
    [final] ).

cnf(i_0_15672,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9266]),
    [final] ).

cnf(i_0_15673,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9266]),
    [final] ).

cnf(i_0_15674,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = X4
    | X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_9267]),
    [final] ).

cnf(i_0_15675,plain,
    ( X2 = esk493_3(X3,X4,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_List_Olist__ex1(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_15676,plain,
    ( X2 = esk485_3(X3,X4,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_List_Olist__ex1(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_15677,plain,
    ( hBOOL(hAPP(X1,esk252_3(X2,X1,X3)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7444]),
    [final] ).

cnf(i_0_15678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9268]),
    [final] ).

cnf(i_0_15679,plain,
    ( hAPP(hAPP(c_List_Otake(X2),X1),c_List_Obutlast(X2,X3)) = hAPP(hAPP(c_List_Otake(X2),X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9269]),
    [final] ).

cnf(i_0_15680,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Odrop(X2),X1),X3)) = c_List_Olast(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9270]),
    [final] ).

cnf(i_0_15681,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9271,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15682,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(rw,[status(thm)],[i_0_9272,c_0_9273]),
    [final] ).

cnf(i_0_15683,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_9274]),
    [final] ).

cnf(i_0_15684,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_9275]),
    [final] ).

cnf(i_0_15685,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_8404]),
    [final] ).

cnf(i_0_15686,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))) = c_List_Oreplicate(X1,X3,X2),
    inference(rw,[status(thm)],[i_0_9276,c_0_6189]),
    [final] ).

cnf(i_0_15687,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9277]),
    [final] ).

cnf(i_0_15688,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9278]),
    [final] ).

cnf(i_0_15689,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk578_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_15690,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk574_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_15691,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8658]),
    [final] ).

cnf(i_0_15692,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9279]),
    [final] ).

cnf(i_0_15693,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9082]),
    [final] ).

cnf(i_0_15694,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9083]),
    [final] ).

cnf(i_0_15695,plain,
    ( hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9280]),
    [final] ).

cnf(i_0_15696,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15697,plain,
    ( X1 = X2
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X1),X4) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X2),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9281]),
    [final] ).

cnf(i_0_15698,plain,
    ( X1 = X2
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4),X1) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X5),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9281]),
    [final] ).

cnf(i_0_15699,plain,
    ( X2 = X4
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9282]),
    [final] ).

cnf(i_0_15700,plain,
    ( X3 = X5
    | ~ class_Orderings_Olinorder(X1)
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9283]),
    [final] ).

cnf(i_0_15701,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9284]),
    [final] ).

cnf(i_0_15702,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_9285,c_0_6224]),
    [final] ).

cnf(i_0_15703,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OposDivAlg(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9286]),
    [final] ).

cnf(i_0_15704,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9287]),
    [final] ).

cnf(i_0_15705,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9288]),
    [final] ).

cnf(i_0_15706,plain,
    hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4)) = hAPP(hAPP(c_Relation_Oinv__image(X2,X1),hAPP(c_Relation_Oconverse(X2,X2),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_9289]),
    [final] ).

cnf(i_0_15707,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9290]),
    [final] ).

cnf(i_0_15708,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9291]),
    [final] ).

cnf(i_0_15709,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9292]),
    [final] ).

cnf(i_0_15710,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9293]),
    [final] ).

cnf(i_0_15711,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1))
    | c_Random_Olog(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9294]),
    [final] ).

cnf(i_0_15712,plain,
    ( esk127_3(X4,X3,X1) = X2
    | hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_15713,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk422_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8742]),
    [final] ).

cnf(i_0_15714,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk319_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_15715,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_15716,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9295]),
    [final] ).

cnf(i_0_15717,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9296]),
    [final] ).

cnf(i_0_15718,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9297,c_0_6189]),c_0_6189]),
    [final] ).

cnf(i_0_15719,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9298]),
    [final] ).

cnf(i_0_15720,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9299]),
    [final] ).

cnf(i_0_15721,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_List_Olistsp(X3,X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9129]),
    [final] ).

cnf(i_0_15722,plain,
    hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9300]),
    [final] ).

cnf(i_0_15723,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
    | hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9301]),
    [final] ).

cnf(i_0_15724,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9302]),
    [final] ).

cnf(i_0_15725,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9303]),
    [final] ).

cnf(i_0_15726,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9304]),
    [final] ).

cnf(i_0_15727,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9305]),
    [final] ).

cnf(i_0_15728,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9306]),
    [final] ).

cnf(i_0_15729,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9307]),
    [final] ).

cnf(i_0_15730,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OnegDivAlg(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9308]),
    [final] ).

cnf(i_0_15731,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8795]),
    [final] ).

cnf(i_0_15732,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9309]),
    [final] ).

cnf(i_0_15733,plain,
    ( hAPP(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Fun_Oid(X2)
    | ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9310]),
    [final] ).

cnf(i_0_15734,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X1,X2) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9311]),
    [final] ).

cnf(i_0_15735,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk126_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15736,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk125_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_15737,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8645]),
    [final] ).

cnf(i_0_15738,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9312]),
    [final] ).

cnf(i_0_15739,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15740,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9313]),
    [final] ).

cnf(i_0_15741,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9314]),
    [final] ).

cnf(i_0_15742,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9315]),
    [final] ).

cnf(i_0_15743,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9316]),
    [final] ).

cnf(i_0_15744,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9317]),
    [final] ).

cnf(i_0_15745,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9318]),
    [final] ).

cnf(i_0_15746,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk489_3(X2,X3,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7928]),
    [final] ).

cnf(i_0_15747,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk208_3(X2,X3,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7027]),
    [final] ).

cnf(i_0_15748,plain,
    ( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4)),X1) = hAPP(hAPP(c_List_Onth(X3),X4),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9319]),
    [final] ).

cnf(i_0_15749,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9320]),
    [final] ).

cnf(i_0_15750,plain,
    ( hAPP(c_List_Orev(X2),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9321]),
    [final] ).

cnf(i_0_15751,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9050]),
    [final] ).

cnf(i_0_15752,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8810]),
    [final] ).

cnf(i_0_15753,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8810]),
    [final] ).

cnf(i_0_15754,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9322]),
    [final] ).

cnf(i_0_15755,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9323]),
    [final] ).

cnf(i_0_15756,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9324]),
    [final] ).

cnf(i_0_15757,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9325]),
    [final] ).

cnf(i_0_15758,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9326]),
    [final] ).

cnf(i_0_15759,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9327]),
    [final] ).

cnf(i_0_15760,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9328]),
    [final] ).

cnf(i_0_15761,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9329]),
    [final] ).

cnf(i_0_15762,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9330]),
    [final] ).

cnf(i_0_15763,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9331]),
    [final] ).

cnf(i_0_15764,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9332]),
    [final] ).

cnf(i_0_15765,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9333]),
    [final] ).

cnf(i_0_15766,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9334]),
    [final] ).

cnf(i_0_15767,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9229]),
    [final] ).

cnf(i_0_15768,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8996]),
    [final] ).

cnf(i_0_15769,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8997]),
    [final] ).

cnf(i_0_15770,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8998]),
    [final] ).

cnf(i_0_15771,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8999]),
    [final] ).

cnf(i_0_15772,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9335]),
    [final] ).

cnf(i_0_15773,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9336]),
    [final] ).

cnf(i_0_15774,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9337]),
    [final] ).

cnf(i_0_15775,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9338]),
    [final] ).

cnf(i_0_15776,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9339]),
    [final] ).

cnf(i_0_15777,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9340]),
    [final] ).

cnf(i_0_15778,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9341]),
    [final] ).

cnf(i_0_15779,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9342]),
    [final] ).

cnf(i_0_15780,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9343]),
    [final] ).

cnf(i_0_15781,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9344]),
    [final] ).

cnf(i_0_15782,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9345]),
    [final] ).

cnf(i_0_15783,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk394_3(X2,X3,X1)) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8313]),
    [final] ).

cnf(i_0_15784,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8742]),
    [final] ).

cnf(i_0_15785,plain,
    ( esk129_3(X4,X3,X1) = X2
    | hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_15786,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))) = c_List_OtakeWhile(X3,X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9346]),
    [final] ).

cnf(i_0_15787,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9347]),
    [final] ).

cnf(i_0_15788,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9347]),
    [final] ).

cnf(i_0_15789,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9348]),
    [final] ).

cnf(i_0_15790,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9348]),
    [final] ).

cnf(i_0_15791,plain,
    ( X1 = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9349]),
    [final] ).

cnf(i_0_15792,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9350]),
    [final] ).

cnf(i_0_15793,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9351,c_0_6097]),
    [final] ).

cnf(i_0_15794,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9233]),
    [final] ).

cnf(i_0_15795,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9352,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15796,plain,
    c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremdups(X2,X4))) = c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9353]),
    [final] ).

cnf(i_0_15797,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9354]),
    [final] ).

cnf(i_0_15798,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9355,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15799,plain,
    ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9356,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15800,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9357]),
    [final] ).

cnf(i_0_15801,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9358]),
    [final] ).

cnf(i_0_15802,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9359]),
    [final] ).

cnf(i_0_15803,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9360]),
    [final] ).

cnf(i_0_15804,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9361]),
    [final] ).

cnf(i_0_15805,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9362]),
    [final] ).

cnf(i_0_15806,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),c_Com_Ocom_Ocom__size(X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9363]),
    [final] ).

cnf(i_0_15807,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9364]),
    [final] ).

cnf(i_0_15808,plain,
    ( c_List_OtakeWhile(X3,X1,X2) = X2
    | ~ hBOOL(hAPP(X1,esk441_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8804]),
    [final] ).

cnf(i_0_15809,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9365]),
    [final] ).

cnf(i_0_15810,plain,
    ( c_List_Oall__interval__nat(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8701]),
    [final] ).

cnf(i_0_15811,plain,
    ( c_List_Oall__interval__int(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk504_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8559]),
    [final] ).

cnf(i_0_15812,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk484_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8808]),
    [final] ).

cnf(i_0_15813,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk483_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_15814,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk482_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8809]),
    [final] ).

cnf(i_0_15815,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8854]),
    [final] ).

cnf(i_0_15816,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9120]),
    [final] ).

cnf(i_0_15817,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9121]),
    [final] ).

cnf(i_0_15818,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9366]),
    [final] ).

cnf(i_0_15819,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9367]),
    [final] ).

cnf(i_0_15820,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15821,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_15822,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9086]),
    [final] ).

cnf(i_0_15823,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9087]),
    [final] ).

cnf(i_0_15824,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9088]),
    [final] ).

cnf(i_0_15825,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9089]),
    [final] ).

cnf(i_0_15826,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9090]),
    [final] ).

cnf(i_0_15827,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9091]),
    [final] ).

cnf(i_0_15828,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8869]),
    [final] ).

cnf(i_0_15829,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9092]),
    [final] ).

cnf(i_0_15830,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_15831,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_15832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9093]),
    [final] ).

cnf(i_0_15833,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9162]),
    [final] ).

cnf(i_0_15834,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9368]),
    [final] ).

cnf(i_0_15835,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9369]),
    [final] ).

cnf(i_0_15836,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(X2,X3,X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_15837,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(X2,X3,X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_15838,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))
    | hAPP(hAPP(c_List_Odrop(X1),X2),X3) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8965]),
    [final] ).

cnf(i_0_15839,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9370]),
    [final] ).

cnf(i_0_15840,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9371]),
    [final] ).

cnf(i_0_15841,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
    inference(rw,[status(thm)],[i_0_9372,c_0_6071]),
    [final] ).

cnf(i_0_15842,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_9373]),
    [final] ).

cnf(i_0_15843,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9374]),
    [final] ).

cnf(i_0_15844,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_15845,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_15846,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6618]),
    [final] ).

cnf(i_0_15847,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6619]),
    [final] ).

cnf(i_0_15848,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9375]),
    [final] ).

cnf(i_0_15849,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15850,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8492]),
    [final] ).

cnf(i_0_15851,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8492]),
    [final] ).

cnf(i_0_15852,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8788]),
    [final] ).

cnf(i_0_15853,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9376]),
    [final] ).

cnf(i_0_15854,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9377,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_15855,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_8869]),
    [final] ).

cnf(i_0_15856,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9378]),
    [final] ).

cnf(i_0_15857,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9379]),
    [final] ).

cnf(i_0_15858,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9380,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15859,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9381,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15860,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9382,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15861,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9383,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15862,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9384]),
    [final] ).

cnf(i_0_15863,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9385]),
    [final] ).

cnf(i_0_15864,plain,
    c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9386]),
    [final] ).

cnf(i_0_15865,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9131]),
    [final] ).

cnf(i_0_15866,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9132]),
    [final] ).

cnf(i_0_15867,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9387]),
    [final] ).

cnf(i_0_15868,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9388]),
    [final] ).

cnf(i_0_15869,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9389]),
    [final] ).

cnf(i_0_15870,plain,
    ( c_Random_Ominus__shift(X3,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X3),X1)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9390]),
    [final] ).

cnf(i_0_15871,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9391]),
    [final] ).

cnf(i_0_15872,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9392]),
    [final] ).

cnf(i_0_15873,plain,
    ( epred2_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9393]),
    [final] ).

cnf(i_0_15874,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9394]),
    [final] ).

cnf(i_0_15875,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Relation_ORange(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9395]),
    [final] ).

cnf(i_0_15876,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,X3),X4))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9396]),
    [final] ).

cnf(i_0_15877,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_9397]),
    [final] ).

cnf(i_0_15878,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Odrop(X3),X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9398]),
    [final] ).

cnf(i_0_15879,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Otake(X3),X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9399]),
    [final] ).

cnf(i_0_15880,plain,
    hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9400]),
    [final] ).

cnf(i_0_15881,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1)))
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8429]),
    [final] ).

cnf(i_0_15882,plain,
    ( c_List_Oupto(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9401]),
    [final] ).

cnf(i_0_15883,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8832]),
    [final] ).

cnf(i_0_15884,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5759]),
    [final] ).

cnf(i_0_15885,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk288_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9402]),
    [final] ).

cnf(i_0_15886,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9403]),
    [final] ).

cnf(i_0_15887,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9404]),
    [final] ).

cnf(i_0_15888,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9405]),
    [final] ).

cnf(i_0_15889,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_15890,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9406]),
    [final] ).

cnf(i_0_15891,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9407]),
    [final] ).

cnf(i_0_15892,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Oring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9408]),
    [final] ).

cnf(i_0_15893,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9409,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15894,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9410,c_0_6070]),c_0_6071]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_15895,plain,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk136_3(X3,X1,X2)),esk137_3(X3,X1,X2))
    | hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_15896,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9411]),
    [final] ).

cnf(i_0_15897,plain,
    ( hAPP(c_List_Ofilter(X3,X1),X2) = X2
    | ~ hBOOL(hAPP(X1,esk431_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8844]),
    [final] ).

cnf(i_0_15898,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9412]),
    [final] ).

cnf(i_0_15899,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9413]),
    [final] ).

cnf(i_0_15900,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9200]),
    [final] ).

cnf(i_0_15901,plain,
    c_Random__Sequence_Oempty(X1,X2,X3) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X1)),
    inference(split_conjunct,[status(thm)],[i_0_9414]),
    [final] ).

cnf(i_0_15902,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),X3),X4)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9415]),
    [final] ).

cnf(i_0_15903,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9416]),
    [final] ).

cnf(i_0_15904,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9417]),
    [final] ).

cnf(i_0_15905,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9418]),
    [final] ).

cnf(i_0_15906,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9419]),
    [final] ).

cnf(i_0_15907,plain,
    c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
    inference(rw,[status(thm)],[i_0_9420,c_0_7122]),
    [final] ).

cnf(i_0_15908,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Nat_OSuc,X4)) = hAPP(hAPP(X3,X4),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9421]),
    [final] ).

cnf(i_0_15909,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9422]),
    [final] ).

cnf(i_0_15910,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9423]),
    [final] ).

cnf(i_0_15911,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9424]),
    [final] ).

cnf(i_0_15912,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9425]),
    [final] ).

cnf(i_0_15913,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9426]),
    [final] ).

cnf(i_0_15914,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9427]),
    [final] ).

cnf(i_0_15915,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9428]),
    [final] ).

cnf(i_0_15916,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9429]),
    [final] ).

cnf(i_0_15917,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9430]),
    [final] ).

cnf(i_0_15918,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9431]),
    [final] ).

cnf(i_0_15919,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk123_2(X1,X2)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9432]),
    [final] ).

cnf(i_0_15920,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk126_3(X2,X1,X3))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15921,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk125_3(X2,X1,X3))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_15922,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4)))) = hAPP(X3,X4),
    inference(rw,[status(thm)],[i_0_9433,c_0_8304]),
    [final] ).

cnf(i_0_15923,plain,
    ( hBOOL(hAPP(X3,esk511_1(X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9434]),
    [final] ).

cnf(i_0_15924,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9296]),
    [final] ).

cnf(i_0_15925,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Orotate1(X2),X1) = hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Otl(X2),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),c_List_Olist_ONil(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9435]),
    [final] ).

cnf(i_0_15926,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))),
    inference(rw,[status(thm)],[i_0_9436,c_0_6189]),
    [final] ).

cnf(i_0_15927,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X3,X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9437]),
    [final] ).

cnf(i_0_15928,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X3,X4)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9438]),
    [final] ).

cnf(i_0_15929,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9439]),
    [final] ).

cnf(i_0_15930,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9440]),
    [final] ).

cnf(i_0_15931,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9441]),
    [final] ).

cnf(i_0_15932,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9442]),
    [final] ).

cnf(i_0_15933,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9443]),
    [final] ).

cnf(i_0_15934,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9444]),
    [final] ).

cnf(i_0_15935,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9445]),
    [final] ).

cnf(i_0_15936,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9446]),
    [final] ).

cnf(i_0_15937,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9447]),
    [final] ).

cnf(i_0_15938,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9448]),
    [final] ).

cnf(i_0_15939,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9449]),
    [final] ).

cnf(i_0_15940,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9450]),
    [final] ).

cnf(i_0_15941,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9451]),
    [final] ).

cnf(i_0_15942,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9452]),
    [final] ).

cnf(i_0_15943,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9453]),
    [final] ).

cnf(i_0_15944,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9454]),
    [final] ).

cnf(i_0_15945,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9455]),
    [final] ).

cnf(i_0_15946,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9456]),
    [final] ).

cnf(i_0_15947,plain,
    ( c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = c_List_Oremdups(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9457]),
    [final] ).

cnf(i_0_15948,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,X1) = hAPP(hAPP(c_List_Onth(X2),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9458]),
    [final] ).

cnf(i_0_15949,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9459]),
    [final] ).

cnf(i_0_15950,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9460]),
    [final] ).

cnf(i_0_15951,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9461]),
    [final] ).

cnf(i_0_15952,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9462]),
    [final] ).

cnf(i_0_15953,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9463]),
    [final] ).

cnf(i_0_15954,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9464]),
    [final] ).

cnf(i_0_15955,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9268]),
    [final] ).

cnf(i_0_15956,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5343]),
    [final] ).

cnf(i_0_15957,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9465]),
    [final] ).

cnf(i_0_15958,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_9466]),
    [final] ).

cnf(i_0_15959,plain,
    ( hAPP(hAPP(c_List_Onth(X3),c_List_Oreplicate(X3,X2,X4)),X1) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9467]),
    [final] ).

cnf(i_0_15960,plain,
    ( c_Sum__Type_OPlus(X2,X4,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X4),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15961,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9468]),
    [final] ).

cnf(i_0_15962,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9469]),
    [final] ).

cnf(i_0_15963,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9470]),
    [final] ).

cnf(i_0_15964,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9471]),
    [final] ).

cnf(i_0_15965,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9472]),
    [final] ).

cnf(i_0_15966,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9473]),
    [final] ).

cnf(i_0_15967,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Finite__Set_Ocard(X2),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9474]),
    [final] ).

cnf(i_0_15968,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X2),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9475]),
    [final] ).

cnf(i_0_15969,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9476]),
    [final] ).

cnf(i_0_15970,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9477]),
    [final] ).

cnf(i_0_15971,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9478]),
    [final] ).

cnf(i_0_15972,plain,
    hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9479]),
    [final] ).

cnf(i_0_15973,plain,
    hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9480]),
    [final] ).

cnf(i_0_15974,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9481]),
    [final] ).

cnf(i_0_15975,plain,
    ( hBOOL(hAPP(X2,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_15976,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X3)),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(hAPP(c_List_Otake(X2),X3),hAPP(c_List_Otl(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9482]),
    [final] ).

cnf(i_0_15977,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9280]),
    [final] ).

cnf(i_0_15978,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9483]),
    [final] ).

cnf(i_0_15979,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9484]),
    [final] ).

cnf(i_0_15980,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X2,X3,hAPP(c_COMBK(X3,X2),X4)),X1) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9485]),
    [final] ).

cnf(i_0_15981,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk433_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | c_List_Otranspose(X1,X2) = c_List_Olist_ONil(tc_List_Olist(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9253]),
    [final] ).

cnf(i_0_15982,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(rw,[status(thm)],[i_0_9486,c_0_6071]),
    [final] ).

cnf(i_0_15983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[i_0_9487,c_0_6071]),
    [final] ).

cnf(i_0_15984,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(rw,[status(thm)],[i_0_9488,c_0_6071]),
    [final] ).

cnf(i_0_15985,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[i_0_9489,c_0_6071]),
    [final] ).

cnf(i_0_15986,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_List_Oset(X2),X3))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9490]),
    [final] ).

cnf(i_0_15987,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9491]),
    [final] ).

cnf(i_0_15988,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9492]),
    [final] ).

cnf(i_0_15989,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9493]),
    [final] ).

cnf(i_0_15990,plain,
    ( hBOOL(hAPP(X2,X4))
    | c_List_OtakeWhile(X1,X2,X3) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8804]),
    [final] ).

cnf(i_0_15991,plain,
    ( hAPP(c_List_Ofilter(X1,X2),X3) != c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8834]),
    [final] ).

cnf(i_0_15992,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9494]),
    [final] ).

cnf(i_0_15993,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9495]),
    [final] ).

cnf(i_0_15994,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8808]),
    [final] ).

cnf(i_0_15995,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_15996,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8809]),
    [final] ).

cnf(i_0_15997,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[i_0_9496,c_0_6097]),
    [final] ).

cnf(i_0_15998,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[i_0_9497,c_0_6097]),
    [final] ).

cnf(i_0_15999,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9498]),
    [final] ).

cnf(i_0_16000,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9499]),
    [final] ).

cnf(i_0_16001,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9500]),
    [final] ).

cnf(i_0_16002,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9501]),
    [final] ).

cnf(i_0_16003,plain,
    ( X2 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(X1),X2) != hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9502]),
    [final] ).

cnf(i_0_16004,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9503]),
    [final] ).

cnf(i_0_16005,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))),
    inference(split_conjunct,[status(thm)],[i_0_9504]),
    [final] ).

cnf(i_0_16006,plain,
    ( X2 = X4
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9505]),
    [final] ).

cnf(i_0_16007,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9333]),
    [final] ).

cnf(i_0_16008,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9334]),
    [final] ).

cnf(i_0_16009,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9506]),
    [final] ).

cnf(i_0_16010,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9507]),
    [final] ).

cnf(i_0_16011,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9508]),
    [final] ).

cnf(i_0_16012,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9509]),
    [final] ).

cnf(i_0_16013,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9510]),
    [final] ).

cnf(i_0_16014,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9511]),
    [final] ).

cnf(i_0_16015,plain,
    ( hAPP(hAPP(X2,X5),hAPP(X3,X4)) = hAPP(X3,X4)
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9512]),
    [final] ).

cnf(i_0_16016,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9513]),
    [final] ).

cnf(i_0_16017,plain,
    ( c_List_Oall__interval__nat(X1,X2,X3)
    | ~ c_List_Olist__all(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) ),
    inference(rw,[status(thm)],[i_0_9514,c_0_6189]),
    [final] ).

cnf(i_0_16018,plain,
    ( c_Divides_OnegDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5342]),
    [final] ).

cnf(i_0_16019,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9515]),
    [final] ).

cnf(i_0_16020,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9516]),
    [final] ).

cnf(i_0_16021,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_9517]),
    [final] ).

cnf(i_0_16022,plain,
    hAPP(c_Relation_OField(X1),X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9518]),
    [final] ).

cnf(i_0_16023,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_9519,c_0_6104]),
    [final] ).

cnf(i_0_16024,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9520]),
    [final] ).

cnf(i_0_16025,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9407]),
    [final] ).

cnf(i_0_16026,plain,
    ( c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9521]),
    [final] ).

cnf(i_0_16027,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9522]),
    [final] ).

cnf(i_0_16028,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9523]),
    [final] ).

cnf(i_0_16029,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_9373]),
    [final] ).

cnf(i_0_16030,plain,
    ( hBOOL(hAPP(hAPP(c_List_Oset(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(rw,[status(thm)],[i_0_9524,c_0_8358]),
    [final] ).

cnf(i_0_16031,plain,
    ( hBOOL(hAPP(hAPP(c_List_Oset(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(rw,[status(thm)],[i_0_9525,c_0_8358]),
    [final] ).

cnf(i_0_16032,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | c_Divides_Odivmod__int(X2,X1) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9311]),
    [final] ).

cnf(i_0_16033,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9526]),
    [final] ).

cnf(i_0_16034,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
    | c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9011]),
    [final] ).

cnf(i_0_16035,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9010]),
    [final] ).

cnf(i_0_16036,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9527]),
    [final] ).

cnf(i_0_16037,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(split_conjunct,[status(thm)],[fact_Integ__def]),
    [final] ).

cnf(i_0_16038,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9528]),
    [final] ).

cnf(i_0_16039,plain,
    c_Relation_Osingle__valued(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9529,c_0_6097]),
    [final] ).

cnf(i_0_16040,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9530]),
    [final] ).

cnf(i_0_16041,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9531]),
    [final] ).

cnf(i_0_16042,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X4,X3),X2) = c_Divides_Odiv__class_Omod(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9532]),
    [final] ).

cnf(i_0_16043,plain,
    ( hAPP(X2,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8760]),
    [final] ).

cnf(i_0_16044,plain,
    ( hAPP(X2,X4) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_16045,plain,
    ( c_List_Olist__ex(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_16046,plain,
    ( c_List_Olist__ex(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_16047,plain,
    ( c_List_Olist__ex(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8739]),
    [final] ).

cnf(i_0_16048,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = c_List_Olast(X2,X3)
    | X3 = c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9267]),
    [final] ).

cnf(i_0_16049,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9533]),
    [final] ).

cnf(i_0_16050,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9534]),
    [final] ).

cnf(i_0_16051,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9535]),
    [final] ).

cnf(i_0_16052,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_6151]),
    [final] ).

cnf(i_0_16053,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Oring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9536]),
    [final] ).

cnf(i_0_16054,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9008]),
    [final] ).

cnf(i_0_16055,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9537]),
    [final] ).

cnf(i_0_16056,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9538]),
    [final] ).

cnf(i_0_16057,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9539]),
    [final] ).

cnf(i_0_16058,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9540]),
    [final] ).

cnf(i_0_16059,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9541]),
    [final] ).

cnf(i_0_16060,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9542]),
    [final] ).

cnf(i_0_16061,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_9543]),
    [final] ).

cnf(i_0_16062,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_9544]),
    [final] ).

cnf(i_0_16063,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16064,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9546]),
    [final] ).

cnf(i_0_16065,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk143_1(X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9547]),
    [final] ).

cnf(i_0_16066,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9548]),
    [final] ).

cnf(i_0_16067,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9549]),
    [final] ).

cnf(i_0_16068,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_16069,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_16070,plain,
    ( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9311]),
    [final] ).

cnf(i_0_16071,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9550]),
    [final] ).

cnf(i_0_16072,plain,
    ( c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(tc_List_Olist(X1))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9551]),
    [final] ).

cnf(i_0_16073,plain,
    ( hBOOL(hAPP(X2,X4))
    | hAPP(c_List_Ofilter(X1,X2),X3) != X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8844]),
    [final] ).

cnf(i_0_16074,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9552]),
    [final] ).

cnf(i_0_16075,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9360]),
    [final] ).

cnf(i_0_16076,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9361]),
    [final] ).

cnf(i_0_16077,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9362]),
    [final] ).

cnf(i_0_16078,plain,
    ( X1 = X2
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9553]),
    [final] ).

cnf(i_0_16079,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_9412]),
    [final] ).

cnf(i_0_16080,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_9413]),
    [final] ).

cnf(i_0_16081,plain,
    ( hBOOL(hAPP(hAPP(X1,esk525_1(X1)),esk525_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk525_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_16082,plain,
    ( hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk524_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk525_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_16083,plain,
    hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9554]),
    [final] ).

cnf(i_0_16084,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9313]),
    [final] ).

cnf(i_0_16085,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9312]),
    [final] ).

cnf(i_0_16086,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9314]),
    [final] ).

cnf(i_0_16087,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9555]),
    [final] ).

cnf(i_0_16088,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9317]),
    [final] ).

cnf(i_0_16089,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9316]),
    [final] ).

cnf(i_0_16090,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9318]),
    [final] ).

cnf(i_0_16091,plain,
    ( X3 = X4
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9556]),
    [final] ).

cnf(i_0_16092,plain,
    ( X3 = X4
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9557]),
    [final] ).

cnf(i_0_16093,plain,
    c_List_Olistset(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = c_List_Oset__Cons(X1,X2,c_List_Olistset(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_9558]),
    [final] ).

cnf(i_0_16094,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9559]),
    [final] ).

cnf(i_0_16095,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9415]),
    [final] ).

cnf(i_0_16096,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),c_Orderings_Obot__class_Obot(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9560]),
    [final] ).

cnf(i_0_16097,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9561]),
    [final] ).

cnf(i_0_16098,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8771]),
    [final] ).

cnf(i_0_16099,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9562]),
    [final] ).

cnf(i_0_16100,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9563]),
    [final] ).

cnf(i_0_16101,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9564]),
    [final] ).

cnf(i_0_16102,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(c_Finite__Set_Ocard(X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9565]),
    [final] ).

cnf(i_0_16103,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremdups(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9457]),
    [final] ).

cnf(i_0_16104,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))),
    inference(split_conjunct,[status(thm)],[i_0_9566]),
    [final] ).

cnf(i_0_16105,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9567]),
    [final] ).

cnf(i_0_16106,plain,
    c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9568]),
    [final] ).

cnf(i_0_16107,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_9569]),
    [final] ).

cnf(i_0_16108,plain,
    ( X1 = X2
    | hAPP(c_Int_Onat,X1) != hAPP(c_Int_Onat,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9570]),
    [final] ).

cnf(i_0_16109,plain,
    ( X1 = X2
    | hAPP(c_Int_Onat,X1) != hAPP(c_Int_Onat,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9571]),
    [final] ).

cnf(i_0_16110,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk139_2(X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9572]),
    [final] ).

cnf(i_0_16111,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9470]),
    [final] ).

cnf(i_0_16112,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9471]),
    [final] ).

cnf(i_0_16113,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_9573,c_0_6189]),
    [final] ).

cnf(i_0_16114,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9574]),
    [final] ).

cnf(i_0_16115,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9575]),
    [final] ).

cnf(i_0_16116,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9576]),
    [final] ).

cnf(i_0_16117,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)
    | X1 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9577]),
    [final] ).

cnf(i_0_16118,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X4),X3) = c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(X4,X2) != c_Groups_Ozero__class_Ozero(X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Rings_Ocomm__semiring__1(X5)
    | ~ class_Rings_Ono__zero__divisors(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7356]),
    [final] ).

cnf(i_0_16119,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9578]),
    [final] ).

cnf(i_0_16120,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9177]),
    [final] ).

cnf(i_0_16121,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9579]),
    [final] ).

cnf(i_0_16122,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9037]),
    [final] ).

cnf(i_0_16123,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9580]),
    [final] ).

cnf(i_0_16124,plain,
    ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_16125,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osplice(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9581]),
    [final] ).

cnf(i_0_16126,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | X2 != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9582]),
    [final] ).

cnf(i_0_16127,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9583]),
    [final] ).

cnf(i_0_16128,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9584]),
    [final] ).

cnf(i_0_16129,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X1,
    inference(rw,[status(thm)],[i_0_9585,c_0_8304]),
    [final] ).

cnf(i_0_16130,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9586]),
    [final] ).

cnf(i_0_16131,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9143]),
    [final] ).

cnf(i_0_16132,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_16133,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9587]),
    [final] ).

cnf(i_0_16134,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9588]),
    [final] ).

cnf(i_0_16135,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))),
    inference(rw,[status(thm)],[i_0_9589,c_0_6189]),
    [final] ).

cnf(i_0_16136,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9590]),
    [final] ).

cnf(i_0_16137,plain,
    ( X1 = X2
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)
    | ~ c_Nat__Transfer_Onat__set(X2)
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9591]),
    [final] ).

cnf(i_0_16138,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_9592]),
    [final] ).

cnf(i_0_16139,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_9592]),
    [final] ).

cnf(i_0_16140,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9592]),
    [final] ).

cnf(i_0_16141,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8039]),
    [final] ).

cnf(i_0_16142,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9015]),
    [final] ).

cnf(i_0_16143,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9016]),
    [final] ).

cnf(i_0_16144,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(X5,X4) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9593]),
    [final] ).

cnf(i_0_16145,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9594]),
    [final] ).

cnf(i_0_16146,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk402_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
    | hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_16147,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk401_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
    | hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_16148,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9595]),
    [final] ).

cnf(i_0_16149,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_9596]),
    [final] ).

cnf(i_0_16150,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(rw,[status(thm)],[i_0_9597,c_0_6097]),
    [final] ).

cnf(i_0_16151,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9598]),
    [final] ).

cnf(i_0_16152,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16153,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8588]),
    [final] ).

cnf(i_0_16154,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9600]),
    [final] ).

cnf(i_0_16155,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4) = c_List_Oreplicate(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9601]),
    [final] ).

cnf(i_0_16156,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9056]),
    [final] ).

cnf(i_0_16157,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X5))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9602]),
    [final] ).

cnf(i_0_16158,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X5))
    | ~ c_Predicate_Otransp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9603]),
    [final] ).

cnf(i_0_16159,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X5))
    | ~ c_Equiv__Relations_Oequivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9604]),
    [final] ).

cnf(i_0_16160,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9605]),
    [final] ).

cnf(i_0_16161,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)
    | ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9606]),
    [final] ).

cnf(i_0_16162,plain,
    ( c_Divides_Odivmod__int(X2,X1) = c_Divides_OposDivAlg(X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9311]),
    [final] ).

cnf(i_0_16163,plain,
    hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_Osublists(X1,X2))) = hAPP(c_Set_OPow(X1),hAPP(c_List_Oset(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9607]),
    [final] ).

cnf(i_0_16164,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9608]),
    [final] ).

cnf(i_0_16165,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9609]),
    [final] ).

cnf(i_0_16166,plain,
    ( c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_OtakeWhile(X3,X1,X4))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16167,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9611]),
    [final] ).

cnf(i_0_16168,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9612]),
    [final] ).

cnf(i_0_16169,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8222]),
    [final] ).

cnf(i_0_16170,plain,
    ( hAPP(X1,esk127_3(X1,X2,X3)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_16171,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk204_2(X2,X3)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9185]),
    [final] ).

cnf(i_0_16172,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9613]),
    [final] ).

cnf(i_0_16173,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9614]),
    [final] ).

cnf(i_0_16174,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9615]),
    [final] ).

cnf(i_0_16175,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_9616]),
    [final] ).

cnf(i_0_16176,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9617]),
    [final] ).

cnf(i_0_16177,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9618]),
    [final] ).

cnf(i_0_16178,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9619]),
    [final] ).

cnf(i_0_16179,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9620]),
    [final] ).

cnf(i_0_16180,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9621]),
    [final] ).

cnf(i_0_16181,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9622]),
    [final] ).

cnf(i_0_16182,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_9623]),
    [final] ).

cnf(i_0_16183,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk512_2(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9434]),
    [final] ).

cnf(i_0_16184,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9624]),
    [final] ).

cnf(i_0_16185,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9625]),
    [final] ).

cnf(i_0_16186,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9626]),
    [final] ).

cnf(i_0_16187,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9627]),
    [final] ).

cnf(i_0_16188,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9628]),
    [final] ).

cnf(i_0_16189,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9391]),
    [final] ).

cnf(i_0_16190,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9392]),
    [final] ).

cnf(i_0_16191,plain,
    hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9629]),
    [final] ).

cnf(i_0_16192,plain,
    hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9630]),
    [final] ).

cnf(i_0_16193,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_9631]),
    [final] ).

cnf(i_0_16194,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9632]),
    [final] ).

cnf(i_0_16195,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9633]),
    [final] ).

cnf(i_0_16196,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9506]),
    [final] ).

cnf(i_0_16197,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9509]),
    [final] ).

cnf(i_0_16198,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9507]),
    [final] ).

cnf(i_0_16199,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9510]),
    [final] ).

cnf(i_0_16200,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9508]),
    [final] ).

cnf(i_0_16201,plain,
    ( X2 = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))
    | hAPP(c_List_Orev(X1),X2) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9321]),
    [final] ).

cnf(i_0_16202,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9634]),
    [final] ).

cnf(i_0_16203,plain,
    ( c_List_Olist__ex(X1,X2,X3)
    | c_List_Olist__ex(X1,X2,X4)
    | ~ c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9635]),
    [final] ).

cnf(i_0_16204,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9636]),
    [final] ).

cnf(i_0_16205,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16206,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9637,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16207,plain,
    ( X1 = c_Int_OMin
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != c_Int_OMin ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9638,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16208,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8954]),
    [final] ).

cnf(i_0_16209,plain,
    hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9639]),
    [final] ).

cnf(i_0_16210,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X1,X2),X3) = c_Lazy__Sequence_Oproduct(X1,X2,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | ~ class_Lazy__Sequence_Osmall__lazy(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9640]),
    [final] ).

cnf(i_0_16211,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X7)
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X5,X2),X6),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_9641]),
    [final] ).

cnf(i_0_16212,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != c_Int_OPls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9642,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16213,plain,
    c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9643,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16214,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9644]),
    [final] ).

cnf(i_0_16215,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_9645]),
    [final] ).

cnf(i_0_16216,plain,
    ( X3 = X5
    | hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_9646]),
    [final] ).

cnf(i_0_16217,plain,
    ( X4 = X5
    | hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_9647]),
    [final] ).

cnf(i_0_16218,plain,
    c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9648,c_0_6097]),
    [final] ).

cnf(i_0_16219,plain,
    c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9649,c_0_6097]),
    [final] ).

cnf(i_0_16220,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9650,c_0_6097]),
    [final] ).

cnf(i_0_16221,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_9651,c_0_8358]),
    [final] ).

cnf(i_0_16222,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_9652,c_0_8358]),
    [final] ).

cnf(i_0_16223,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)) = X1
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9653]),
    [final] ).

cnf(i_0_16224,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(X1,esk79_3(X1,X2,X3)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_16225,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(X1,esk124_3(X1,X2,X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8760]),
    [final] ).

cnf(i_0_16226,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_OField(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9654]),
    [final] ).

cnf(i_0_16227,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9655]),
    [final] ).

cnf(i_0_16228,plain,
    ( hAPP(c_Nat_OSuc,X1) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9656]),
    [final] ).

cnf(i_0_16229,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk81_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9657]),
    [final] ).

cnf(i_0_16230,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk78_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9658]),
    [final] ).

cnf(i_0_16231,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9659]),
    [final] ).

cnf(i_0_16232,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | X1 != X2
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_9114]),
    [final] ).

cnf(i_0_16233,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9660]),
    [final] ).

cnf(i_0_16234,plain,
    ( hAPP(c_Set_Oimage(X2,X3,hAPP(c_COMBK(X3,X2),X4)),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9485]),
    [final] ).

cnf(i_0_16235,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9661]),
    [final] ).

cnf(i_0_16236,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9565]),
    [final] ).

cnf(i_0_16237,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9662]),
    [final] ).

cnf(i_0_16238,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9663]),
    [final] ).

cnf(i_0_16239,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9664]),
    [final] ).

cnf(i_0_16240,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9665]),
    [final] ).

cnf(i_0_16241,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_9666]),
    [final] ).

cnf(i_0_16242,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_9667]),
    [final] ).

cnf(i_0_16243,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),X3) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X1),c_COMBK(X1,X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_9668]),
    [final] ).

cnf(i_0_16244,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9669]),
    [final] ).

cnf(i_0_16245,plain,
    ( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9670]),
    [final] ).

cnf(i_0_16246,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9671]),
    [final] ).

cnf(i_0_16247,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9672]),
    [final] ).

cnf(i_0_16248,plain,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9673]),
    [final] ).

cnf(i_0_16249,plain,
    ( X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9674]),
    [final] ).

cnf(i_0_16250,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk445_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7679]),
    [final] ).

cnf(i_0_16251,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk439_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_16252,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9675]),
    [final] ).

cnf(i_0_16253,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9676]),
    [final] ).

cnf(i_0_16254,plain,
    ( c_List_Oinsert(X1,X2,X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9677]),
    [final] ).

cnf(i_0_16255,plain,
    ( c_List_Oinsert(X1,X2,X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9678]),
    [final] ).

cnf(i_0_16256,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9679]),
    [final] ).

cnf(i_0_16257,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9680]),
    [final] ).

cnf(i_0_16258,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9681]),
    [final] ).

cnf(i_0_16259,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9682]),
    [final] ).

cnf(i_0_16260,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9683]),
    [final] ).

cnf(i_0_16261,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9684]),
    [final] ).

cnf(i_0_16262,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9685]),
    [final] ).

cnf(i_0_16263,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9686]),
    [final] ).

cnf(i_0_16264,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9687]),
    [final] ).

cnf(i_0_16265,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9688]),
    [final] ).

cnf(i_0_16266,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9534]),
    [final] ).

cnf(i_0_16267,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9689]),
    [final] ).

cnf(i_0_16268,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9690]),
    [final] ).

cnf(i_0_16269,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9691]),
    [final] ).

cnf(i_0_16270,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9692]),
    [final] ).

cnf(i_0_16271,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9693]),
    [final] ).

cnf(i_0_16272,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_16273,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_16274,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9694]),
    [final] ).

cnf(i_0_16275,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9695]),
    [final] ).

cnf(i_0_16276,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9696]),
    [final] ).

cnf(i_0_16277,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9697]),
    [final] ).

cnf(i_0_16278,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9698]),
    [final] ).

cnf(i_0_16279,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9699]),
    [final] ).

cnf(i_0_16280,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(c_List_Oset(X1),X2)) = c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),c_List_Oremdups(X1,X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9700]),
    [final] ).

cnf(i_0_16281,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9576]),
    [final] ).

cnf(i_0_16282,plain,
    ( hBOOL(hAPP(X1,esk446_3(X2,X1,X3)))
    | c_List_OtakeWhile(X3,X1,X2) = hAPP(c_List_Ofilter(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5456]),
    [final] ).

cnf(i_0_16283,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9701]),
    [final] ).

cnf(i_0_16284,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_On__lists(X1,X2,X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9702]),
    [final] ).

cnf(i_0_16285,plain,
    ( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk144_1(X2))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9703]),
    [final] ).

cnf(i_0_16286,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9538]),
    [final] ).

cnf(i_0_16287,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9539]),
    [final] ).

cnf(i_0_16288,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9704]),
    [final] ).

cnf(i_0_16289,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9705]),
    [final] ).

cnf(i_0_16290,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9706]),
    [final] ).

cnf(i_0_16291,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9707]),
    [final] ).

cnf(i_0_16292,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9708]),
    [final] ).

cnf(i_0_16293,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9709]),
    [final] ).

cnf(i_0_16294,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_9710,c_0_6189]),
    [final] ).

cnf(i_0_16295,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_List_Olist__ex1(X3,X1,X4)
    | ~ c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6580]),
    [final] ).

cnf(i_0_16296,plain,
    ( hBOOL(hAPP(X2,X3))
    | c_List_Olist__ex(X1,X2,X4)
    | ~ c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9711]),
    [final] ).

cnf(i_0_16297,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9712]),
    [final] ).

cnf(i_0_16298,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9713]),
    [final] ).

cnf(i_0_16299,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)) = hAPP(hAPP(c_List_Onth(X1),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_9714]),
    [final] ).

cnf(i_0_16300,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Otl(X1),X4)) = hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9715]),
    [final] ).

cnf(i_0_16301,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Orev(X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9716]),
    [final] ).

cnf(i_0_16302,plain,
    ( hBOOL(hAPP(hAPP(X3,X2),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9717]),
    [final] ).

cnf(i_0_16303,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9718]),
    [final] ).

cnf(i_0_16304,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9719]),
    [final] ).

cnf(i_0_16305,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9720]),
    [final] ).

cnf(i_0_16306,plain,
    ( hBOOL(hAPP(X2,esk161_1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9721]),
    [final] ).

cnf(i_0_16307,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9713]),
    [final] ).

cnf(i_0_16308,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9722]),
    [final] ).

cnf(i_0_16309,plain,
    ( hBOOL(hAPP(X1,esk514_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_16310,plain,
    ( hBOOL(hAPP(X1,esk513_3(X1,X2,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_16311,plain,
    ( hBOOL(hAPP(X1,esk493_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_16312,plain,
    ( hBOOL(hAPP(X1,esk485_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7290]),
    [final] ).

cnf(i_0_16313,plain,
    ( hBOOL(hAPP(X1,esk476_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8739]),
    [final] ).

cnf(i_0_16314,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_9723,c_0_6071]),
    [final] ).

cnf(i_0_16315,plain,
    ( hAPP(X1,esk129_3(X1,X2,X3)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7318]),
    [final] ).

cnf(i_0_16316,plain,
    ( c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ c_List_Olist__all(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9724]),
    [final] ).

cnf(i_0_16317,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9725]),
    [final] ).

cnf(i_0_16318,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9726]),
    [final] ).

cnf(i_0_16319,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9727]),
    [final] ).

cnf(i_0_16320,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_16321,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3) != X4
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9729]),
    [final] ).

cnf(i_0_16322,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9730]),
    [final] ).

cnf(i_0_16323,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9731]),
    [final] ).

cnf(i_0_16324,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),c_List_Obutlast(X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),c_List_Olast(X2,X1)),c_List_Olist_ONil(X2))) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_9732]),
    [final] ).

cnf(i_0_16325,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))),
    inference(rw,[status(thm)],[i_0_9733,c_0_6189]),
    [final] ).

cnf(i_0_16326,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_16327,plain,
    hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Product__Type_Osnd(X1,X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9734]),
    [final] ).

cnf(i_0_16328,plain,
    X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(c_Product__Type_Ofst(X2,X3),X1)),hAPP(c_Product__Type_Osnd(X2,X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9735]),
    [final] ).

cnf(i_0_16329,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9736]),
    [final] ).

cnf(i_0_16330,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olist_ONil(X2)) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9737]),
    [final] ).

cnf(i_0_16331,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9594]),
    [final] ).

cnf(i_0_16332,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred2_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9393]),
    [final] ).

cnf(i_0_16333,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oinsert(X1,X3,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9738]),
    [final] ).

cnf(i_0_16334,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X3,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9739]),
    [final] ).

cnf(i_0_16335,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X3,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9740]),
    [final] ).

cnf(i_0_16336,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9741]),
    [final] ).

cnf(i_0_16337,plain,
    c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,c_Lazy__Sequence_Oappend(X1,X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_9742]),
    [final] ).

cnf(i_0_16338,plain,
    c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4)) = c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_9743]),
    [final] ).

cnf(i_0_16339,plain,
    ( hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X4),X6))
    | ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9744]),
    [final] ).

cnf(i_0_16340,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = X3
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9745]),
    [final] ).

cnf(i_0_16341,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = X3
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9746]),
    [final] ).

cnf(i_0_16342,plain,
    c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))),
    inference(split_conjunct,[status(thm)],[i_0_9747]),
    [final] ).

cnf(i_0_16343,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = X3
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9001]),
    [final] ).

cnf(i_0_16344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9663]),
    [final] ).

cnf(i_0_16345,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk536_2(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9748]),
    [final] ).

cnf(i_0_16346,plain,
    ( hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,X1),X4))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9749]),
    [final] ).

cnf(i_0_16347,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_16348,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9750]),
    [final] ).

cnf(i_0_16349,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9751]),
    [final] ).

cnf(i_0_16350,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9752]),
    [final] ).

cnf(i_0_16351,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9753]),
    [final] ).

cnf(i_0_16352,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9754]),
    [final] ).

cnf(i_0_16353,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9755]),
    [final] ).

cnf(i_0_16354,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9756]),
    [final] ).

cnf(i_0_16355,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9757]),
    [final] ).

cnf(i_0_16356,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9758]),
    [final] ).

cnf(i_0_16357,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9759]),
    [final] ).

cnf(i_0_16358,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9760]),
    [final] ).

cnf(i_0_16359,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9761]),
    [final] ).

cnf(i_0_16360,plain,
    ( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_9762,c_0_6732]),
    [final] ).

cnf(i_0_16361,plain,
    ( X1 = X2
    | c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Oremove1(X3,X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9763]),
    [final] ).

cnf(i_0_16362,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),X1),X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X4),X1))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9764]),
    [final] ).

cnf(i_0_16363,plain,
    ( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != X4
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9764]),
    [final] ).

cnf(i_0_16364,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9765]),
    [final] ).

cnf(i_0_16365,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9766]),
    [final] ).

cnf(i_0_16366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9767]),
    [final] ).

cnf(i_0_16367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9768]),
    [final] ).

cnf(i_0_16368,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))),
    inference(rw,[status(thm)],[i_0_9769,c_0_7122]),
    [final] ).

cnf(i_0_16369,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_9770,c_0_8304]),
    [final] ).

cnf(i_0_16370,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))),
    inference(rw,[status(thm)],[i_0_9771,c_0_6189]),
    [final] ).

cnf(i_0_16371,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9772]),
    [final] ).

cnf(i_0_16372,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9773]),
    [final] ).

cnf(i_0_16373,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9774]),
    [final] ).

cnf(i_0_16374,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9775]),
    [final] ).

cnf(i_0_16375,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9776]),
    [final] ).

cnf(i_0_16376,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9777]),
    [final] ).

cnf(i_0_16377,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9778]),
    [final] ).

cnf(i_0_16378,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9779]),
    [final] ).

cnf(i_0_16379,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9780]),
    [final] ).

cnf(i_0_16380,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9781]),
    [final] ).

cnf(i_0_16381,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9782]),
    [final] ).

cnf(i_0_16382,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9783]),
    [final] ).

cnf(i_0_16383,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9784]),
    [final] ).

cnf(i_0_16384,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9785]),
    [final] ).

cnf(i_0_16385,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9786]),
    [final] ).

cnf(i_0_16386,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9787]),
    [final] ).

cnf(i_0_16387,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_9788]),
    [final] ).

cnf(i_0_16388,plain,
    ( hBOOL(hAPP(X1,esk544_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ c_Equiv__Relations_Oequivp(X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8831]),
    [final] ).

cnf(i_0_16389,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_16390,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9264]),
    [final] ).

cnf(i_0_16391,plain,
    ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_16392,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9790]),
    [final] ).

cnf(i_0_16393,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9791]),
    [final] ).

cnf(i_0_16394,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9376]),
    [final] ).

cnf(i_0_16395,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9792]),
    [final] ).

cnf(i_0_16396,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9793]),
    [final] ).

cnf(i_0_16397,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9794]),
    [final] ).

cnf(i_0_16398,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9795]),
    [final] ).

cnf(i_0_16399,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2),
    inference(split_conjunct,[status(thm)],[i_0_9796]),
    [final] ).

cnf(i_0_16400,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Obutlast(X1,X4)) = c_List_Obutlast(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9797]),
    [final] ).

cnf(i_0_16401,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,esk536_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9748]),
    [final] ).

cnf(i_0_16402,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk317_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8663]),
    [final] ).

cnf(i_0_16403,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9798]),
    [final] ).

cnf(i_0_16404,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9799]),
    [final] ).

cnf(i_0_16405,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk80_1(X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9657]),
    [final] ).

cnf(i_0_16406,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk77_1(X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9658]),
    [final] ).

cnf(i_0_16407,plain,
    ( X1 = hAPP(c_Code__Numeral_Onat__of,esk533_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9800]),
    [final] ).

cnf(i_0_16408,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5249]),
    [final] ).

cnf(i_0_16409,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,esk158_1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9801]),
    [final] ).

cnf(i_0_16410,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_9802]),
    [final] ).

cnf(i_0_16411,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X3)))
    | X1 != hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9432]),
    [final] ).

cnf(i_0_16412,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(split_conjunct,[status(thm)],[fact_transfer__morphism__int__nat]),
    [final] ).

cnf(i_0_16413,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_16414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9634]),
    [final] ).

cnf(i_0_16415,plain,
    ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9803]),
    [final] ).

cnf(i_0_16416,plain,
    c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Fun_Oid(X1)) = c_Fun_Oid(X1),
    inference(split_conjunct,[status(thm)],[i_0_9804]),
    [final] ).

cnf(i_0_16417,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_16418,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_9805,c_0_6072]),
    [final] ).

cnf(i_0_16419,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_9806,c_0_6224]),
    [final] ).

cnf(i_0_16420,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9807]),
    [final] ).

cnf(i_0_16421,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8857]),
    [final] ).

cnf(i_0_16422,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk170_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8697]),
    [final] ).

cnf(i_0_16423,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk147_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8862]),
    [final] ).

cnf(i_0_16424,plain,
    ( hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X4
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9808]),
    [final] ).

cnf(i_0_16425,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
    inference(split_conjunct,[status(thm)],[i_0_9809]),
    [final] ).

cnf(i_0_16426,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9810]),
    [final] ).

cnf(i_0_16427,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(X2,esk162_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_16428,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9374]),
    [final] ).

cnf(i_0_16429,plain,
    ( c_List_Olist__all(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | ~ c_List_Oall__interval__nat(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_9811,c_0_6189]),
    [final] ).

cnf(i_0_16430,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9812]),
    [final] ).

cnf(i_0_16431,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9813]),
    [final] ).

cnf(i_0_16432,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_9814,c_0_6224]),
    [final] ).

cnf(i_0_16433,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,X1,c_Nat_Osemiring__1__class_Oof__nat(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9815]),
    [final] ).

cnf(i_0_16434,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3)) = hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9816]),
    [final] ).

cnf(i_0_16435,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk112_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9817]),
    [final] ).

cnf(i_0_16436,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Oreplicate(X1,X3,X4)) = c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2),X4),
    inference(split_conjunct,[status(thm)],[i_0_9818]),
    [final] ).

cnf(i_0_16437,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4)) = c_List_Oreplicate(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_9819]),
    [final] ).

cnf(i_0_16438,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = X2
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(rw,[status(thm)],[i_0_9820,c_0_6104]),
    [final] ).

cnf(i_0_16439,plain,
    ( hAPP(X1,esk524_1(X1)) = hAPP(X1,esk525_1(X1))
    | hBOOL(hAPP(hAPP(X1,esk524_1(X1)),esk525_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_16440,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9821]),
    [final] ).

cnf(i_0_16441,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9822]),
    [final] ).

cnf(i_0_16442,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9823]),
    [final] ).

cnf(i_0_16443,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9824]),
    [final] ).

cnf(i_0_16444,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_9373]),
    [final] ).

cnf(i_0_16445,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_6462]),
    [final] ).

cnf(i_0_16446,plain,
    ( c_Divides_Odivmod__int(X2,X1) = c_Divides_OnegDivAlg(X2,X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9311]),
    [final] ).

cnf(i_0_16447,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_9825]),
    [final] ).

cnf(i_0_16448,plain,
    ( hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8662]),
    [final] ).

cnf(i_0_16449,plain,
    ( c_List_Olist__all(X1,X2,X3)
    | ~ c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9724]),
    [final] ).

cnf(i_0_16450,plain,
    ( c_List_Olist__all(X1,X2,X3)
    | ~ c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9724]),
    [final] ).

cnf(i_0_16451,plain,
    ( c_List_Olist__all(X1,X2,X3)
    | ~ c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9826]),
    [final] ).

cnf(i_0_16452,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9827]),
    [final] ).

cnf(i_0_16453,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | c_Nitpick_Osetsum_H(X1,X3,X4,X2) = c_Groups_Ozero__class_Ozero(X3)
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6180]),
    [final] ).

cnf(i_0_16454,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
    | hAPP(c_Finite__Set_Ocard(X2),X3) = hAPP(c_Nat_OSuc,X5)
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X3 != hAPP(hAPP(c_Set_Oinsert(X2),X4),X1)
    | hAPP(c_Finite__Set_Ocard(X2),X1) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_16455,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_16456,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk251_2(X2,X1)),X2))
    | hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9828]),
    [final] ).

cnf(i_0_16457,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9829]),
    [final] ).

cnf(i_0_16458,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9830]),
    [final] ).

cnf(i_0_16459,plain,
    ( hBOOL(hAPP(X1,esk496_3(X2,X3,X1)))
    | c_FunDef_OTHE__default(X3,X2,X1) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8083]),
    [final] ).

cnf(i_0_16460,plain,
    c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9831]),
    [final] ).

cnf(i_0_16461,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9832]),
    [final] ).

cnf(i_0_16462,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9833]),
    [final] ).

cnf(i_0_16463,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4) ),
    inference(rw,[status(thm)],[i_0_9834,c_0_6189]),
    [final] ).

cnf(i_0_16464,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9835]),
    [final] ).

cnf(i_0_16465,plain,
    ( c_Quotient_OBabs(X1,X3,c_Quotient_ORespects(X1,X2),X4) = X4
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9836]),
    [final] ).

cnf(i_0_16466,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9837]),
    [final] ).

cnf(i_0_16467,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9838]),
    [final] ).

cnf(i_0_16468,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9839]),
    [final] ).

cnf(i_0_16469,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9840]),
    [final] ).

cnf(i_0_16470,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))
    | ~ epred1_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16471,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9841]),
    [final] ).

cnf(i_0_16472,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9841]),
    [final] ).

cnf(i_0_16473,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9842]),
    [final] ).

cnf(i_0_16474,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9843]),
    [final] ).

cnf(i_0_16475,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9844]),
    [final] ).

cnf(i_0_16476,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9845]),
    [final] ).

cnf(i_0_16477,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9846]),
    [final] ).

cnf(i_0_16478,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9847]),
    [final] ).

cnf(i_0_16479,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9848]),
    [final] ).

cnf(i_0_16480,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9849]),
    [final] ).

cnf(i_0_16481,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9850]),
    [final] ).

cnf(i_0_16482,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_16483,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9729]),
    [final] ).

cnf(i_0_16484,plain,
    ( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_9851,c_0_7122]),
    [final] ).

cnf(i_0_16485,plain,
    ( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_9852,c_0_7122]),
    [final] ).

cnf(i_0_16486,plain,
    hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X3) != hAPP(c_Set_OPow(X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_9853]),
    [final] ).

cnf(i_0_16487,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_inj__int]),
    [final] ).

cnf(i_0_16488,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8368]),
    [final] ).

cnf(i_0_16489,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8368]),
    [final] ).

cnf(i_0_16490,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_9854]),
    [final] ).

cnf(i_0_16491,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9854]),
    [final] ).

cnf(i_0_16492,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8646]),
    [final] ).

cnf(i_0_16493,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9855]),
    [final] ).

cnf(i_0_16494,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9856]),
    [final] ).

cnf(i_0_16495,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9050]),
    [final] ).

cnf(i_0_16496,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9584]),
    [final] ).

cnf(i_0_16497,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9857]),
    [final] ).

cnf(i_0_16498,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | c_SMT_Oz3div(X2,X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9858]),
    [final] ).

cnf(i_0_16499,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hBOOL(hAPP(hAPP(c_member(X2),c_List_Olast(X2,X1)),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9859]),
    [final] ).

cnf(i_0_16500,plain,
    ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8198]),
    [final] ).

cnf(i_0_16501,plain,
    ( c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_List_Olist__all(X3,X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9826]),
    [final] ).

cnf(i_0_16502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9572]),
    [final] ).

cnf(i_0_16503,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9860]),
    [final] ).

cnf(i_0_16504,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_9861]),
    [final] ).

cnf(i_0_16505,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_9862]),
    [final] ).

cnf(i_0_16506,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9861]),
    [final] ).

cnf(i_0_16507,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9862]),
    [final] ).

cnf(i_0_16508,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9863]),
    [final] ).

cnf(i_0_16509,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9864]),
    [final] ).

cnf(i_0_16510,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9865]),
    [final] ).

cnf(i_0_16511,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_16512,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Oinsert(X1,X2,X3) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9866]),
    [final] ).

cnf(i_0_16513,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Oinsert(X1,X2,X3) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9678]),
    [final] ).

cnf(i_0_16514,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9867]),
    [final] ).

cnf(i_0_16515,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9868]),
    [final] ).

cnf(i_0_16516,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9869]),
    [final] ).

cnf(i_0_16517,plain,
    hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_9870]),
    [final] ).

cnf(i_0_16518,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9765]),
    [final] ).

cnf(i_0_16519,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9871]),
    [final] ).

cnf(i_0_16520,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9787]),
    [final] ).

cnf(i_0_16521,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9872]),
    [final] ).

cnf(i_0_16522,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9730]),
    [final] ).

cnf(i_0_16523,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9873]),
    [final] ).

cnf(i_0_16524,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_9694]),
    [final] ).

cnf(i_0_16525,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9142]),
    [final] ).

cnf(i_0_16526,plain,
    ( hBOOL(hAPP(X1,esk432_3(X2,X1,X3)))
    | hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8834]),
    [final] ).

cnf(i_0_16527,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9874]),
    [final] ).

cnf(i_0_16528,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9875]),
    [final] ).

cnf(i_0_16529,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),c_Quotient_ORespects(X3,X1)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9717]),
    [final] ).

cnf(i_0_16530,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16531,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9876]),
    [final] ).

cnf(i_0_16532,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_9877]),
    [final] ).

cnf(i_0_16533,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_9878]),
    [final] ).

cnf(i_0_16534,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9879]),
    [final] ).

cnf(i_0_16535,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9364]),
    [final] ).

cnf(i_0_16536,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk205_1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9880]),
    [final] ).

cnf(i_0_16537,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9881]),
    [final] ).

cnf(i_0_16538,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9881]),
    [final] ).

cnf(i_0_16539,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),
    inference(split_conjunct,[status(thm)],[i_0_9882]),
    [final] ).

cnf(i_0_16540,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),
    inference(split_conjunct,[status(thm)],[i_0_9883]),
    [final] ).

cnf(i_0_16541,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_9884]),
    [final] ).

cnf(i_0_16542,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_9885]),
    [final] ).

cnf(i_0_16543,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_9886]),
    [final] ).

cnf(i_0_16544,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_9887]),
    [final] ).

cnf(i_0_16545,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9888]),
    [final] ).

cnf(i_0_16546,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9889]),
    [final] ).

cnf(i_0_16547,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_9890]),
    [final] ).

cnf(i_0_16548,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9891]),
    [final] ).

cnf(i_0_16549,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9892]),
    [final] ).

cnf(i_0_16550,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9893]),
    [final] ).

cnf(i_0_16551,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9894]),
    [final] ).

cnf(i_0_16552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9895]),
    [final] ).

cnf(i_0_16553,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9896]),
    [final] ).

cnf(i_0_16554,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9897]),
    [final] ).

cnf(i_0_16555,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9898]),
    [final] ).

cnf(i_0_16556,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9664]),
    [final] ).

cnf(i_0_16557,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9899]),
    [final] ).

cnf(i_0_16558,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9900]),
    [final] ).

cnf(i_0_16559,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9901]),
    [final] ).

cnf(i_0_16560,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9902]),
    [final] ).

cnf(i_0_16561,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9903]),
    [final] ).

cnf(i_0_16562,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9904]),
    [final] ).

cnf(i_0_16563,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9905]),
    [final] ).

cnf(i_0_16564,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9906]),
    [final] ).

cnf(i_0_16565,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9907]),
    [final] ).

cnf(i_0_16566,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9908]),
    [final] ).

cnf(i_0_16567,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9909]),
    [final] ).

cnf(i_0_16568,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_INT__greaterThan__UNIV]),
    [final] ).

cnf(i_0_16569,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_UN__atMost__UNIV]),
    [final] ).

cnf(i_0_16570,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_UN__atLeast__UNIV]),
    [final] ).

cnf(i_0_16571,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_UN__lessThan__UNIV]),
    [final] ).

cnf(i_0_16572,plain,
    c_Enum_Oproduct(X1,X2,c_List_Olist_ONil(X1),X3) = c_List_Olist_ONil(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_9910]),
    [final] ).

cnf(i_0_16573,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9911]),
    [final] ).

cnf(i_0_16574,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Oone__class_Oone(X1))),X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9912]),
    [final] ).

cnf(i_0_16575,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9913]),
    [final] ).

cnf(i_0_16576,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk204_2(X1,X2)),X1))
    | hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9185]),
    [final] ).

cnf(i_0_16577,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9505]),
    [final] ).

cnf(i_0_16578,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_9914]),
    [final] ).

cnf(i_0_16579,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16580,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9892]),
    [final] ).

cnf(i_0_16581,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9893]),
    [final] ).

cnf(i_0_16582,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9534]),
    [final] ).

cnf(i_0_16583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9915]),
    [final] ).

cnf(i_0_16584,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Otl(X2),c_List_Oreplicate(X2,X1,X3)) = c_List_Oreplicate(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9916]),
    [final] ).

cnf(i_0_16585,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9917]),
    [final] ).

cnf(i_0_16586,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[fact_transfer__morphism__nat__int]),
    [final] ).

cnf(i_0_16587,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9918]),
    [final] ).

cnf(i_0_16588,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9358]),
    [final] ).

cnf(i_0_16589,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9919]),
    [final] ).

cnf(i_0_16590,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9920]),
    [final] ).

cnf(i_0_16591,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_9921,c_0_6072]),
    [final] ).

cnf(i_0_16592,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1) = c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9521]),
    [final] ).

cnf(i_0_16593,plain,
    ( esk89_3(X1,X2,X3) = esk90_3(X1,X2,X3)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8725]),
    [final] ).

cnf(i_0_16594,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9922]),
    [final] ).

cnf(i_0_16595,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9923]),
    [final] ).

cnf(i_0_16596,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk141_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9924]),
    [final] ).

cnf(i_0_16597,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oreplicate(X1,X4,X5)) = c_List_Oreplicate(X2,X4,hAPP(X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_9925]),
    [final] ).

cnf(i_0_16598,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4)) = c_List_Oremove1(X1,X3,hAPP(c_List_Ofilter(X1,X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9926]),
    [final] ).

cnf(i_0_16599,plain,
    ( hBOOL(hAPP(X1,esk171_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8661]),
    [final] ).

cnf(i_0_16600,plain,
    ( hBOOL(hAPP(X1,esk148_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8827]),
    [final] ).

cnf(i_0_16601,plain,
    ( c_List_Olast(X1,X2) = X3
    | hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9927]),
    [final] ).

cnf(i_0_16602,plain,
    ( c_List_Obutlast(X1,X2) = X3
    | hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9927]),
    [final] ).

cnf(i_0_16603,plain,
    ( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk174_1(X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9928]),
    [final] ).

cnf(i_0_16604,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9929]),
    [final] ).

cnf(i_0_16605,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9930]),
    [final] ).

cnf(i_0_16606,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9931]),
    [final] ).

cnf(i_0_16607,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9932]),
    [final] ).

cnf(i_0_16608,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X2),X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9713]),
    [final] ).

cnf(i_0_16609,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9933]),
    [final] ).

cnf(i_0_16610,plain,
    ( X1 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9934]),
    [final] ).

cnf(i_0_16611,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9578]),
    [final] ).

cnf(i_0_16612,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9935]),
    [final] ).

cnf(i_0_16613,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9826]),
    [final] ).

cnf(i_0_16614,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9936]),
    [final] ).

cnf(i_0_16615,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk368_2(X2,X1)),esk367_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7075]),
    [final] ).

cnf(i_0_16616,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_9937]),
    [final] ).

cnf(i_0_16617,plain,
    hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9938]),
    [final] ).

cnf(i_0_16618,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8945]),
    [final] ).

cnf(i_0_16619,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9939]),
    [final] ).

cnf(i_0_16620,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16621,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9940]),
    [final] ).

cnf(i_0_16622,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9941]),
    [final] ).

cnf(i_0_16623,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9942]),
    [final] ).

cnf(i_0_16624,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9942]),
    [final] ).

cnf(i_0_16625,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9943]),
    [final] ).

cnf(i_0_16626,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9944]),
    [final] ).

cnf(i_0_16627,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9945]),
    [final] ).

cnf(i_0_16628,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9946]),
    [final] ).

cnf(i_0_16629,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
    inference(split_conjunct,[status(thm)],[i_0_9947]),
    [final] ).

cnf(i_0_16630,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9948]),
    [final] ).

cnf(i_0_16631,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
    inference(split_conjunct,[status(thm)],[i_0_9949]),
    [final] ).

cnf(i_0_16632,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = X4
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9950]),
    [final] ).

cnf(i_0_16633,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = X4
    | X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9951]),
    [final] ).

cnf(i_0_16634,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X4
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9951]),
    [final] ).

cnf(i_0_16635,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X4
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9950]),
    [final] ).

cnf(i_0_16636,plain,
    ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_7660]),
    [final] ).

cnf(i_0_16637,plain,
    ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8214]),
    [final] ).

cnf(i_0_16638,plain,
    ( hBOOL(hAPP(X2,X4))
    | c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ c_List_Olist__ex1(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6580]),
    [final] ).

cnf(i_0_16639,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | X2 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9952]),
    [final] ).

cnf(i_0_16640,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_9953]),
    [final] ).

cnf(i_0_16641,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9528]),
    [final] ).

cnf(i_0_16642,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
    | X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_16643,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
    | X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_9954]),
    [final] ).

cnf(i_0_16644,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
    | X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_9955]),
    [final] ).

cnf(i_0_16645,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
    | X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_16646,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),X3),X6)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X4)
    | hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6634]),
    [final] ).

cnf(i_0_16647,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
    | hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_16648,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9956]),
    [final] ).

cnf(i_0_16649,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9957]),
    [final] ).

cnf(i_0_16650,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(split_conjunct,[status(thm)],[i_0_9958]),
    [final] ).

cnf(i_0_16651,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_9959]),
    [final] ).

cnf(i_0_16652,plain,
    ( X1 != c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_9927]),
    [final] ).

cnf(i_0_16653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk444_2(X1,X2)),esk445_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7679]),
    [final] ).

cnf(i_0_16654,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk440_2(X1,X2)),esk439_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_16655,plain,
    ( c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))) = c_Orderings_Oord__class_Omin(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9960]),
    [final] ).

cnf(i_0_16656,plain,
    ( c_Orderings_Oord_Omin(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))) = c_Orderings_Oord__class_Omax(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9961]),
    [final] ).

cnf(i_0_16657,plain,
    ( c_List_Omonoid__add__class_Olistsum(X1) = c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9962]),
    [final] ).

cnf(i_0_16658,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9963]),
    [final] ).

cnf(i_0_16659,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9964]),
    [final] ).

cnf(i_0_16660,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3) = X2
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9965]),
    [final] ).

cnf(i_0_16661,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9965]),
    [final] ).

cnf(i_0_16662,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9966]),
    [final] ).

cnf(i_0_16663,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_16664,plain,
    ( c_List_Oremove1(X1,X3,c_List_Oremdups(X1,X2)) = c_List_Oremdups(X1,c_List_Oremove1(X1,X3,X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9967]),
    [final] ).

cnf(i_0_16665,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk145_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9703]),
    [final] ).

cnf(i_0_16666,plain,
    ( c_Nitpick_Owf_H(X1,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9968]),
    [final] ).

cnf(i_0_16667,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9969]),
    [final] ).

cnf(i_0_16668,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9970]),
    [final] ).

cnf(i_0_16669,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9969]),
    [final] ).

cnf(i_0_16670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_16671,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_16672,plain,
    c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_9971]),
    [final] ).

cnf(i_0_16673,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X3),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9972]),
    [final] ).

cnf(i_0_16674,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9973]),
    [final] ).

cnf(i_0_16675,plain,
    ( c_Equiv__Relations_Oequivp(X2,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk278_1(X1)),esk279_1(X1)))
    | hAPP(X1,esk278_1(X1)) != hAPP(X1,esk279_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9974]),
    [final] ).

cnf(i_0_16676,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9975]),
    [final] ).

cnf(i_0_16677,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9976]),
    [final] ).

cnf(i_0_16678,plain,
    ( c_List_Olinorder__class_Osort__key(X2,X1,X3,c_List_Olist_ONil(X2)) = c_List_Olist_ONil(X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9977]),
    [final] ).

cnf(i_0_16679,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3) = hAPP(c_Relation_ODomain(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9978]),
    [final] ).

cnf(i_0_16680,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3) = hAPP(c_Relation_ORange(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_9979]),
    [final] ).

cnf(i_0_16681,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk123_2(X2,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9432]),
    [final] ).

cnf(i_0_16682,plain,
    ( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),X1) = X3
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9484]),
    [final] ).

cnf(i_0_16683,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_16684,plain,
    ( c_Relation_Ototal__on(X1,X2,X3)
    | ~ c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9980]),
    [final] ).

cnf(i_0_16685,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9981]),
    [final] ).

cnf(i_0_16686,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X1) = X4
    | hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9729]),
    [final] ).

cnf(i_0_16687,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)),X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) != hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_16688,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk162_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_16689,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9803]),
    [final] ).

cnf(i_0_16690,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9982]),
    [final] ).

cnf(i_0_16691,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9983]),
    [final] ).

cnf(i_0_16692,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9984]),
    [final] ).

cnf(i_0_16693,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9985]),
    [final] ).

cnf(i_0_16694,plain,
    ( X1 = hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)
    | hAPP(hAPP(c_List_Oappend(X2),X3),X1) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_16695,plain,
    ( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),X1),X4) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_16696,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9986]),
    [final] ).

cnf(i_0_16697,plain,
    hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
    inference(split_conjunct,[status(thm)],[i_0_9987]),
    [final] ).

cnf(i_0_16698,plain,
    ( X3 = X4
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9988]),
    [final] ).

cnf(i_0_16699,plain,
    ( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9989]),
    [final] ).

cnf(i_0_16700,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_member(X3),X4),X5))
    | hAPP(c_Finite__Set_Ocard(X3),X2) = hAPP(c_Nat_OSuc,X1)
    | X2 != hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)
    | hAPP(c_Finite__Set_Ocard(X3),X5) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_16701,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_9990]),
    [final] ).

cnf(i_0_16702,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_9991]),
    [final] ).

cnf(i_0_16703,plain,
    ( hBOOL(hAPP(hAPP(X1,esk526_2(X1,X2)),esk526_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9992]),
    [final] ).

cnf(i_0_16704,plain,
    ( hBOOL(hAPP(hAPP(X1,esk522_2(X1,X2)),esk522_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9993]),
    [final] ).

cnf(i_0_16705,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9994]),
    [final] ).

cnf(i_0_16706,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X2,X1,X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9995]),
    [final] ).

cnf(i_0_16707,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_9996]),
    [final] ).

cnf(i_0_16708,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_9997]),
    [final] ).

cnf(i_0_16709,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5950]),
    [final] ).

cnf(i_0_16710,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5951]),
    [final] ).

cnf(i_0_16711,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9841]),
    [final] ).

cnf(i_0_16712,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X3),hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)) = hAPP(X4,hAPP(c_List_Ohd(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9998]),
    [final] ).

cnf(i_0_16713,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2)))
    | ~ class_Int_Oring__char__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9875]),
    [final] ).

cnf(i_0_16714,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9999]),
    [final] ).

cnf(i_0_16715,plain,
    ( X1 = X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2) != hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10000]),
    [final] ).

cnf(i_0_16716,plain,
    ( X1 = X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10000]),
    [final] ).

cnf(i_0_16717,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5) = c_New__DSequence_Opos__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10001]),
    [final] ).

cnf(i_0_16718,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5) = c_New__DSequence_Oneg__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10002]),
    [final] ).

cnf(i_0_16719,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4))
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9950]),
    [final] ).

cnf(i_0_16720,plain,
    ( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9951]),
    [final] ).

cnf(i_0_16721,plain,
    ( c_Divides_OposDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5344]),
    [final] ).

cnf(i_0_16722,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10003]),
    [final] ).

cnf(i_0_16723,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10004]),
    [final] ).

cnf(i_0_16724,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10005]),
    [final] ).

cnf(i_0_16725,plain,
    hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10006]),
    [final] ).

cnf(i_0_16726,plain,
    c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2),
    inference(split_conjunct,[status(thm)],[i_0_10007]),
    [final] ).

cnf(i_0_16727,plain,
    c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_10008]),
    [final] ).

cnf(i_0_16728,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9817]),
    [final] ).

cnf(i_0_16729,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10009,c_0_8304]),c_0_8304]),
    [final] ).

cnf(i_0_16730,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10010]),
    [final] ).

cnf(i_0_16731,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10011]),
    [final] ).

cnf(i_0_16732,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10012]),
    [final] ).

cnf(i_0_16733,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_10013]),
    [final] ).

cnf(i_0_16734,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Otl(X2),X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10014]),
    [final] ).

cnf(i_0_16735,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10015]),
    [final] ).

cnf(i_0_16736,plain,
    ( X3 = X4
    | hAPP(c_Product__Type_Ofst(X1,X2),X3) != hAPP(c_Product__Type_Ofst(X1,X2),X4)
    | hAPP(c_Product__Type_Osnd(X1,X2),X3) != hAPP(c_Product__Type_Osnd(X1,X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10016]),
    [final] ).

cnf(i_0_16737,plain,
    ( X3 = X4
    | hAPP(c_Product__Type_Ofst(X1,X2),X3) != hAPP(c_Product__Type_Ofst(X1,X2),X4)
    | hAPP(c_Product__Type_Osnd(X1,X2),X3) != hAPP(c_Product__Type_Osnd(X1,X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10017]),
    [final] ).

cnf(i_0_16738,plain,
    c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10018]),
    [final] ).

cnf(i_0_16739,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10019]),
    [final] ).

cnf(i_0_16740,plain,
    ( hAPP(hAPP(c_List_Otake(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = c_List_Olist_ONil(X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_7921]),
    [final] ).

cnf(i_0_16741,plain,
    ( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10020]),
    [final] ).

cnf(i_0_16742,plain,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
    | hAPP(c_List_Oset(X1),X2) != hAPP(c_List_Oset(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_16743,plain,
    hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),X2),X4),
    inference(split_conjunct,[status(thm)],[i_0_10022]),
    [final] ).

cnf(i_0_16744,plain,
    c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),
    inference(rw,[status(thm)],[i_0_10023,c_0_6104]),
    [final] ).

cnf(i_0_16745,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10024]),
    [final] ).

cnf(i_0_16746,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_10025,c_0_8304]),
    [final] ).

cnf(i_0_16747,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10026]),
    [final] ).

cnf(i_0_16748,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10027]),
    [final] ).

cnf(i_0_16749,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10028]),
    [final] ).

cnf(i_0_16750,plain,
    ( c_Nitpick_Onorm__frac(X2,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_16751,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10029]),
    [final] ).

cnf(i_0_16752,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10030]),
    [final] ).

cnf(i_0_16753,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10031]),
    [final] ).

cnf(i_0_16754,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10032]),
    [final] ).

cnf(i_0_16755,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10033]),
    [final] ).

cnf(i_0_16756,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10034]),
    [final] ).

cnf(i_0_16757,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10035]),
    [final] ).

cnf(i_0_16758,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10036]),
    [final] ).

cnf(i_0_16759,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10037]),
    [final] ).

cnf(i_0_16760,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10038,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_16761,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10039]),
    [final] ).

cnf(i_0_16762,plain,
    ( hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2)) = c_List_Oreplicate(X3,X4,X2)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10040]),
    [final] ).

cnf(i_0_16763,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10041]),
    [final] ).

cnf(i_0_16764,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10042]),
    [final] ).

cnf(i_0_16765,plain,
    ( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5344]),
    [final] ).

cnf(i_0_16766,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10043]),
    [final] ).

cnf(i_0_16767,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10043]),
    [final] ).

cnf(i_0_16768,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10044,c_0_6070]),c_0_6071]),c_0_6072]),c_0_6072]),
    [final] ).

cnf(i_0_16769,plain,
    hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10045]),
    [final] ).

cnf(i_0_16770,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_10046]),
    [final] ).

cnf(i_0_16771,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10047]),
    [final] ).

cnf(i_0_16772,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10048]),
    [final] ).

cnf(i_0_16773,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10049]),
    [final] ).

cnf(i_0_16774,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10050]),
    [final] ).

cnf(i_0_16775,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10051]),
    [final] ).

cnf(i_0_16776,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10052]),
    [final] ).

cnf(i_0_16777,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10053]),
    [final] ).

cnf(i_0_16778,plain,
    ( hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1)) = X1
    | ~ c_List_Onat__list(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10054,c_0_7999]),c_0_8000]),
    [final] ).

cnf(i_0_16779,plain,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X4
    | X1 != c_Finite__Set_Ofold1(X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10055]),
    [final] ).

cnf(i_0_16780,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_10056]),
    [final] ).

cnf(i_0_16781,plain,
    ( hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X4),X5)) = hAPP(hAPP(X3,X4),X5)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10057]),
    [final] ).

cnf(i_0_16782,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10058]),
    [final] ).

cnf(i_0_16783,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10059]),
    [final] ).

cnf(i_0_16784,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10060]),
    [final] ).

cnf(i_0_16785,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10061]),
    [final] ).

cnf(i_0_16786,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10062]),
    [final] ).

cnf(i_0_16787,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10063]),
    [final] ).

cnf(i_0_16788,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10064]),
    [final] ).

cnf(i_0_16789,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_10065]),
    [final] ).

cnf(i_0_16790,plain,
    ( c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9635]),
    [final] ).

cnf(i_0_16791,plain,
    ( c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9635]),
    [final] ).

cnf(i_0_16792,plain,
    ( c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9711]),
    [final] ).

cnf(i_0_16793,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_10066]),
    [final] ).

cnf(i_0_16794,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10050]),
    [final] ).

cnf(i_0_16795,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10067]),
    [final] ).

cnf(i_0_16796,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10068]),
    [final] ).

cnf(i_0_16797,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10069]),
    [final] ).

cnf(i_0_16798,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10052]),
    [final] ).

cnf(i_0_16799,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10053]),
    [final] ).

cnf(i_0_16800,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10070]),
    [final] ).

cnf(i_0_16801,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_10071]),
    [final] ).

cnf(i_0_16802,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_pair__less__def]),
    [final] ).

cnf(i_0_16803,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X3,hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)) = hAPP(X4,c_List_Olast(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10072]),
    [final] ).

cnf(i_0_16804,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[i_0_10073,c_0_6072]),
    [final] ).

cnf(i_0_16805,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | X2 = X1
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_16806,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10074]),
    [final] ).

cnf(i_0_16807,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X2),esk2_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10075]),
    [final] ).

cnf(i_0_16808,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk3_2(X2,X1)),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10076]),
    [final] ).

cnf(i_0_16809,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_List_Oremove1(X1,X2,X3) = X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10077]),
    [final] ).

cnf(i_0_16810,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
    inference(rw,[status(thm)],[i_0_10078,c_0_6189]),
    [final] ).

cnf(i_0_16811,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9766]),
    [final] ).

cnf(i_0_16812,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9505]),
    [final] ).

cnf(i_0_16813,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10079]),
    [final] ).

cnf(i_0_16814,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10080]),
    [final] ).

cnf(i_0_16815,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10081]),
    [final] ).

cnf(i_0_16816,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10082]),
    [final] ).

cnf(i_0_16817,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9582]),
    [final] ).

cnf(i_0_16818,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10083]),
    [final] ).

cnf(i_0_16819,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10084]),
    [final] ).

cnf(i_0_16820,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10085]),
    [final] ).

cnf(i_0_16821,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10086]),
    [final] ).

cnf(i_0_16822,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10087]),
    [final] ).

cnf(i_0_16823,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10088]),
    [final] ).

cnf(i_0_16824,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10089]),
    [final] ).

cnf(i_0_16825,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10090]),
    [final] ).

cnf(i_0_16826,plain,
    ( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10091]),
    [final] ).

cnf(i_0_16827,plain,
    c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oreplicate(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10092]),
    [final] ).

cnf(i_0_16828,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_10093,c_0_6189]),
    [final] ).

cnf(i_0_16829,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_10094,c_0_6189]),
    [final] ).

cnf(i_0_16830,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
    | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_10095,c_0_6189]),
    [final] ).

cnf(i_0_16831,plain,
    ( c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10096]),
    [final] ).

cnf(i_0_16832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9588]),
    [final] ).

cnf(i_0_16833,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_10097]),
    [final] ).

cnf(i_0_16834,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_10098]),
    [final] ).

cnf(i_0_16835,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk81_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9657]),
    [final] ).

cnf(i_0_16836,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk78_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9658]),
    [final] ).

cnf(i_0_16837,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9611]),
    [final] ).

cnf(i_0_16838,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9612]),
    [final] ).

cnf(i_0_16839,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10099]),
    [final] ).

cnf(i_0_16840,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10100]),
    [final] ).

cnf(i_0_16841,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oabs__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10101]),
    [final] ).

cnf(i_0_16842,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10102]),
    [final] ).

cnf(i_0_16843,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10103]),
    [final] ).

cnf(i_0_16844,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10104]),
    [final] ).

cnf(i_0_16845,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10105]),
    [final] ).

cnf(i_0_16846,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_16847,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_16848,plain,
    ( hBOOL(hAPP(hAPP(X2,X4),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10106]),
    [final] ).

cnf(i_0_16849,plain,
    ( hBOOL(hAPP(hAPP(X2,X4),X3))
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10107]),
    [final] ).

cnf(i_0_16850,plain,
    ( hBOOL(hAPP(hAPP(X2,X4),X3))
    | ~ c_Equiv__Relations_Oequivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10108]),
    [final] ).

cnf(i_0_16851,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9659]),
    [final] ).

cnf(i_0_16852,plain,
    ( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10109]),
    [final] ).

cnf(i_0_16853,plain,
    ( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10110]),
    [final] ).

cnf(i_0_16854,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_10111]),
    [final] ).

cnf(i_0_16855,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10112]),
    [final] ).

cnf(i_0_16856,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10113]),
    [final] ).

cnf(i_0_16857,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10114]),
    [final] ).

cnf(i_0_16858,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10115]),
    [final] ).

cnf(i_0_16859,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10116]),
    [final] ).

cnf(i_0_16860,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10117]),
    [final] ).

cnf(i_0_16861,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10118]),
    [final] ).

cnf(i_0_16862,plain,
    c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10119]),
    [final] ).

cnf(i_0_16863,plain,
    c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10120]),
    [final] ).

cnf(i_0_16864,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_OCollect(X3),X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9758]),
    [final] ).

cnf(i_0_16865,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_OCollect(X3),X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10121]),
    [final] ).

cnf(i_0_16866,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5968]),
    [final] ).

cnf(i_0_16867,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_10122]),
    [final] ).

cnf(i_0_16868,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_10123]),
    [final] ).

cnf(i_0_16869,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10124]),
    [final] ).

cnf(i_0_16870,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)) = c_Fun_Oid(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10125]),
    [final] ).

cnf(i_0_16871,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10043]),
    [final] ).

cnf(i_0_16872,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10126]),
    [final] ).

cnf(i_0_16873,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10127]),
    [final] ).

cnf(i_0_16874,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2) = X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10128]),
    [final] ).

cnf(i_0_16875,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10129]),
    [final] ).

cnf(i_0_16876,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10130]),
    [final] ).

cnf(i_0_16877,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2) = X3
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10131]),
    [final] ).

cnf(i_0_16878,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10132]),
    [final] ).

cnf(i_0_16879,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10133]),
    [final] ).

cnf(i_0_16880,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10134]),
    [final] ).

cnf(i_0_16881,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10135]),
    [final] ).

cnf(i_0_16882,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10136]),
    [final] ).

cnf(i_0_16883,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10137]),
    [final] ).

cnf(i_0_16884,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10138]),
    [final] ).

cnf(i_0_16885,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10139]),
    [final] ).

cnf(i_0_16886,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10140]),
    [final] ).

cnf(i_0_16887,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10141]),
    [final] ).

cnf(i_0_16888,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10142]),
    [final] ).

cnf(i_0_16889,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10143]),
    [final] ).

cnf(i_0_16890,plain,
    ( c_SMT_Oz3div(X2,X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9858]),
    [final] ).

cnf(i_0_16891,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10144]),
    [final] ).

cnf(i_0_16892,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10145]),
    [final] ).

cnf(i_0_16893,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10146,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16894,plain,
    ( c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)
    | c_Int_OMin != X1 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10147,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16895,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_10148,c_0_6189]),
    [final] ).

cnf(i_0_16896,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10149]),
    [final] ).

cnf(i_0_16897,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10150]),
    [final] ).

cnf(i_0_16898,plain,
    hAPP(c_New__DSequence_Opos__union(X1,X2,X3),X4) = c_Lazy__Sequence_Oappend(X1,hAPP(X2,X4),hAPP(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_10151]),
    [final] ).

cnf(i_0_16899,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)) = X2
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10152]),
    [final] ).

cnf(i_0_16900,plain,
    ( c_Relation_Ototal__on(X3,X2,X1)
    | esk347_3(X1,X2,X3) != esk348_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6822]),
    [final] ).

cnf(i_0_16901,plain,
    ( c_Relation_Osingle__valued(X3,X2,X1)
    | esk343_3(X1,X2,X3) != esk344_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7017]),
    [final] ).

cnf(i_0_16902,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10153]),
    [final] ).

cnf(i_0_16903,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10154]),
    [final] ).

cnf(i_0_16904,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10155]),
    [final] ).

cnf(i_0_16905,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10156]),
    [final] ).

cnf(i_0_16906,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9234]),
    [final] ).

cnf(i_0_16907,plain,
    ( c_Wellfounded_OwfP(X1,X2)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk311_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10157]),
    [final] ).

cnf(i_0_16908,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10158]),
    [final] ).

cnf(i_0_16909,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))),
    inference(rw,[status(thm)],[i_0_10159,c_0_6189]),
    [final] ).

cnf(i_0_16910,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9577]),
    [final] ).

cnf(i_0_16911,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10160]),
    [final] ).

cnf(i_0_16912,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10161]),
    [final] ).

cnf(i_0_16913,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | X1 != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9898]),
    [final] ).

cnf(i_0_16914,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10162]),
    [final] ).

cnf(i_0_16915,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10163]),
    [final] ).

cnf(i_0_16916,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10164]),
    [final] ).

cnf(i_0_16917,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | X2 = X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9681]),
    [final] ).

cnf(i_0_16918,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10165]),
    [final] ).

cnf(i_0_16919,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10166]),
    [final] ).

cnf(i_0_16920,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10167]),
    [final] ).

cnf(i_0_16921,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10168]),
    [final] ).

cnf(i_0_16922,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10169]),
    [final] ).

cnf(i_0_16923,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10170]),
    [final] ).

cnf(i_0_16924,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10171]),
    [final] ).

cnf(i_0_16925,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10172]),
    [final] ).

cnf(i_0_16926,plain,
    hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10173]),
    [final] ).

cnf(i_0_16927,plain,
    hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10174]),
    [final] ).

cnf(i_0_16928,plain,
    hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10175]),
    [final] ).

cnf(i_0_16929,plain,
    hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_10176]),
    [final] ).

cnf(i_0_16930,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10177,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_16931,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk76_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10178]),
    [final] ).

cnf(i_0_16932,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10179]),
    [final] ).

cnf(i_0_16933,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk162_2(X1,X2))
    | hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_16934,plain,
    c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10180]),
    [final] ).

cnf(i_0_16935,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) = X1
    | c_List_Obutlast(X2,X1) != X3
    | c_List_Olast(X2,X1) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_9927]),
    [final] ).

cnf(i_0_16936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9684]),
    [final] ).

cnf(i_0_16937,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10181]),
    [final] ).

cnf(i_0_16938,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10182]),
    [final] ).

cnf(i_0_16939,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9682]),
    [final] ).

cnf(i_0_16940,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10183]),
    [final] ).

cnf(i_0_16941,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10184]),
    [final] ).

cnf(i_0_16942,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10185]),
    [final] ).

cnf(i_0_16943,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2),
    inference(rw,[status(thm)],[i_0_10186,c_0_6189]),
    [final] ).

cnf(i_0_16944,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
    inference(rw,[status(thm)],[i_0_10187,c_0_6189]),
    [final] ).

cnf(i_0_16945,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9692]),
    [final] ).

cnf(i_0_16946,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10188]),
    [final] ).

cnf(i_0_16947,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10189]),
    [final] ).

cnf(i_0_16948,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10190]),
    [final] ).

cnf(i_0_16949,plain,
    c_List_Opartition(X1,X2,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10191]),
    [final] ).

cnf(i_0_16950,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),c_Int_OMin) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10192,c_0_6072]),c_0_6224]),
    [final] ).

cnf(i_0_16951,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9924]),
    [final] ).

cnf(i_0_16952,plain,
    ( c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))
    | ~ c_Relation_Ototal__on(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9980]),
    [final] ).

cnf(i_0_16953,plain,
    ( c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))
    | ~ c_Relation_Orefl__on(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9981]),
    [final] ).

cnf(i_0_16954,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10193]),
    [final] ).

cnf(i_0_16955,plain,
    ( c_Relation_Osym(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10194]),
    [final] ).

cnf(i_0_16956,plain,
    ( c_Relation_Otrans(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10195]),
    [final] ).

cnf(i_0_16957,plain,
    ( c_Wellfounded_Owf(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10196]),
    [final] ).

cnf(i_0_16958,plain,
    ( c_FunDef_Oreduction__pair(X3,hAPP(hAPP(c_FunDef_Orp__inv__image(X1,X3),X2),X4))
    | ~ c_FunDef_Oreduction__pair(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10197]),
    [final] ).

cnf(i_0_16959,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10198]),
    [final] ).

cnf(i_0_16960,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10199]),
    [final] ).

cnf(i_0_16961,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10200]),
    [final] ).

cnf(i_0_16962,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X3),X2) = X4
    | hAPP(hAPP(c_List_Odrop(X1),X2),X3) != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10201]),
    [final] ).

cnf(i_0_16963,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10202]),
    [final] ).

cnf(i_0_16964,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10203]),
    [final] ).

cnf(i_0_16965,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10204]),
    [final] ).

cnf(i_0_16966,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10205]),
    [final] ).

cnf(i_0_16967,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10206]),
    [final] ).

cnf(i_0_16968,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10207]),
    [final] ).

cnf(i_0_16969,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10208]),
    [final] ).

cnf(i_0_16970,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10209]),
    [final] ).

cnf(i_0_16971,plain,
    hAPP(c_List_Oset(X1),c_List_Oinsert(X1,X2,X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10210]),
    [final] ).

cnf(i_0_16972,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_10211,c_0_6072]),
    [final] ).

cnf(i_0_16973,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3)))
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8265]),
    [final] ).

cnf(i_0_16974,plain,
    c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10212]),
    [final] ).

cnf(i_0_16975,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10213]),
    [final] ).

cnf(i_0_16976,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10214]),
    [final] ).

cnf(i_0_16977,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10215]),
    [final] ).

cnf(i_0_16978,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10216]),
    [final] ).

cnf(i_0_16979,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10217]),
    [final] ).

cnf(i_0_16980,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10218]),
    [final] ).

cnf(i_0_16981,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10219]),
    [final] ).

cnf(i_0_16982,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10220]),
    [final] ).

cnf(i_0_16983,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10221]),
    [final] ).

cnf(i_0_16984,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10222]),
    [final] ).

cnf(i_0_16985,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10223]),
    [final] ).

cnf(i_0_16986,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10224]),
    [final] ).

cnf(i_0_16987,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10225]),
    [final] ).

cnf(i_0_16988,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10226]),
    [final] ).

cnf(i_0_16989,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk142_1(X1)))
    | hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9547]),
    [final] ).

cnf(i_0_16990,plain,
    c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X1),X2,X3)) = c_Lazy__Sequence_Oappend(X1,X2,c_Lazy__Sequence_Oflat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10227]),
    [final] ).

cnf(i_0_16991,plain,
    ( X2 = esk460_2(X3,X1)
    | hAPP(c_List_Oset(X1),X2) != X3
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10228]),
    [final] ).

cnf(i_0_16992,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(c_List_Ofilter(X3,X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9749]),
    [final] ).

cnf(i_0_16993,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)) = hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10229]),
    [final] ).

cnf(i_0_16994,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10230]),
    [final] ).

cnf(i_0_16995,plain,
    hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10231]),
    [final] ).

cnf(i_0_16996,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1),
    inference(split_conjunct,[status(thm)],[i_0_10232]),
    [final] ).

cnf(i_0_16997,plain,
    ( hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9503]),
    [final] ).

cnf(i_0_16998,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10076]),
    [final] ).

cnf(i_0_16999,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10233]),
    [final] ).

cnf(i_0_17000,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10075]),
    [final] ).

cnf(i_0_17001,plain,
    hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10234]),
    [final] ).

cnf(i_0_17002,plain,
    ( hBOOL(hAPP(c_Quotient_ORespects(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10235]),
    [final] ).

cnf(i_0_17003,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ hBOOL(hAPP(c_Quotient_ORespects(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10235]),
    [final] ).

cnf(i_0_17004,plain,
    ( hBOOL(hAPP(X1,esk329_2(X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10236]),
    [final] ).

cnf(i_0_17005,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3)) = hAPP(c_List_Ofilter(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10237]),
    [final] ).

cnf(i_0_17006,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10238]),
    [final] ).

cnf(i_0_17007,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk535_1(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10239]),
    [final] ).

cnf(i_0_17008,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10240]),
    [final] ).

cnf(i_0_17009,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10241]),
    [final] ).

cnf(i_0_17010,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10242]),
    [final] ).

cnf(i_0_17011,plain,
    ( hAPP(c_Int_Onat,X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10243]),
    [final] ).

cnf(i_0_17012,plain,
    ( X2 = hAPP(c_Int_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10244]),
    [final] ).

cnf(i_0_17013,plain,
    ( c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_17014,plain,
    ( c_Nitpick_Onorm__frac(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_17015,plain,
    ( X2 = X3
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10245]),
    [final] ).

cnf(i_0_17016,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10246]),
    [final] ).

cnf(i_0_17017,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10247]),
    [final] ).

cnf(i_0_17018,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10248]),
    [final] ).

cnf(i_0_17019,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10249]),
    [final] ).

cnf(i_0_17020,plain,
    ( c_Nat__Transfer_Otsub(X2,X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10250]),
    [final] ).

cnf(i_0_17021,plain,
    ( c_Nat__Transfer_Otsub(X2,X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10251]),
    [final] ).

cnf(i_0_17022,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10252]),
    [final] ).

cnf(i_0_17023,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X2
    | X1 != hAPP(c_Int_Onat,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10253]),
    [final] ).

cnf(i_0_17024,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | hAPP(c_Int_Onat,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10243]),
    [final] ).

cnf(i_0_17025,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X2 != hAPP(c_Int_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10244]),
    [final] ).

cnf(i_0_17026,plain,
    ( hAPP(X3,X4) = hAPP(c_Finite__Set_Ofold1(X1,X2),X4)
    | ~ c_Big__Operators_Osemilattice__big(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10254]),
    [final] ).

cnf(i_0_17027,plain,
    ( hAPP(X3,X4) = hAPP(c_Finite__Set_Ofold1(X1,X2),X4)
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10255]),
    [final] ).

cnf(i_0_17028,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10256]),
    [final] ).

cnf(i_0_17029,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10257]),
    [final] ).

cnf(i_0_17030,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10258]),
    [final] ).

cnf(i_0_17031,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10259]),
    [final] ).

cnf(i_0_17032,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10260]),
    [final] ).

cnf(i_0_17033,plain,
    ( X1 = X2
    | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4) ),
    inference(rw,[status(thm)],[i_0_10261,c_0_6189]),
    [final] ).

cnf(i_0_17034,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10262]),
    [final] ).

cnf(i_0_17035,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) = c_Int_OMin,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10263,c_0_6070]),c_0_6071]),c_0_6072]),
    [final] ).

cnf(i_0_17036,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10109]),
    [final] ).

cnf(i_0_17037,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4)) = X4
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10264]),
    [final] ).

cnf(i_0_17038,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4)) = X4
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10265]),
    [final] ).

cnf(i_0_17039,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),X2)),
    inference(rw,[status(thm)],[i_0_10266,c_0_8358]),
    [final] ).

cnf(i_0_17040,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10267]),
    [final] ).

cnf(i_0_17041,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10096]),
    [final] ).

cnf(i_0_17042,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10268]),
    [final] ).

cnf(i_0_17043,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_17044,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7882]),
    [final] ).

cnf(i_0_17045,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8612]),
    [final] ).

cnf(i_0_17046,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_17047,plain,
    ( c_List_Olist__ex(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9711]),
    [final] ).

cnf(i_0_17048,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))),
    inference(rw,[status(thm)],[i_0_10269,c_0_7122]),
    [final] ).

cnf(i_0_17049,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(split_conjunct,[status(thm)],[fact_equiv__intrel]),
    [final] ).

cnf(i_0_17050,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10270]),
    [final] ).

cnf(i_0_17051,plain,
    c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)) = c_List_Otranspose(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10271]),
    [final] ).

cnf(i_0_17052,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk397_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9891]),
    [final] ).

cnf(i_0_17053,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_List_Oremove1(X3,X2,hAPP(c_List_Ofilter(X3,X1),X4)) = hAPP(c_List_Ofilter(X3,X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10272]),
    [final] ).

cnf(i_0_17054,plain,
    hAPP(c_Relation_OField(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10273]),
    [final] ).

cnf(i_0_17055,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9865]),
    [final] ).

cnf(i_0_17056,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10274]),
    [final] ).

cnf(i_0_17057,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10275]),
    [final] ).

cnf(i_0_17058,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X3
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9950]),
    [final] ).

cnf(i_0_17059,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9951]),
    [final] ).

cnf(i_0_17060,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10276]),
    [final] ).

cnf(i_0_17061,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10277]),
    [final] ).

cnf(i_0_17062,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10278]),
    [final] ).

cnf(i_0_17063,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10279]),
    [final] ).

cnf(i_0_17064,plain,
    c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3)) = c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10280]),
    [final] ).

cnf(i_0_17065,plain,
    ( c_List_Olist__all(X1,X2,X3)
    | ~ c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10281]),
    [final] ).

cnf(i_0_17066,plain,
    ( c_List_Olist__ex(X1,X2,X3)
    | ~ c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10282]),
    [final] ).

cnf(i_0_17067,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = hAPP(hAPP(c_List_Oappend(X2),X3),c_List_Obutlast(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10283]),
    [final] ).

cnf(i_0_17068,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Obutlast(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10284]),
    [final] ).

cnf(i_0_17069,plain,
    hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10285]),
    [final] ).

cnf(i_0_17070,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10286]),
    [final] ).

cnf(i_0_17071,plain,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10287]),
    [final] ).

cnf(i_0_17072,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10288]),
    [final] ).

cnf(i_0_17073,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))
    | ~ c_Relation_Orefl__on(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10289]),
    [final] ).

cnf(i_0_17074,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10290]),
    [final] ).

cnf(i_0_17075,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk401_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk402_2(X2,X1))
    | hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_17076,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10291]),
    [final] ).

cnf(i_0_17077,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10292]),
    [final] ).

cnf(i_0_17078,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != X2
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10127]),
    [final] ).

cnf(i_0_17079,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) != X3
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10130]),
    [final] ).

cnf(i_0_17080,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10132]),
    [final] ).

cnf(i_0_17081,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10135]),
    [final] ).

cnf(i_0_17082,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Rings_Odvd(X1)
    | X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10293]),
    [final] ).

cnf(i_0_17083,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))),
    inference(rw,[status(thm)],[i_0_10294,c_0_7122]),
    [final] ).

cnf(i_0_17084,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10295]),
    [final] ).

cnf(i_0_17085,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10296]),
    [final] ).

cnf(i_0_17086,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10297]),
    [final] ).

cnf(i_0_17087,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X2),X1),X5)
    | X1 != c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_6872]),
    [final] ).

cnf(i_0_17088,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
    | X1 != c_List_Olist_ONil(X2)
    | X3 != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6873]),
    [final] ).

cnf(i_0_17089,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10298]),
    [final] ).

cnf(i_0_17090,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10299]),
    [final] ).

cnf(i_0_17091,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10300]),
    [final] ).

cnf(i_0_17092,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10301]),
    [final] ).

cnf(i_0_17093,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10302]),
    [final] ).

cnf(i_0_17094,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10303]),
    [final] ).

cnf(i_0_17095,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9821]),
    [final] ).

cnf(i_0_17096,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9822]),
    [final] ).

cnf(i_0_17097,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9823]),
    [final] ).

cnf(i_0_17098,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9824]),
    [final] ).

cnf(i_0_17099,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
    | c_Random_Ominus__shift(X3,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9390]),
    [final] ).

cnf(i_0_17100,plain,
    hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10304]),
    [final] ).

cnf(i_0_17101,plain,
    ( X2 = X3
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10305]),
    [final] ).

cnf(i_0_17102,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10306]),
    [final] ).

cnf(i_0_17103,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)) = c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10307]),
    [final] ).

cnf(i_0_17104,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10308]),
    [final] ).

cnf(i_0_17105,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))
    | X1 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10309]),
    [final] ).

cnf(i_0_17106,plain,
    ( hAPP(c_Relation_ODomain(X2,X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10310]),
    [final] ).

cnf(i_0_17107,plain,
    ( hAPP(c_Relation_ORange(X2,X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10311]),
    [final] ).

cnf(i_0_17108,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_10312]),
    [final] ).

cnf(i_0_17109,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10313]),
    [final] ).

cnf(i_0_17110,plain,
    ( hAPP(c_Set_Oimage(X2,X3,X4),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9994]),
    [final] ).

cnf(i_0_17111,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X3,X4),X1)
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9995]),
    [final] ).

cnf(i_0_17112,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk205_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9880]),
    [final] ).

cnf(i_0_17113,plain,
    ( c_Nat__Transfer_Onat__set(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk163_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9985]),
    [final] ).

cnf(i_0_17114,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10314]),
    [final] ).

cnf(i_0_17115,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10315]),
    [final] ).

cnf(i_0_17116,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10316]),
    [final] ).

cnf(i_0_17117,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_17118,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10317]),
    [final] ).

cnf(i_0_17119,plain,
    ( hBOOL(hAPP(X1,esk145_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9703]),
    [final] ).

cnf(i_0_17120,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5975]),
    [final] ).

cnf(i_0_17121,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]),
    [final] ).

cnf(i_0_17122,plain,
    ( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = X3
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3)) ),
    inference(rw,[status(thm)],[i_0_10318,c_0_7122]),
    [final] ).

cnf(i_0_17123,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10319]),
    [final] ).

cnf(i_0_17124,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_10320]),
    [final] ).

cnf(i_0_17125,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | c_Groups_Osgn__class_Osgn(X1,X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10104]),
    [final] ).

cnf(i_0_17126,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Predicate_Osymp(X3,X1)
    | ~ c_Predicate_Otransp(X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9993]),
    [final] ).

cnf(i_0_17127,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Predicate_Osymp(X3,X1)
    | ~ c_Predicate_Otransp(X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10321]),
    [final] ).

cnf(i_0_17128,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10322]),
    [final] ).

cnf(i_0_17129,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10323]),
    [final] ).

cnf(i_0_17130,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk159_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9801]),
    [final] ).

cnf(i_0_17131,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10324]),
    [final] ).

cnf(i_0_17132,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10325]),
    [final] ).

cnf(i_0_17133,plain,
    hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10326]),
    [final] ).

cnf(i_0_17134,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk122_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10327]),
    [final] ).

cnf(i_0_17135,plain,
    ( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10328]),
    [final] ).

cnf(i_0_17136,plain,
    ( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10329]),
    [final] ).

cnf(i_0_17137,plain,
    ( c_Finite__Set_Ofun__left__comm(X1,tc_List_Olist(X1),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10330]),
    [final] ).

cnf(i_0_17138,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10331]),
    [final] ).

cnf(i_0_17139,plain,
    ( c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Osym(X1,X3)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10332]),
    [final] ).

cnf(i_0_17140,plain,
    ( c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Osym(X1,X3)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10333]),
    [final] ).

cnf(i_0_17141,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10122]),
    [final] ).

cnf(i_0_17142,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10334]),
    [final] ).

cnf(i_0_17143,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10123]),
    [final] ).

cnf(i_0_17144,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10335]),
    [final] ).

cnf(i_0_17145,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_10336]),
    [final] ).

cnf(i_0_17146,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10310]),
    [final] ).

cnf(i_0_17147,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10311]),
    [final] ).

cnf(i_0_17148,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10337]),
    [final] ).

cnf(i_0_17149,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10338]),
    [final] ).

cnf(i_0_17150,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10083]),
    [final] ).

cnf(i_0_17151,plain,
    ( X3 = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))
    | hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)) != hAPP(c_List_Orev(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10339]),
    [final] ).

cnf(i_0_17152,plain,
    ( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))
    | hAPP(c_List_Orev(X1),X2) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10340]),
    [final] ).

cnf(i_0_17153,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10341]),
    [final] ).

cnf(i_0_17154,plain,
    c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10342]),
    [final] ).

cnf(i_0_17155,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10343]),
    [final] ).

cnf(i_0_17156,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_10344,c_0_6189]),
    [final] ).

cnf(i_0_17157,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2)) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10040]),
    [final] ).

cnf(i_0_17158,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J]),
    [final] ).

cnf(i_0_17159,plain,
    hAPP(c_List_Orev(X1),c_List_Oreplicate(X1,X2,X3)) = c_List_Oreplicate(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10345]),
    [final] ).

cnf(i_0_17160,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10346]),
    [final] ).

cnf(i_0_17161,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9402]),
    [final] ).

cnf(i_0_17162,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9919]),
    [final] ).

cnf(i_0_17163,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9920]),
    [final] ).

cnf(i_0_17164,plain,
    ( hAPP(X1,X2) = hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_17165,plain,
    ( hAPP(X1,X2) = hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Equiv__Relations_Oequivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9974]),
    [final] ).

cnf(i_0_17166,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10347]),
    [final] ).

cnf(i_0_17167,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10348]),
    [final] ).

cnf(i_0_17168,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10349]),
    [final] ).

cnf(i_0_17169,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),esk137_3(X2,X3,X1)) = X2
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_17170,plain,
    ( c_List_Oall__interval__int(X1,X2,X3)
    | ~ c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10350]),
    [final] ).

cnf(i_0_17171,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk470_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10351]),
    [final] ).

cnf(i_0_17172,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk469_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10352]),
    [final] ).

cnf(i_0_17173,plain,
    ( c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))
    | ~ c_List_Olist__all(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10281]),
    [final] ).

cnf(i_0_17174,plain,
    ( c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10282]),
    [final] ).

cnf(i_0_17175,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10353]),
    [final] ).

cnf(i_0_17176,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
    inference(rw,[status(thm)],[i_0_10354,c_0_6189]),
    [final] ).

cnf(i_0_17177,plain,
    ( hBOOL(hAPP(X3,X2))
    | X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
    | ~ hBOOL(hAPP(X3,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_17178,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10013]),
    [final] ).

cnf(i_0_17179,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9892]),
    [final] ).

cnf(i_0_17180,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9681]),
    [final] ).

cnf(i_0_17181,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10355]),
    [final] ).

cnf(i_0_17182,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10356]),
    [final] ).

cnf(i_0_17183,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10357]),
    [final] ).

cnf(i_0_17184,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10163]),
    [final] ).

cnf(i_0_17185,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10163]),
    [final] ).

cnf(i_0_17186,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9736]),
    [final] ).

cnf(i_0_17187,plain,
    ( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk162_2(X2,X1))
    | hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9789]),
    [final] ).

cnf(i_0_17188,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_greaterThan__0]),
    [final] ).

cnf(i_0_17189,plain,
    c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2)),
    inference(rw,[status(thm)],[i_0_10358,c_0_7324]),
    [final] ).

cnf(i_0_17190,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_List_Oreplicate(X4,X1,X2) != c_List_Oreplicate(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10359]),
    [final] ).

cnf(i_0_17191,plain,
    ( X3 = X4
    | X1 != X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4)
    | ~ class_Groups_Oab__group__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10360]),
    [final] ).

cnf(i_0_17192,plain,
    ( X3 = X4
    | X1 != X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)
    | ~ class_Groups_Oab__group__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10360]),
    [final] ).

cnf(i_0_17193,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10361]),
    [final] ).

cnf(i_0_17194,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4) != hAPP(c_List_Ofilter(X3,X1),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_17195,plain,
    ( hBOOL(hAPP(X1,X2))
    | hAPP(c_List_Ofilter(X3,X1),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6171]),
    [final] ).

cnf(i_0_17196,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9863]),
    [final] ).

cnf(i_0_17197,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10362]),
    [final] ).

cnf(i_0_17198,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9526]),
    [final] ).

cnf(i_0_17199,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10363]),
    [final] ).

cnf(i_0_17200,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10364]),
    [final] ).

cnf(i_0_17201,plain,
    ( c_Random_Olog(X1,X2) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(split_conjunct,[status(thm)],[i_0_9294]),
    [final] ).

cnf(i_0_17202,plain,
    ( hBOOL(hAPP(hAPP(X1,esk278_1(X1)),esk279_1(X1)))
    | hAPP(X1,esk278_1(X1)) = hAPP(X1,esk279_1(X1))
    | c_Equiv__Relations_Oequivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9974]),
    [final] ).

cnf(i_0_17203,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10365]),
    [final] ).

cnf(i_0_17204,plain,
    ( c_Enum_On__lists(X2,X1,c_List_Olist_ONil(X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X2)),c_List_Olist_ONil(X2)),c_List_Olist_ONil(tc_List_Olist(X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10366]),
    [final] ).

cnf(i_0_17205,plain,
    ( X2 = X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10367]),
    [final] ).

cnf(i_0_17206,plain,
    ( X2 = X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10368]),
    [final] ).

cnf(i_0_17207,plain,
    ( X3 = X4
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10369]),
    [final] ).

cnf(i_0_17208,plain,
    ( X3 = X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10370]),
    [final] ).

cnf(i_0_17209,plain,
    ( X3 = X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10371]),
    [final] ).

cnf(i_0_17210,plain,
    ( X1 = X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) != c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10372]),
    [final] ).

cnf(i_0_17211,plain,
    ( X1 = X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) != c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10372]),
    [final] ).

cnf(i_0_17212,plain,
    ( X1 = X2
    | c_List_Oreplicate(X3,X1,X4) != c_List_Oreplicate(X3,X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10359]),
    [final] ).

cnf(i_0_17213,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10373]),
    [final] ).

cnf(i_0_17214,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10373]),
    [final] ).

cnf(i_0_17215,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10373]),
    [final] ).

cnf(i_0_17216,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10374]),
    [final] ).

cnf(i_0_17217,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10374]),
    [final] ).

cnf(i_0_17218,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10374]),
    [final] ).

cnf(i_0_17219,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_10375]),
    [final] ).

cnf(i_0_17220,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_10376]),
    [final] ).

cnf(i_0_17221,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
    | X1 != X2
    | X2 != X3
    | ~ class_Orderings_Oorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10000]),
    [final] ).

cnf(i_0_17222,plain,
    ( c_Nat__Transfer_Ois__nat(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10377]),
    [final] ).

cnf(i_0_17223,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
    | c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ c_Nitpick_Owf_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9968]),
    [final] ).

cnf(i_0_17224,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7092]),
    [final] ).

cnf(i_0_17225,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),X1)
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10339]),
    [final] ).

cnf(i_0_17226,plain,
    ( hAPP(c_List_Orev(X2),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))
    | X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10340]),
    [final] ).

cnf(i_0_17227,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10378]),
    [final] ).

cnf(i_0_17228,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10379]),
    [final] ).

cnf(i_0_17229,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10380]),
    [final] ).

cnf(i_0_17230,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10296]),
    [final] ).

cnf(i_0_17231,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)
    | ~ class_Int_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10256]),
    [final] ).

cnf(i_0_17232,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,X1))
    | ~ class_Rings_Oring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9459]),
    [final] ).

cnf(i_0_17233,plain,
    hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10381]),
    [final] ).

cnf(i_0_17234,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10382]),
    [final] ).

cnf(i_0_17235,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10383]),
    [final] ).

cnf(i_0_17236,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10384]),
    [final] ).

cnf(i_0_17237,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)) = hAPP(c_Int_Onat,X2)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6469]),
    [final] ).

cnf(i_0_17238,plain,
    c_Relation_Oantisym(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10385]),
    [final] ).

cnf(i_0_17239,plain,
    c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10386]),
    [final] ).

cnf(i_0_17240,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10387]),
    [final] ).

cnf(i_0_17241,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3)
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10160]),
    [final] ).

cnf(i_0_17242,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10161]),
    [final] ).

cnf(i_0_17243,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),esk460_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10228]),
    [final] ).

cnf(i_0_17244,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10388]),
    [final] ).

cnf(i_0_17245,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10178]),
    [final] ).

cnf(i_0_17246,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10389]),
    [final] ).

cnf(i_0_17247,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10390]),
    [final] ).

cnf(i_0_17248,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10116]),
    [final] ).

cnf(i_0_17249,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hBOOL(hAPP(c_List_Odistinct(X2),c_List_Obutlast(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10391]),
    [final] ).

cnf(i_0_17250,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10392]),
    [final] ).

cnf(i_0_17251,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk160_1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9721]),
    [final] ).

cnf(i_0_17252,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk450_2(X1,X2)),esk449_2(X1,X2))
    | X1 = c_List_Olist_ONil(X2)
    | ~ c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_17253,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10393]),
    [final] ).

cnf(i_0_17254,plain,
    ( X1 = X2
    | hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1) != hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10393]),
    [final] ).

cnf(i_0_17255,plain,
    ( X2 = X4
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10394]),
    [final] ).

cnf(i_0_17256,plain,
    ( X3 = X4
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10395]),
    [final] ).

cnf(i_0_17257,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10396]),
    [final] ).

cnf(i_0_17258,plain,
    ( c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3))
    | ~ c_List_Oall__interval__int(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10350]),
    [final] ).

cnf(i_0_17259,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(X1,X2) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9475]),
    [final] ).

cnf(i_0_17260,plain,
    ( c_List_Oupto(X2,X1) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10397]),
    [final] ).

cnf(i_0_17261,plain,
    ( c_Random_Olog(X2,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9294]),
    [final] ).

cnf(i_0_17262,plain,
    c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10398]),
    [final] ).

cnf(i_0_17263,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_number__of2]),
    [final] ).

cnf(i_0_17264,plain,
    ( hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = c_List_Olist_ONil(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8735]),
    [final] ).

cnf(i_0_17265,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10399]),
    [final] ).

cnf(i_0_17266,plain,
    ( c_Quickcheck_Obeyond(X1,X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10400]),
    [final] ).

cnf(i_0_17267,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_10401]),
    [final] ).

cnf(i_0_17268,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10402]),
    [final] ).

cnf(i_0_17269,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_10403]),
    [final] ).

cnf(i_0_17270,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_List_Orotate1(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(rw,[status(thm)],[i_0_10404,c_0_6732]),
    [final] ).

cnf(i_0_17271,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10405]),
    [final] ).

cnf(i_0_17272,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10406]),
    [final] ).

cnf(i_0_17273,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10407]),
    [final] ).

cnf(i_0_17274,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10408]),
    [final] ).

cnf(i_0_17275,plain,
    c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10409]),
    [final] ).

cnf(i_0_17276,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_10410]),
    [final] ).

cnf(i_0_17277,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9730]),
    [final] ).

cnf(i_0_17278,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X1,esk142_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9547]),
    [final] ).

cnf(i_0_17279,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10411]),
    [final] ).

cnf(i_0_17280,plain,
    ( c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = X4
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9763]),
    [final] ).

cnf(i_0_17281,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1) != hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_17282,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9729]),
    [final] ).

cnf(i_0_17283,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10412]),
    [final] ).

cnf(i_0_17284,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10413]),
    [final] ).

cnf(i_0_17285,plain,
    hAPP(c_Finite__Set_Ofold1(X1,X2),X3) = c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10414]),
    [final] ).

cnf(i_0_17286,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk214_2(X2,X1))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10415]),
    [final] ).

cnf(i_0_17287,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk215_2(X2,X1))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10416]),
    [final] ).

cnf(i_0_17288,plain,
    ( c_Nat__Transfer_Ois__nat(X2)
    | ~ c_Nat__Transfer_Onat__set(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10417]),
    [final] ).

cnf(i_0_17289,plain,
    ( hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10097]),
    [final] ).

cnf(i_0_17290,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10418]),
    [final] ).

cnf(i_0_17291,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10419]),
    [final] ).

cnf(i_0_17292,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10420]),
    [final] ).

cnf(i_0_17293,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10421]),
    [final] ).

cnf(i_0_17294,plain,
    ( X2 = esk496_3(X3,X4,X1)
    | c_FunDef_OTHE__default(X4,X3,X1) = X3
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8083]),
    [final] ).

cnf(i_0_17295,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10065]),
    [final] ).

cnf(i_0_17296,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10422]),
    [final] ).

cnf(i_0_17297,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10423]),
    [final] ).

cnf(i_0_17298,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10424]),
    [final] ).

cnf(i_0_17299,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10425]),
    [final] ).

cnf(i_0_17300,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10426]),
    [final] ).

cnf(i_0_17301,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10303]),
    [final] ).

cnf(i_0_17302,plain,
    hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = hAPP(c_Relation_ORange(X2,X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_10427]),
    [final] ).

cnf(i_0_17303,plain,
    hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = hAPP(c_Relation_ODomain(X2,X1),X3),
    inference(split_conjunct,[status(thm)],[i_0_10428]),
    [final] ).

cnf(i_0_17304,plain,
    c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10429]),
    [final] ).

cnf(i_0_17305,plain,
    c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10430]),
    [final] ).

cnf(i_0_17306,plain,
    hAPP(c_Relation_ORange(X1,X2),X3) = hAPP(c_Relation_ODomain(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_10431]),
    [final] ).

cnf(i_0_17307,plain,
    ( hBOOL(hAPP(X2,esk457_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10432]),
    [final] ).

cnf(i_0_17308,plain,
    ( hBOOL(hAPP(X2,esk456_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10433]),
    [final] ).

cnf(i_0_17309,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10434]),
    [final] ).

cnf(i_0_17310,plain,
    ( X4 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10435]),
    [final] ).

cnf(i_0_17311,plain,
    ( X4 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Omap(X2,X1),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10436]),
    [final] ).

cnf(i_0_17312,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10071]),
    [final] ).

cnf(i_0_17313,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10437]),
    [final] ).

cnf(i_0_17314,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10438]),
    [final] ).

cnf(i_0_17315,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10439]),
    [final] ).

cnf(i_0_17316,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10440]),
    [final] ).

cnf(i_0_17317,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10441]),
    [final] ).

cnf(i_0_17318,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10291]),
    [final] ).

cnf(i_0_17319,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10442]),
    [final] ).

cnf(i_0_17320,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10443]),
    [final] ).

cnf(i_0_17321,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10444]),
    [final] ).

cnf(i_0_17322,plain,
    ( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10445]),
    [final] ).

cnf(i_0_17323,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10446]),
    [final] ).

cnf(i_0_17324,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9950]),
    [final] ).

cnf(i_0_17325,plain,
    ( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Fields_Ofield__inverse__zero(X2)
    | ~ class_Int_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9951]),
    [final] ).

cnf(i_0_17326,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_10447]),
    [final] ).

cnf(i_0_17327,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10050]),
    [final] ).

cnf(i_0_17328,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10448]),
    [final] ).

cnf(i_0_17329,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10449]),
    [final] ).

cnf(i_0_17330,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10316]),
    [final] ).

cnf(i_0_17331,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10316]),
    [final] ).

cnf(i_0_17332,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10053]),
    [final] ).

cnf(i_0_17333,plain,
    c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(rw,[status(thm)],[i_0_10450,c_0_7122]),
    [final] ).

cnf(i_0_17334,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10451]),
    [final] ).

cnf(i_0_17335,plain,
    ( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_10452,c_0_7122]),
    [final] ).

cnf(i_0_17336,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_OtakeWhile(X1,X3,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10453]),
    [final] ).

cnf(i_0_17337,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X3,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10454]),
    [final] ).

cnf(i_0_17338,plain,
    ( X1 = X3
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10455]),
    [final] ).

cnf(i_0_17339,plain,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10456]),
    [final] ).

cnf(i_0_17340,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10457]),
    [final] ).

cnf(i_0_17341,plain,
    ( hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10458]),
    [final] ).

cnf(i_0_17342,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10459]),
    [final] ).

cnf(i_0_17343,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10460]),
    [final] ).

cnf(i_0_17344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10461]),
    [final] ).

cnf(i_0_17345,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10462]),
    [final] ).

cnf(i_0_17346,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10463]),
    [final] ).

cnf(i_0_17347,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_ONats(X1)))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10464]),
    [final] ).

cnf(i_0_17348,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10465]),
    [final] ).

cnf(i_0_17349,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) = X4
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10444]),
    [final] ).

cnf(i_0_17350,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = X4
    | X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10445]),
    [final] ).

cnf(i_0_17351,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
    | ~ class_Rings_Odivision__ring(X1)
    | X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10466]),
    [final] ).

cnf(i_0_17352,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
    | ~ class_Rings_Odivision__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10467]),
    [final] ).

cnf(i_0_17353,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
    | ~ class_Rings_Odivision__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10468]),
    [final] ).

cnf(i_0_17354,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10445]),
    [final] ).

cnf(i_0_17355,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10444]),
    [final] ).

cnf(i_0_17356,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
    | ~ class_Rings_Odivision__ring(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_10469]),
    [final] ).

cnf(i_0_17357,plain,
    ( X2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != X4
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10468]),
    [final] ).

cnf(i_0_17358,plain,
    ( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != X4
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10467]),
    [final] ).

cnf(i_0_17359,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10470]),
    [final] ).

cnf(i_0_17360,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10471]),
    [final] ).

cnf(i_0_17361,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10472]),
    [final] ).

cnf(i_0_17362,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10473]),
    [final] ).

cnf(i_0_17363,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10474]),
    [final] ).

cnf(i_0_17364,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10475]),
    [final] ).

cnf(i_0_17365,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Equiv__Relations_Oequivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9974]),
    [final] ).

cnf(i_0_17366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10249]),
    [final] ).

cnf(i_0_17367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk159_1(X1)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9801]),
    [final] ).

cnf(i_0_17368,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10476]),
    [final] ).

cnf(i_0_17369,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10477]),
    [final] ).

cnf(i_0_17370,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10478]),
    [final] ).

cnf(i_0_17371,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk160_1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9721]),
    [final] ).

cnf(i_0_17372,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10458]),
    [final] ).

cnf(i_0_17373,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10479]),
    [final] ).

cnf(i_0_17374,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
    | ~ class_Groups_Oabs__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10101]),
    [final] ).

cnf(i_0_17375,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10480,c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_17376,plain,
    ( X1 = X3
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10481]),
    [final] ).

cnf(i_0_17377,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10482]),
    [final] ).

cnf(i_0_17378,plain,
    hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10483]),
    [final] ).

cnf(i_0_17379,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10484]),
    [final] ).

cnf(i_0_17380,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Otake(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10485]),
    [final] ).

cnf(i_0_17381,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10486]),
    [final] ).

cnf(i_0_17382,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10487]),
    [final] ).

cnf(i_0_17383,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9432]),
    [final] ).

cnf(i_0_17384,plain,
    hAPP(c_Set_OPow(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10488]),
    [final] ).

cnf(i_0_17385,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2) = c_Groups_Oone__class_Oone(X3)
    | ~ class_Groups_Ocomm__monoid__mult(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8650]),
    [final] ).

cnf(i_0_17386,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10489]),
    [final] ).

cnf(i_0_17387,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10490]),
    [final] ).

cnf(i_0_17388,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2) = c_Groups_Ozero__class_Ozero(X3)
    | ~ class_Groups_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8652]),
    [final] ).

cnf(i_0_17389,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10491]),
    [final] ).

cnf(i_0_17390,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10492]),
    [final] ).

cnf(i_0_17391,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10305]),
    [final] ).

cnf(i_0_17392,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10493]),
    [final] ).

cnf(i_0_17393,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10494]),
    [final] ).

cnf(i_0_17394,plain,
    hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10495]),
    [final] ).

cnf(i_0_17395,plain,
    c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10496]),
    [final] ).

cnf(i_0_17396,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10497]),
    [final] ).

cnf(i_0_17397,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10498]),
    [final] ).

cnf(i_0_17398,plain,
    ( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10499]),
    [final] ).

cnf(i_0_17399,plain,
    ( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10500]),
    [final] ).

cnf(i_0_17400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9765]),
    [final] ).

cnf(i_0_17401,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10501]),
    [final] ).

cnf(i_0_17402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10336]),
    [final] ).

cnf(i_0_17403,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10331]),
    [final] ).

cnf(i_0_17404,plain,
    ( hBOOL(hAPP(hAPP(X1,esk523_1(X1)),esk523_1(X1)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_17405,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10502]),
    [final] ).

cnf(i_0_17406,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10333]),
    [final] ).

cnf(i_0_17407,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10503]),
    [final] ).

cnf(i_0_17408,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10504]),
    [final] ).

cnf(i_0_17409,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10505]),
    [final] ).

cnf(i_0_17410,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10506]),
    [final] ).

cnf(i_0_17411,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_10507]),
    [final] ).

cnf(i_0_17412,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oreplicate(X1,X2,X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10508]),
    [final] ).

cnf(i_0_17413,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10509]),
    [final] ).

cnf(i_0_17414,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10510]),
    [final] ).

cnf(i_0_17415,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10511]),
    [final] ).

cnf(i_0_17416,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10512]),
    [final] ).

cnf(i_0_17417,plain,
    ( esk137_3(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(X3),X2) != hAPP(c_Nat_OSuc,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_17418,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10513]),
    [final] ).

cnf(i_0_17419,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10514]),
    [final] ).

cnf(i_0_17420,plain,
    ( c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Obutlast(X2,X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10283]),
    [final] ).

cnf(i_0_17421,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10515]),
    [final] ).

cnf(i_0_17422,plain,
    c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)) = hAPP(hAPP(c_List_Otake(X1),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_10516]),
    [final] ).

cnf(i_0_17423,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10517]),
    [final] ).

cnf(i_0_17424,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),c_Divides_Odivmod__int(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10518]),
    [final] ).

cnf(i_0_17425,plain,
    ( c_Divides_Opdivmod(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10519]),
    [final] ).

cnf(i_0_17426,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10520]),
    [final] ).

cnf(i_0_17427,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10521]),
    [final] ).

cnf(i_0_17428,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10514]),
    [final] ).

cnf(i_0_17429,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10522]),
    [final] ).

cnf(i_0_17430,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10523]),
    [final] ).

cnf(i_0_17431,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nitpick_Onat__gcd(X2,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10524]),
    [final] ).

cnf(i_0_17432,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10525]),
    [final] ).

cnf(i_0_17433,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10253]),
    [final] ).

cnf(i_0_17434,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10526]),
    [final] ).

cnf(i_0_17435,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[i_0_10527]),
    [final] ).

cnf(i_0_17436,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[i_0_10528]),
    [final] ).

cnf(i_0_17437,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[i_0_10529]),
    [final] ).

cnf(i_0_17438,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[i_0_10530]),
    [final] ).

cnf(i_0_17439,hypothesis,
    ~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
    inference(split_conjunct,[status(thm)],[i_0_10531]),
    [final] ).

cnf(i_0_17440,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[i_0_10532]),
    [final] ).

cnf(i_0_17441,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10238]),
    [final] ).

cnf(i_0_17442,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3) = c_List_Olist_ONil(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10533]),
    [final] ).

cnf(i_0_17443,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10534]),
    [final] ).

cnf(i_0_17444,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10535]),
    [final] ).

cnf(i_0_17445,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10536]),
    [final] ).

cnf(i_0_17446,plain,
    hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10537]),
    [final] ).

cnf(i_0_17447,plain,
    hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10538]),
    [final] ).

cnf(i_0_17448,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_17449,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9729]),
    [final] ).

cnf(i_0_17450,plain,
    c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10539]),
    [final] ).

cnf(i_0_17451,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Int_Onat,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10243]),
    [final] ).

cnf(i_0_17452,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Int_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10244]),
    [final] ).

cnf(i_0_17453,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Ohd(X2),c_List_Oreplicate(X2,X1,X3)) = X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10540]),
    [final] ).

cnf(i_0_17454,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(rw,[status(thm)],[i_0_10541,c_0_8304]),
    [final] ).

cnf(i_0_17455,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))),
    inference(rw,[status(thm)],[i_0_10542,c_0_8304]),
    [final] ).

cnf(i_0_17456,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10543]),
    [final] ).

cnf(i_0_17457,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10544]),
    [final] ).

cnf(i_0_17458,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10545]),
    [final] ).

cnf(i_0_17459,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10546]),
    [final] ).

cnf(i_0_17460,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10547]),
    [final] ).

cnf(i_0_17461,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10548]),
    [final] ).

cnf(i_0_17462,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10549]),
    [final] ).

cnf(i_0_17463,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10550]),
    [final] ).

cnf(i_0_17464,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10551]),
    [final] ).

cnf(i_0_17465,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10552]),
    [final] ).

cnf(i_0_17466,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10553]),
    [final] ).

cnf(i_0_17467,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17468,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17469,plain,
    ( hBOOL(hAPP(X1,esk512_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9434]),
    [final] ).

cnf(i_0_17470,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10236]),
    [final] ).

cnf(i_0_17471,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10556]),
    [final] ).

cnf(i_0_17472,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10557]),
    [final] ).

cnf(i_0_17473,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10558]),
    [final] ).

cnf(i_0_17474,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10415]),
    [final] ).

cnf(i_0_17475,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10416]),
    [final] ).

cnf(i_0_17476,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10559]),
    [final] ).

cnf(i_0_17477,plain,
    ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7686]),
    [final] ).

cnf(i_0_17478,plain,
    ( c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10284]),
    [final] ).

cnf(i_0_17479,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10560]),
    [final] ).

cnf(i_0_17480,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10561]),
    [final] ).

cnf(i_0_17481,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10327]),
    [final] ).

cnf(i_0_17482,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10562]),
    [final] ).

cnf(i_0_17483,plain,
    hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2)) = c_List_Olist_ONil(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10563]),
    [final] ).

cnf(i_0_17484,plain,
    ( hAPP(hAPP(X2,X4),X4) = X4
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10564]),
    [final] ).

cnf(i_0_17485,plain,
    c_Enum_Osublists(X1,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10565]),
    [final] ).

cnf(i_0_17486,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | hAPP(c_Int_Onat,X2) = X1
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10243]),
    [final] ).

cnf(i_0_17487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X1 = hAPP(c_Int_Onat,X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10244]),
    [final] ).

cnf(i_0_17488,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10566]),
    [final] ).

cnf(i_0_17489,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10567]),
    [final] ).

cnf(i_0_17490,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10568]),
    [final] ).

cnf(i_0_17491,plain,
    ( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10523]),
    [final] ).

cnf(i_0_17492,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Olast(X2,c_List_Oreplicate(X2,X1,X3)) = X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10569]),
    [final] ).

cnf(i_0_17493,plain,
    hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10570]),
    [final] ).

cnf(i_0_17494,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10571]),
    [final] ).

cnf(i_0_17495,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10572]),
    [final] ).

cnf(i_0_17496,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10376]),
    [final] ).

cnf(i_0_17497,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10573]),
    [final] ).

cnf(i_0_17498,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10574]),
    [final] ).

cnf(i_0_17499,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10575]),
    [final] ).

cnf(i_0_17500,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10576]),
    [final] ).

cnf(i_0_17501,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10577]),
    [final] ).

cnf(i_0_17502,plain,
    ( X1 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10309]),
    [final] ).

cnf(i_0_17503,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk163_1(X1)),X1))
    | c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9985]),
    [final] ).

cnf(i_0_17504,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10578]),
    [final] ).

cnf(i_0_17505,plain,
    hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10579]),
    [final] ).

cnf(i_0_17506,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Rings_Omult__zero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2)
    | ~ class_Rings_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10580]),
    [final] ).

cnf(i_0_17507,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Rings_Omult__zero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2)
    | ~ class_Rings_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10580]),
    [final] ).

cnf(i_0_17508,plain,
    ( hBOOL(hAPP(X2,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred2_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7696]),
    [final] ).

cnf(i_0_17509,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10581]),
    [final] ).

cnf(i_0_17510,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10401]),
    [final] ).

cnf(i_0_17511,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10403]),
    [final] ).

cnf(i_0_17512,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X1),X2)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10582]),
    [final] ).

cnf(i_0_17513,plain,
    ( hAPP(c_Set_OCollect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10583]),
    [final] ).

cnf(i_0_17514,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10584]),
    [final] ).

cnf(i_0_17515,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10585]),
    [final] ).

cnf(i_0_17516,plain,
    ( hAPP(c_List_Oset(X1),esk460_2(X2,X1)) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10228]),
    [final] ).

cnf(i_0_17517,plain,
    ( hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10388]),
    [final] ).

cnf(i_0_17518,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10586]),
    [final] ).

cnf(i_0_17519,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10587]),
    [final] ).

cnf(i_0_17520,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10588]),
    [final] ).

cnf(i_0_17521,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_10589]),
    [final] ).

cnf(i_0_17522,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10312]),
    [final] ).

cnf(i_0_17523,plain,
    c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10590]),
    [final] ).

cnf(i_0_17524,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10591]),
    [final] ).

cnf(i_0_17525,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10592]),
    [final] ).

cnf(i_0_17526,plain,
    ( c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X5)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10359]),
    [final] ).

cnf(i_0_17527,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_atMost__0]),
    [final] ).

cnf(i_0_17528,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10593]),
    [final] ).

cnf(i_0_17529,plain,
    hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_OField(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10594]),
    [final] ).

cnf(i_0_17530,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10595]),
    [final] ).

cnf(i_0_17531,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10596]),
    [final] ).

cnf(i_0_17532,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10597]),
    [final] ).

cnf(i_0_17533,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17534,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17535,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10598]),
    [final] ).

cnf(i_0_17536,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17537,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9671]),
    [final] ).

cnf(i_0_17539,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9671]),
    [final] ).

cnf(i_0_17540,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10599]),
    [final] ).

cnf(i_0_17541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
    | X1 != X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9893]),
    [final] ).

cnf(i_0_17542,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10600]),
    [final] ).

cnf(i_0_17543,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = X3
    | ~ class_Groups_Ogroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10601]),
    [final] ).

cnf(i_0_17544,plain,
    ( X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10602]),
    [final] ).

cnf(i_0_17545,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2)) = hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10603]),
    [final] ).

cnf(i_0_17546,plain,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
    inference(split_conjunct,[status(thm)],[i_0_10604]),
    [final] ).

cnf(i_0_17547,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
    inference(split_conjunct,[status(thm)],[i_0_10605]),
    [final] ).

cnf(i_0_17548,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))
    | ~ c_Nat__Transfer_Ois__nat(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10606]),
    [final] ).

cnf(i_0_17549,plain,
    ( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10418]),
    [final] ).

cnf(i_0_17550,plain,
    ( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10419]),
    [final] ).

cnf(i_0_17551,plain,
    ( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10420]),
    [final] ).

cnf(i_0_17552,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10421]),
    [final] ).

cnf(i_0_17553,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk460_2(X2,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10228]),
    [final] ).

cnf(i_0_17554,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10388]),
    [final] ).

cnf(i_0_17555,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10607]),
    [final] ).

cnf(i_0_17556,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10608]),
    [final] ).

cnf(i_0_17557,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10609]),
    [final] ).

cnf(i_0_17558,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ c_Nat__Transfer_Ois__nat(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10377]),
    [final] ).

cnf(i_0_17559,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10610]),
    [final] ).

cnf(i_0_17560,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10611]),
    [final] ).

cnf(i_0_17561,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10608]),
    [final] ).

cnf(i_0_17562,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10608]),
    [final] ).

cnf(i_0_17563,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) = hAPP(c_Int_Onat,X1),
    inference(split_conjunct,[status(thm)],[i_0_10612]),
    [final] ).

cnf(i_0_17564,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[fact_int__0__less__1]),
    [final] ).

cnf(i_0_17565,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
    [final] ).

cnf(i_0_17566,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
    [final] ).

cnf(i_0_17567,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10613]),
    [final] ).

cnf(i_0_17568,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10614]),
    [final] ).

cnf(i_0_17569,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10615]),
    [final] ).

cnf(i_0_17570,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10616]),
    [final] ).

cnf(i_0_17571,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10617]),
    [final] ).

cnf(i_0_17572,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10618]),
    [final] ).

cnf(i_0_17573,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10619]),
    [final] ).

cnf(i_0_17574,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10620]),
    [final] ).

cnf(i_0_17575,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10621]),
    [final] ).

cnf(i_0_17576,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10622]),
    [final] ).

cnf(i_0_17577,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10623]),
    [final] ).

cnf(i_0_17578,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10624]),
    [final] ).

cnf(i_0_17579,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10625]),
    [final] ).

cnf(i_0_17580,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10626]),
    [final] ).

cnf(i_0_17581,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10627]),
    [final] ).

cnf(i_0_17582,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
    | c_Quickcheck_Obeyond(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_10400]),
    [final] ).

cnf(i_0_17583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | c_List_Oupto(X1,X2) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9401]),
    [final] ).

cnf(i_0_17584,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10251]),
    [final] ).

cnf(i_0_17585,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10628]),
    [final] ).

cnf(i_0_17586,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10629]),
    [final] ).

cnf(i_0_17587,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10365]),
    [final] ).

cnf(i_0_17588,plain,
    ( c_Divides_Odivmod__int(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5240]),
    [final] ).

cnf(i_0_17589,plain,
    ( c_Divides_Odivmod__int(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5238]),
    [final] ).

cnf(i_0_17590,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10630]),
    [final] ).

cnf(i_0_17591,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10631]),
    [final] ).

cnf(i_0_17592,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10632]),
    [final] ).

cnf(i_0_17593,plain,
    ( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5240]),
    [final] ).

cnf(i_0_17594,plain,
    ( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_5238]),
    [final] ).

cnf(i_0_17595,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10633]),
    [final] ).

cnf(i_0_17596,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10633]),
    [final] ).

cnf(i_0_17597,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10634]),
    [final] ).

cnf(i_0_17598,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10635]),
    [final] ).

cnf(i_0_17599,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10636]),
    [final] ).

cnf(i_0_17600,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10637]),
    [final] ).

cnf(i_0_17601,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10638]),
    [final] ).

cnf(i_0_17602,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10639]),
    [final] ).

cnf(i_0_17603,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10640]),
    [final] ).

cnf(i_0_17604,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10641]),
    [final] ).

cnf(i_0_17605,plain,
    hAPP(c_Code__Numeral_Onat__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_10642,c_0_8975]),
    [final] ).

cnf(i_0_17606,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10561]),
    [final] ).

cnf(i_0_17607,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10643]),
    [final] ).

cnf(i_0_17608,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10644]),
    [final] ).

cnf(i_0_17609,plain,
    c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10645]),
    [final] ).

cnf(i_0_17610,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10410]),
    [final] ).

cnf(i_0_17611,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10646]),
    [final] ).

cnf(i_0_17612,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10647]),
    [final] ).

cnf(i_0_17613,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10648]),
    [final] ).

cnf(i_0_17614,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[i_0_10649]),
    [final] ).

cnf(i_0_17615,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10650]),
    [final] ).

cnf(i_0_17616,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10651]),
    [final] ).

cnf(i_0_17617,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10652]),
    [final] ).

cnf(i_0_17618,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10653]),
    [final] ).

cnf(i_0_17619,plain,
    c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10654]),
    [final] ).

cnf(i_0_17620,plain,
    hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10655]),
    [final] ).

cnf(i_0_17621,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10656]),
    [final] ).

cnf(i_0_17622,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10157]),
    [final] ).

cnf(i_0_17623,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Predicate_Oreflp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10657]),
    [final] ).

cnf(i_0_17624,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10658]),
    [final] ).

cnf(i_0_17625,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1) != X3
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10444]),
    [final] ).

cnf(i_0_17626,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10445]),
    [final] ).

cnf(i_0_17627,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10351]),
    [final] ).

cnf(i_0_17628,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10352]),
    [final] ).

cnf(i_0_17629,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17630,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17631,plain,
    ( hAPP(hAPP(c_List_Omap(X2,X3),X4),X1) = c_List_Olist_ONil(X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10435]),
    [final] ).

cnf(i_0_17632,plain,
    ( hAPP(hAPP(c_List_Olist__update(X2,X1),X3),X4) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10434]),
    [final] ).

cnf(i_0_17633,plain,
    ( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10436]),
    [final] ).

cnf(i_0_17634,plain,
    c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10659]),
    [final] ).

cnf(i_0_17635,plain,
    ( X2 = X3
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10660]),
    [final] ).

cnf(i_0_17636,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10661]),
    [final] ).

cnf(i_0_17637,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_10662]),
    [final] ).

cnf(i_0_17638,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,X2))
    | X3 != c_Hilbert__Choice_OEps(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10663]),
    [final] ).

cnf(i_0_17639,plain,
    hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X1),
    inference(split_conjunct,[status(thm)],[i_0_10664]),
    [final] ).

cnf(i_0_17640,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_10665]),
    [final] ).

cnf(i_0_17641,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10666]),
    [final] ).

cnf(i_0_17642,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10667]),
    [final] ).

cnf(i_0_17643,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10668]),
    [final] ).

cnf(i_0_17644,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
    | ~ c_Nat__Transfer_Ois__nat(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10669]),
    [final] ).

cnf(i_0_17645,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | X2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17646,plain,
    ( X1 = c_Orderings_Otop__class_Otop(X2)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3) != c_Orderings_Otop__class_Otop(X2)
    | ~ class_Lattices_Obounded__lattice__top(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10671]),
    [final] ).

cnf(i_0_17647,plain,
    ( X1 = c_Orderings_Otop__class_Otop(X2)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1) != c_Orderings_Otop__class_Otop(X2)
    | ~ class_Lattices_Obounded__lattice__top(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10671]),
    [final] ).

cnf(i_0_17648,plain,
    ( X1 = c_Orderings_Obot__class_Obot(X2)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
    | ~ class_Lattices_Obounded__lattice__bot(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10672]),
    [final] ).

cnf(i_0_17649,plain,
    ( X1 = c_Orderings_Obot__class_Obot(X2)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
    | ~ class_Lattices_Obounded__lattice__bot(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10672]),
    [final] ).

cnf(i_0_17650,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10673]),
    [final] ).

cnf(i_0_17651,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10674]),
    [final] ).

cnf(i_0_17652,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10675]),
    [final] ).

cnf(i_0_17653,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10502]),
    [final] ).

cnf(i_0_17654,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10333]),
    [final] ).

cnf(i_0_17655,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10502]),
    [final] ).

cnf(i_0_17656,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10333]),
    [final] ).

cnf(i_0_17657,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10676]),
    [final] ).

cnf(i_0_17658,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))),
    inference(split_conjunct,[status(thm)],[i_0_10677]),
    [final] ).

cnf(i_0_17659,plain,
    ( X1 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9577]),
    [final] ).

cnf(i_0_17660,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(rw,[status(thm)],[i_0_10678,c_0_8975]),
    [final] ).

cnf(i_0_17661,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9828]),
    [final] ).

cnf(i_0_17662,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10679]),
    [final] ).

cnf(i_0_17663,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10456]),
    [final] ).

cnf(i_0_17664,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10457]),
    [final] ).

cnf(i_0_17665,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10455]),
    [final] ).

cnf(i_0_17666,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10680]),
    [final] ).

cnf(i_0_17667,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10681]),
    [final] ).

cnf(i_0_17668,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10068]),
    [final] ).

cnf(i_0_17669,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10052]),
    [final] ).

cnf(i_0_17670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10682]),
    [final] ).

cnf(i_0_17671,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X3),X1))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10432]),
    [final] ).

cnf(i_0_17672,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X3),X1))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10433]),
    [final] ).

cnf(i_0_17673,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Otake(X1),X2),X3) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10683]),
    [final] ).

cnf(i_0_17674,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Rings_Omult__zero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2)
    | ~ class_Rings_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10580]),
    [final] ).

cnf(i_0_17675,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10684]),
    [final] ).

cnf(i_0_17676,plain,
    ( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17677,plain,
    ( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17678,plain,
    ( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17679,plain,
    ( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17680,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10602]),
    [final] ).

cnf(i_0_17681,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10685]),
    [final] ).

cnf(i_0_17682,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10686]),
    [final] ).

cnf(i_0_17683,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Olist_ONil(X1) != c_List_Oreplicate(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10687]),
    [final] ).

cnf(i_0_17684,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Opdivmod(X2,X1) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10519]),
    [final] ).

cnf(i_0_17685,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10688]),
    [final] ).

cnf(i_0_17686,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10689]),
    [final] ).

cnf(i_0_17687,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10690]),
    [final] ).

cnf(i_0_17688,plain,
    ~ c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10691]),
    [final] ).

cnf(i_0_17689,plain,
    ~ c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10692]),
    [final] ).

cnf(i_0_17690,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10693]),
    [final] ).

cnf(i_0_17691,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[fact_bin__less__0__simps_I2_J]),
    [final] ).

cnf(i_0_17692,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10694]),
    [final] ).

cnf(i_0_17693,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10695]),
    [final] ).

cnf(i_0_17694,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10696]),
    [final] ).

cnf(i_0_17695,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10697]),
    [final] ).

cnf(i_0_17696,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10698]),
    [final] ).

cnf(i_0_17697,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10699]),
    [final] ).

cnf(i_0_17698,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17699,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10554]),
    [final] ).

cnf(i_0_17700,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17701,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10555]),
    [final] ).

cnf(i_0_17702,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),X1),X3) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10700]),
    [final] ).

cnf(i_0_17703,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(hAPP(c_List_Oappend(X2),X3),X1) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10700]),
    [final] ).

cnf(i_0_17704,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10701]),
    [final] ).

cnf(i_0_17705,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10701]),
    [final] ).

cnf(i_0_17706,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(rw,[status(thm)],[i_0_10702,c_0_6224]),
    [final] ).

cnf(i_0_17707,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(rw,[status(thm)],[i_0_10703,c_0_6072]),
    [final] ).

cnf(i_0_17708,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(rw,[status(thm)],[i_0_10704,c_0_6189]),
    [final] ).

cnf(i_0_17709,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10705]),
    [final] ).

cnf(i_0_17710,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10706]),
    [final] ).

cnf(i_0_17711,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10707]),
    [final] ).

cnf(i_0_17712,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_10708,c_0_6189]),
    [final] ).

cnf(i_0_17713,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_10709]),
    [final] ).

cnf(i_0_17714,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) != c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10710]),
    [final] ).

cnf(i_0_17715,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),
    inference(split_conjunct,[status(thm)],[i_0_10711]),
    [final] ).

cnf(i_0_17716,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10712]),
    [final] ).

cnf(i_0_17717,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10713]),
    [final] ).

cnf(i_0_17718,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10714]),
    [final] ).

cnf(i_0_17719,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_10715]),
    [final] ).

cnf(i_0_17720,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3) = c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10716]),
    [final] ).

cnf(i_0_17721,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10717]),
    [final] ).

cnf(i_0_17722,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10718]),
    [final] ).

cnf(i_0_17723,plain,
    ( hBOOL(hAPP(X1,esk237_1(X1)))
    | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10582]),
    [final] ).

cnf(i_0_17724,plain,
    ( hBOOL(hAPP(X1,esk238_1(X1)))
    | hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10583]),
    [final] ).

cnf(i_0_17725,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10719]),
    [final] ).

cnf(i_0_17726,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10720]),
    [final] ).

cnf(i_0_17727,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10721]),
    [final] ).

cnf(i_0_17728,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10722]),
    [final] ).

cnf(i_0_17729,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X2)
    | ~ class_Rings_Osemiring__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_17730,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10724]),
    [final] ).

cnf(i_0_17731,plain,
    c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10725]),
    [final] ).

cnf(i_0_17732,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10726]),
    [final] ).

cnf(i_0_17733,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10598]),
    [final] ).

cnf(i_0_17734,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin),
    inference(rw,[status(thm)],[i_0_10727,c_0_6224]),
    [final] ).

cnf(i_0_17735,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),X1))
    | esk401_2(X1,X2) != esk402_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_17736,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Rings_Osemiring__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_17737,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_10728]),
    [final] ).

cnf(i_0_17738,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_10729]),
    [final] ).

cnf(i_0_17739,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10730]),
    [final] ).

cnf(i_0_17740,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10731]),
    [final] ).

cnf(i_0_17741,plain,
    c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10732]),
    [final] ).

cnf(i_0_17742,plain,
    ( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10733]),
    [final] ).

cnf(i_0_17743,plain,
    ( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10734]),
    [final] ).

cnf(i_0_17744,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10735]),
    [final] ).

cnf(i_0_17745,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = hAPP(c_Groups_Oabs__class_Oabs(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10736]),
    [final] ).

cnf(i_0_17746,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10737]),
    [final] ).

cnf(i_0_17747,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Oabs__class_Oabs(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10738]),
    [final] ).

cnf(i_0_17748,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J]),
    [final] ).

cnf(i_0_17749,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I24_J]),
    [final] ).

cnf(i_0_17750,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I23_J]),
    [final] ).

cnf(i_0_17751,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I19_J]),
    [final] ).

cnf(i_0_17752,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min]),
    [final] ).

cnf(i_0_17753,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_10739]),
    [final] ).

cnf(i_0_17754,plain,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10740]),
    [final] ).

cnf(i_0_17755,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10741]),
    [final] ).

cnf(i_0_17756,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10742]),
    [final] ).

cnf(i_0_17757,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10743]),
    [final] ).

cnf(i_0_17758,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
    inference(split_conjunct,[status(thm)],[i_0_10744]),
    [final] ).

cnf(i_0_17759,plain,
    X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
    inference(split_conjunct,[status(thm)],[i_0_10745]),
    [final] ).

cnf(i_0_17760,plain,
    c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10746]),
    [final] ).

cnf(i_0_17761,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10747]),
    [final] ).

cnf(i_0_17762,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10748]),
    [final] ).

cnf(i_0_17763,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10749]),
    [final] ).

cnf(i_0_17764,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10750]),
    [final] ).

cnf(i_0_17765,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10751]),
    [final] ).

cnf(i_0_17766,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10752]),
    [final] ).

cnf(i_0_17767,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10753]),
    [final] ).

cnf(i_0_17768,plain,
    ( c_Equiv__Relations_Oequivp(X1,X2)
    | ~ c_Predicate_Oreflp(X1,X2)
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10754]),
    [final] ).

cnf(i_0_17769,plain,
    ( c_Equiv__Relations_Oequivp(X1,X2)
    | ~ c_Predicate_Oreflp(X1,X2)
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10755]),
    [final] ).

cnf(i_0_17770,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10756]),
    [final] ).

cnf(i_0_17771,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10757]),
    [final] ).

cnf(i_0_17772,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10758]),
    [final] ).

cnf(i_0_17773,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),c_List_Olist_ONil(tc_Int_Oint)),
    inference(rw,[status(thm)],[i_0_10759,c_0_7999]),
    [final] ).

cnf(i_0_17774,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10760]),
    [final] ).

cnf(i_0_17775,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),X1) = hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10761]),
    [final] ).

cnf(i_0_17776,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10762]),
    [final] ).

cnf(i_0_17777,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10763]),
    [final] ).

cnf(i_0_17778,plain,
    c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10764]),
    [final] ).

cnf(i_0_17779,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10765]),
    [final] ).

cnf(i_0_17780,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10765]),
    [final] ).

cnf(i_0_17781,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10766]),
    [final] ).

cnf(i_0_17782,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10766]),
    [final] ).

cnf(i_0_17783,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10767]),
    [final] ).

cnf(i_0_17784,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10767]),
    [final] ).

cnf(i_0_17785,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3) = c_Orderings_Otop__class_Otop(X2)
    | X1 != c_Orderings_Otop__class_Otop(X2)
    | X3 != c_Orderings_Otop__class_Otop(X2)
    | ~ class_Lattices_Obounded__lattice__top(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10671]),
    [final] ).

cnf(i_0_17786,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) = c_Orderings_Obot__class_Obot(X2)
    | X1 != c_Orderings_Obot__class_Obot(X2)
    | X3 != c_Orderings_Obot__class_Obot(X2)
    | ~ class_Lattices_Obounded__lattice__bot(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10672]),
    [final] ).

cnf(i_0_17787,plain,
    ( X2 = X3
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10768]),
    [final] ).

cnf(i_0_17788,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2)) = c_Relation_OId__on(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10769]),
    [final] ).

cnf(i_0_17789,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10770]),
    [final] ).

cnf(i_0_17790,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10771]),
    [final] ).

cnf(i_0_17791,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10772]),
    [final] ).

cnf(i_0_17792,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Oset(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10773]),
    [final] ).

cnf(i_0_17793,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(c_List_Oset(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10774]),
    [final] ).

cnf(i_0_17794,plain,
    ( c_Wellfounded_Owf(X2,X1)
    | esk328_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8240]),
    [final] ).

cnf(i_0_17795,plain,
    ( c_Relation_Osym(X1,X2)
    | hAPP(c_Relation_Oconverse(X1,X1),X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10775]),
    [final] ).

cnf(i_0_17796,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10776]),
    [final] ).

cnf(i_0_17797,plain,
    hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10777]),
    [final] ).

cnf(i_0_17798,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10633]),
    [final] ).

cnf(i_0_17799,plain,
    ( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10778]),
    [final] ).

cnf(i_0_17800,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10779]),
    [final] ).

cnf(i_0_17801,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | hAPP(c_List_Ohd(X2),hAPP(c_List_Orev(X2),X1)) = c_List_Olast(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10780]),
    [final] ).

cnf(i_0_17802,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(c_List_Orev(X2),X1)) = hAPP(c_List_Ohd(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10781]),
    [final] ).

cnf(i_0_17803,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10444]),
    [final] ).

cnf(i_0_17804,plain,
    ( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10445]),
    [final] ).

cnf(i_0_17805,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_List_Olist_ONil(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10782]),
    [final] ).

cnf(i_0_17806,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10783]),
    [final] ).

cnf(i_0_17807,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10784]),
    [final] ).

cnf(i_0_17808,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10785]),
    [final] ).

cnf(i_0_17809,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10786]),
    [final] ).

cnf(i_0_17810,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10787]),
    [final] ).

cnf(i_0_17811,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10788]),
    [final] ).

cnf(i_0_17812,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10789]),
    [final] ).

cnf(i_0_17813,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10790]),
    [final] ).

cnf(i_0_17814,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice__bot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10791]),
    [final] ).

cnf(i_0_17815,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10792]),
    [final] ).

cnf(i_0_17816,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice__top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10793]),
    [final] ).

cnf(i_0_17817,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10794]),
    [final] ).

cnf(i_0_17818,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10795]),
    [final] ).

cnf(i_0_17819,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk449_2(X2,X1))
    | X2 = c_List_Olist_ONil(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_17820,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olinorder__class_Osorted(X1,c_List_Obutlast(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10796]),
    [final] ).

cnf(i_0_17821,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10797]),
    [final] ).

cnf(i_0_17822,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Enum_On__lists(X2,X1,c_List_Olist_ONil(X2)) = c_List_Olist_ONil(tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10366]),
    [final] ).

cnf(i_0_17823,plain,
    hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10798]),
    [final] ).

cnf(i_0_17824,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) ),
    inference(rw,[status(thm)],[i_0_10799,c_0_6071]),
    [final] ).

cnf(i_0_17825,plain,
    ( X1 = c_Int_OPls
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_10800,c_0_6071]),
    [final] ).

cnf(i_0_17826,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10801]),
    [final] ).

cnf(i_0_17827,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2)
    | X3 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10700]),
    [final] ).

cnf(i_0_17828,plain,
    ( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
    | X1 != c_List_Olist_ONil(X2)
    | X3 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10701]),
    [final] ).

cnf(i_0_17829,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10802]),
    [final] ).

cnf(i_0_17830,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
    inference(rw,[status(thm)],[i_0_10803,c_0_6071]),
    [final] ).

cnf(i_0_17831,plain,
    c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[i_0_10804,c_0_6071]),
    [final] ).

cnf(i_0_17832,plain,
    ( X2 = X3
    | hAPP(c_SetInterval_Oord__class_OatMost(X1),X2) != hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10805]),
    [final] ).

cnf(i_0_17833,plain,
    ( X2 = X3
    | hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2) != hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10806]),
    [final] ).

cnf(i_0_17834,plain,
    ( X2 = X3
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10807]),
    [final] ).

cnf(i_0_17835,plain,
    ( X2 = X3
    | hAPP(c_Int_Oring__1__class_Oof__int(X1),X2) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10808]),
    [final] ).

cnf(i_0_17836,plain,
    ( X2 = X3
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)
    | ~ class_Nat_Osemiring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10809]),
    [final] ).

cnf(i_0_17837,plain,
    ( X2 = X3
    | hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2) != hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10810]),
    [final] ).

cnf(i_0_17838,plain,
    ( X2 = X3
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10811]),
    [final] ).

cnf(i_0_17839,plain,
    ( X2 = X3
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10812]),
    [final] ).

cnf(i_0_17840,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
    | ~ class_Lattices_Obounded__lattice__top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10813]),
    [final] ).

cnf(i_0_17841,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
    | ~ class_Lattices_Obounded__lattice__bot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10814]),
    [final] ).

cnf(i_0_17842,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10815]),
    [final] ).

cnf(i_0_17843,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10816]),
    [final] ).

cnf(i_0_17844,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10817]),
    [final] ).

cnf(i_0_17845,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10818]),
    [final] ).

cnf(i_0_17846,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10819]),
    [final] ).

cnf(i_0_17847,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10820]),
    [final] ).

cnf(i_0_17848,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X2) = c_Groups_Oone__class_Oone(X3)
    | X2 = c_Groups_Ozero__class_Ozero(X3)
    | X1 != X2
    | ~ class_Rings_Odivision__ring(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10660]),
    [final] ).

cnf(i_0_17849,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10821]),
    [final] ).

cnf(i_0_17850,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10561]),
    [final] ).

cnf(i_0_17851,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10646]),
    [final] ).

cnf(i_0_17852,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10646]),
    [final] ).

cnf(i_0_17853,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10674]),
    [final] ).

cnf(i_0_17854,plain,
    ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10675]),
    [final] ).

cnf(i_0_17855,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10822]),
    [final] ).

cnf(i_0_17856,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10823]),
    [final] ).

cnf(i_0_17857,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10824]),
    [final] ).

cnf(i_0_17858,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10825]),
    [final] ).

cnf(i_0_17859,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10826]),
    [final] ).

cnf(i_0_17860,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice__bot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10827]),
    [final] ).

cnf(i_0_17861,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice__top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10828]),
    [final] ).

cnf(i_0_17862,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10829]),
    [final] ).

cnf(i_0_17863,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10830]),
    [final] ).

cnf(i_0_17864,plain,
    ( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10831]),
    [final] ).

cnf(i_0_17865,plain,
    ( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10832]),
    [final] ).

cnf(i_0_17866,plain,
    ( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10833]),
    [final] ).

cnf(i_0_17867,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10834]),
    [final] ).

cnf(i_0_17868,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10835]),
    [final] ).

cnf(i_0_17869,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10836]),
    [final] ).

cnf(i_0_17870,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10685]),
    [final] ).

cnf(i_0_17871,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10821]),
    [final] ).

cnf(i_0_17872,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10837]),
    [final] ).

cnf(i_0_17873,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10838]),
    [final] ).

cnf(i_0_17874,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10839]),
    [final] ).

cnf(i_0_17875,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10840]),
    [final] ).

cnf(i_0_17876,plain,
    ( c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10841]),
    [final] ).

cnf(i_0_17877,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10842]),
    [final] ).

cnf(i_0_17878,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10843]),
    [final] ).

cnf(i_0_17879,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10844]),
    [final] ).

cnf(i_0_17880,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10845]),
    [final] ).

cnf(i_0_17881,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10846]),
    [final] ).

cnf(i_0_17882,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10598]),
    [final] ).

cnf(i_0_17883,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
    | X1 != X2
    | ~ class_Groups_Ogroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10680]),
    [final] ).

cnf(i_0_17884,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
    | X1 != X2
    | ~ class_Groups_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10681]),
    [final] ).

cnf(i_0_17885,plain,
    ( hAPP(c_Finite__Set_Ocard(X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10548]),
    [final] ).

cnf(i_0_17886,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10847]),
    [final] ).

cnf(i_0_17887,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10848]),
    [final] ).

cnf(i_0_17888,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10849]),
    [final] ).

cnf(i_0_17889,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10850]),
    [final] ).

cnf(i_0_17890,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10851]),
    [final] ).

cnf(i_0_17891,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10852]),
    [final] ).

cnf(i_0_17892,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
    | ~ class_Lattices_Obounded__lattice__top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10853]),
    [final] ).

cnf(i_0_17893,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
    | ~ class_Lattices_Obounded__lattice__bot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10854]),
    [final] ).

cnf(i_0_17894,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10855]),
    [final] ).

cnf(i_0_17895,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10856]),
    [final] ).

cnf(i_0_17896,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10857]),
    [final] ).

cnf(i_0_17897,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10858]),
    [final] ).

cnf(i_0_17898,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10859]),
    [final] ).

cnf(i_0_17899,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10860]),
    [final] ).

cnf(i_0_17900,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10861]),
    [final] ).

cnf(i_0_17901,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10862]),
    [final] ).

cnf(i_0_17902,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10863]),
    [final] ).

cnf(i_0_17903,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | c_List_Oremdups(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10757]),
    [final] ).

cnf(i_0_17904,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),
    inference(split_conjunct,[status(thm)],[i_0_10864]),
    [final] ).

cnf(i_0_17905,plain,
    hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),
    inference(split_conjunct,[status(thm)],[i_0_10865]),
    [final] ).

cnf(i_0_17906,plain,
    hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10866]),
    [final] ).

cnf(i_0_17907,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10867]),
    [final] ).

cnf(i_0_17908,plain,
    ( X2 = X3
    | hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10868]),
    [final] ).

cnf(i_0_17909,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8309]),
    [final] ).

cnf(i_0_17910,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10548]),
    [final] ).

cnf(i_0_17911,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10869]),
    [final] ).

cnf(i_0_17912,plain,
    ( X1 = X2
    | c_Random_Oinc__shift(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
    inference(split_conjunct,[status(thm)],[i_0_10870]),
    [final] ).

cnf(i_0_17913,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]),
    [final] ).

cnf(i_0_17914,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10871]),
    [final] ).

cnf(i_0_17915,plain,
    ( hAPP(hAPP(c_List_Otake(X2),X3),X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10683]),
    [final] ).

cnf(i_0_17916,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
    inference(split_conjunct,[status(thm)],[i_0_10872]),
    [final] ).

cnf(i_0_17917,plain,
    c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10873]),
    [final] ).

cnf(i_0_17918,plain,
    c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10874]),
    [final] ).

cnf(i_0_17919,plain,
    c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10875]),
    [final] ).

cnf(i_0_17920,plain,
    ( c_List_Oreplicate(X2,X1,X3) = c_List_Olist_ONil(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10686]),
    [final] ).

cnf(i_0_17921,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oreplicate(X2,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10687]),
    [final] ).

cnf(i_0_17922,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10876]),
    [final] ).

cnf(i_0_17923,plain,
    ( hAPP(c_Relation_Oconverse(X1,X1),X2) = X2
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10775]),
    [final] ).

cnf(i_0_17924,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10877]),
    [final] ).

cnf(i_0_17925,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10878]),
    [final] ).

cnf(i_0_17926,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10879]),
    [final] ).

cnf(i_0_17927,plain,
    c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10880]),
    [final] ).

cnf(i_0_17928,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10881]),
    [final] ).

cnf(i_0_17929,plain,
    ( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10882]),
    [final] ).

cnf(i_0_17930,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10883]),
    [final] ).

cnf(i_0_17931,plain,
    hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10884]),
    [final] ).

cnf(i_0_17932,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10885]),
    [final] ).

cnf(i_0_17933,plain,
    ( hAPP(hAPP(c_List_Otake(X2),X1),X3) = c_List_Olist_ONil(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10683]),
    [final] ).

cnf(i_0_17934,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10886]),
    [final] ).

cnf(i_0_17935,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10886]),
    [final] ).

cnf(i_0_17936,plain,
    ( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10887]),
    [final] ).

cnf(i_0_17937,plain,
    ( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10887]),
    [final] ).

cnf(i_0_17938,plain,
    ( c_List_Onat__list(X1)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10888]),
    [final] ).

cnf(i_0_17939,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10719]),
    [final] ).

cnf(i_0_17940,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10720]),
    [final] ).

cnf(i_0_17941,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10722]),
    [final] ).

cnf(i_0_17942,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10721]),
    [final] ).

cnf(i_0_17943,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)) = hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_10889]),
    [final] ).

cnf(i_0_17944,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10890]),
    [final] ).

cnf(i_0_17945,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10891]),
    [final] ).

cnf(i_0_17946,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10892]),
    [final] ).

cnf(i_0_17947,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_10893]),
    [final] ).

cnf(i_0_17948,plain,
    c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10894]),
    [final] ).

cnf(i_0_17949,plain,
    c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10895]),
    [final] ).

cnf(i_0_17950,plain,
    c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10896]),
    [final] ).

cnf(i_0_17951,plain,
    c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10897]),
    [final] ).

cnf(i_0_17952,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10898]),
    [final] ).

cnf(i_0_17953,plain,
    c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10899]),
    [final] ).

cnf(i_0_17954,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10670]),
    [final] ).

cnf(i_0_17955,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10766]),
    [final] ).

cnf(i_0_17956,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10765]),
    [final] ).

cnf(i_0_17957,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10767]),
    [final] ).

cnf(i_0_17958,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10900]),
    [final] ).

cnf(i_0_17959,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10901]),
    [final] ).

cnf(i_0_17960,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10902]),
    [final] ).

cnf(i_0_17961,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10903]),
    [final] ).

cnf(i_0_17962,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Osemilattice__sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10904]),
    [final] ).

cnf(i_0_17963,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10905]),
    [final] ).

cnf(i_0_17964,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10906]),
    [final] ).

cnf(i_0_17965,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10907]),
    [final] ).

cnf(i_0_17966,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10908]),
    [final] ).

cnf(i_0_17967,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10909]),
    [final] ).

cnf(i_0_17968,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10910]),
    [final] ).

cnf(i_0_17969,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10911]),
    [final] ).

cnf(i_0_17970,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10912]),
    [final] ).

cnf(i_0_17971,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),
    inference(split_conjunct,[status(thm)],[i_0_10913]),
    [final] ).

cnf(i_0_17972,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10914]),
    [final] ).

cnf(i_0_17973,plain,
    hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = hAPP(c_Lazy__Sequence_Osingle(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10915]),
    [final] ).

cnf(i_0_17974,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | c_Nitpick_Ocard_H(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_6232]),
    [final] ).

cnf(i_0_17975,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10916]),
    [final] ).

cnf(i_0_17976,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10917]),
    [final] ).

cnf(i_0_17977,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10918]),
    [final] ).

cnf(i_0_17978,plain,
    ( c_Relation_Oantisym(X2,X1)
    | esk518_2(X1,X2) != esk519_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7087]),
    [final] ).

cnf(i_0_17979,plain,
    c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X1) = c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10919]),
    [final] ).

cnf(i_0_17980,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10920]),
    [final] ).

cnf(i_0_17981,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10921]),
    [final] ).

cnf(i_0_17982,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[fact_code__numeral__zero__minus__one]),
    [final] ).

cnf(i_0_17983,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10922]),
    [final] ).

cnf(i_0_17984,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_10923]),
    [final] ).

cnf(i_0_17985,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_10924]),
    [final] ).

cnf(i_0_17986,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10925]),
    [final] ).

cnf(i_0_17987,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10926]),
    [final] ).

cnf(i_0_17988,plain,
    hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10927]),
    [final] ).

cnf(i_0_17989,plain,
    hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10928]),
    [final] ).

cnf(i_0_17990,plain,
    ( X1 = X2
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10929]),
    [final] ).

cnf(i_0_17991,plain,
    ( X1 = X2
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10930]),
    [final] ).

cnf(i_0_17992,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_List_Oset(X2),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10773]),
    [final] ).

cnf(i_0_17993,plain,
    ( hAPP(c_List_Oset(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10774]),
    [final] ).

cnf(i_0_17994,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10931]),
    [final] ).

cnf(i_0_17995,plain,
    ( hAPP(c_List_Orev(X2),X1) = X3
    | X1 != hAPP(c_List_Orev(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10932]),
    [final] ).

cnf(i_0_17996,plain,
    ( X2 = hAPP(c_List_Orev(X1),X3)
    | hAPP(c_List_Orev(X1),X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10932]),
    [final] ).

cnf(i_0_17997,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10933]),
    [final] ).

cnf(i_0_17998,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10934]),
    [final] ).

cnf(i_0_17999,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10935]),
    [final] ).

cnf(i_0_18000,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10936]),
    [final] ).

cnf(i_0_18001,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10937]),
    [final] ).

cnf(i_0_18002,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_9599]),
    [final] ).

cnf(i_0_18003,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9562]),
    [final] ).

cnf(i_0_18004,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9033]),
    [final] ).

cnf(i_0_18005,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10743]),
    [final] ).

cnf(i_0_18006,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10743]),
    [final] ).

cnf(i_0_18007,plain,
    hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10938]),
    [final] ).

cnf(i_0_18008,plain,
    c_List_Oremdups(X1,c_List_Oremdups(X1,X2)) = c_List_Oremdups(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10939]),
    [final] ).

cnf(i_0_18009,plain,
    c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10940]),
    [final] ).

cnf(i_0_18010,plain,
    hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10941]),
    [final] ).

cnf(i_0_18011,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10942]),
    [final] ).

cnf(i_0_18012,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10943]),
    [final] ).

cnf(i_0_18013,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10944]),
    [final] ).

cnf(i_0_18014,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10945]),
    [final] ).

cnf(i_0_18015,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10946]),
    [final] ).

cnf(i_0_18016,plain,
    c_Predicate_Oconversep(X1,X1,c_fequal) = c_fequal,
    inference(split_conjunct,[status(thm)],[i_0_10947]),
    [final] ).

cnf(i_0_18017,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9118]),
    [final] ).

cnf(i_0_18018,plain,
    ( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
    | esk433_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9253]),
    [final] ).

cnf(i_0_18019,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10948]),
    [final] ).

cnf(i_0_18020,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10949]),
    [final] ).

cnf(i_0_18021,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10950]),
    [final] ).

cnf(i_0_18022,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10951]),
    [final] ).

cnf(i_0_18023,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10952]),
    [final] ).

cnf(i_0_18024,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_10925]),
    [final] ).

cnf(i_0_18025,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10953]),
    [final] ).

cnf(i_0_18026,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10954]),
    [final] ).

cnf(i_0_18027,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10955]),
    [final] ).

cnf(i_0_18028,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Oabs__class_Oabs(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10956]),
    [final] ).

cnf(i_0_18029,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10957]),
    [final] ).

cnf(i_0_18030,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10958]),
    [final] ).

cnf(i_0_18031,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10959]),
    [final] ).

cnf(i_0_18032,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10960]),
    [final] ).

cnf(i_0_18033,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10961]),
    [final] ).

cnf(i_0_18034,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10962]),
    [final] ).

cnf(i_0_18035,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10963]),
    [final] ).

cnf(i_0_18036,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10964]),
    [final] ).

cnf(i_0_18037,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10965]),
    [final] ).

cnf(i_0_18038,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10966]),
    [final] ).

cnf(i_0_18039,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]),
    [final] ).

cnf(i_0_18040,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10967]),
    [final] ).

cnf(i_0_18041,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10968]),
    [final] ).

cnf(i_0_18042,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10969]),
    [final] ).

cnf(i_0_18043,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10970]),
    [final] ).

cnf(i_0_18044,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10971]),
    [final] ).

cnf(i_0_18045,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(split_conjunct,[status(thm)],[fact_eq__number__of__Pls__Min]),
    [final] ).

cnf(i_0_18046,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_10972,c_0_6071]),
    [final] ).

cnf(i_0_18047,plain,
    ( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)
    | c_Int_OPls != X1 ),
    inference(rw,[status(thm)],[i_0_10973,c_0_6071]),
    [final] ).

cnf(i_0_18048,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_int__Suc0__eq__1]),
    [final] ).

cnf(i_0_18049,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10974]),
    [final] ).

cnf(i_0_18050,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10975]),
    [final] ).

cnf(i_0_18051,plain,
    ( hAPP(c_Int_Onat,X2) = X1
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10243]),
    [final] ).

cnf(i_0_18052,plain,
    ( X1 = hAPP(c_Int_Onat,X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10244]),
    [final] ).

cnf(i_0_18053,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10976]),
    [final] ).

cnf(i_0_18054,plain,
    ( X1 = X2
    | c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10977]),
    [final] ).

cnf(i_0_18055,plain,
    ( X1 = X2
    | c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10977]),
    [final] ).

cnf(i_0_18056,plain,
    ( X1 = X2
    | c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10978]),
    [final] ).

cnf(i_0_18057,plain,
    ( X1 = X2
    | c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10978]),
    [final] ).

cnf(i_0_18058,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10979]),
    [final] ).

cnf(i_0_18059,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10980]),
    [final] ).

cnf(i_0_18060,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10981]),
    [final] ).

cnf(i_0_18061,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10982]),
    [final] ).

cnf(i_0_18062,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10983]),
    [final] ).

cnf(i_0_18063,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X2))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | ~ class_Lazy__Sequence_Osmall__lazy(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10984]),
    [final] ).

cnf(i_0_18064,plain,
    ( class_Enum_Oenum(tc_prod(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10985]),
    [final] ).

cnf(i_0_18065,plain,
    ( class_Enum_Oenum(tc_sum(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10986]),
    [final] ).

cnf(i_0_18066,plain,
    ( class_Enum_Oenum(tc_fun(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10987]),
    [final] ).

cnf(i_0_18067,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | ~ c_Nat__Transfer_Ois__nat(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10988]),
    [final] ).

cnf(i_0_18068,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10989]),
    [final] ).

cnf(i_0_18069,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10990]),
    [final] ).

cnf(i_0_18070,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10991]),
    [final] ).

cnf(i_0_18071,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10992]),
    [final] ).

cnf(i_0_18072,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10993]),
    [final] ).

cnf(i_0_18073,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_atLeast__0]),
    [final] ).

cnf(i_0_18074,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[fact_lessThan__0]),
    [final] ).

cnf(i_0_18075,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10994]),
    [final] ).

cnf(i_0_18076,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))
    | ~ c_List_Onat__list(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10888]),
    [final] ).

cnf(i_0_18077,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(c_List_Orev(X1),X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10995]),
    [final] ).

cnf(i_0_18078,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(c_List_Orotate1(X1),X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10996]),
    [final] ).

cnf(i_0_18079,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10997]),
    [final] ).

cnf(i_0_18080,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10912]),
    [final] ).

cnf(i_0_18081,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_10998]),
    [final] ).

cnf(i_0_18082,plain,
    c_Relation_Otrans(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10999]),
    [final] ).

cnf(i_0_18083,plain,
    c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11000]),
    [final] ).

cnf(i_0_18084,plain,
    c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11001]),
    [final] ).

cnf(i_0_18085,plain,
    ( X1 = hAPP(c_Int_Onat,X2)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10253]),
    [final] ).

cnf(i_0_18086,plain,
    ( c_Nitpick_Owf_H(X1,X2)
    | ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9968]),
    [final] ).

cnf(i_0_18087,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) = c_Int_OMin,
    inference(rw,[status(thm)],[i_0_11002,c_0_6224]),
    [final] ).

cnf(i_0_18088,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
    inference(rw,[status(thm)],[i_0_11003,c_0_6071]),
    [final] ).

cnf(i_0_18089,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = c_Int_OPls,
    inference(rw,[status(thm)],[i_0_11004,c_0_6072]),
    [final] ).

cnf(i_0_18090,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11005]),
    [final] ).

cnf(i_0_18091,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11006]),
    [final] ).

cnf(i_0_18092,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11007]),
    [final] ).

cnf(i_0_18093,plain,
    ( X1 = X2
    | hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11008]),
    [final] ).

cnf(i_0_18094,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11009]),
    [final] ).

cnf(i_0_18095,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11010]),
    [final] ).

cnf(i_0_18096,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11011]),
    [final] ).

cnf(i_0_18097,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11012]),
    [final] ).

cnf(i_0_18098,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11013]),
    [final] ).

cnf(i_0_18099,plain,
    c_Relation_Osym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11014]),
    [final] ).

cnf(i_0_18100,plain,
    c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11015]),
    [final] ).

cnf(i_0_18101,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11016]),
    [final] ).

cnf(i_0_18102,plain,
    c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11017]),
    [final] ).

cnf(i_0_18103,plain,
    c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11018]),
    [final] ).

cnf(i_0_18104,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10956]),
    [final] ).

cnf(i_0_18105,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10957]),
    [final] ).

cnf(i_0_18106,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
    | c_Groups_Ozero__class_Ozero(X1) != X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10955]),
    [final] ).

cnf(i_0_18107,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11019]),
    [final] ).

cnf(i_0_18108,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11020]),
    [final] ).

cnf(i_0_18109,plain,
    c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11021]),
    [final] ).

cnf(i_0_18110,plain,
    c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11022]),
    [final] ).

cnf(i_0_18111,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(X1),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11023]),
    [final] ).

cnf(i_0_18112,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11024]),
    [final] ).

cnf(i_0_18113,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11025]),
    [final] ).

cnf(i_0_18114,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11026]),
    [final] ).

cnf(i_0_18115,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11027]),
    [final] ).

cnf(i_0_18116,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11028]),
    [final] ).

cnf(i_0_18117,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11029]),
    [final] ).

cnf(i_0_18118,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11030]),
    [final] ).

cnf(i_0_18119,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11031]),
    [final] ).

cnf(i_0_18120,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11032]),
    [final] ).

cnf(i_0_18121,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11033]),
    [final] ).

cnf(i_0_18122,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11034]),
    [final] ).

cnf(i_0_18123,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11035]),
    [final] ).

cnf(i_0_18124,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11036]),
    [final] ).

cnf(i_0_18125,plain,
    ( class_Lattices_Olattice(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11037]),
    [final] ).

cnf(i_0_18126,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11038]),
    [final] ).

cnf(i_0_18127,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11039]),
    [final] ).

cnf(i_0_18128,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11040]),
    [final] ).

cnf(i_0_18129,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11041]),
    [final] ).

cnf(i_0_18130,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11042]),
    [final] ).

cnf(i_0_18131,plain,
    ( class_Groups_Ominus(tc_fun(X2,X1))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11043]),
    [final] ).

cnf(i_0_18132,plain,
    ( class_Orderings_Obot(tc_fun(X2,X1))
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11044]),
    [final] ).

cnf(i_0_18133,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10970]),
    [final] ).

cnf(i_0_18134,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5249]),
    [final] ).

cnf(i_0_18135,plain,
    ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10971]),
    [final] ).

cnf(i_0_18136,plain,
    ( c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11045]),
    [final] ).

cnf(i_0_18137,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9992]),
    [final] ).

cnf(i_0_18138,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9993]),
    [final] ).

cnf(i_0_18139,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10754]),
    [final] ).

cnf(i_0_18140,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11046]),
    [final] ).

cnf(i_0_18141,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9992]),
    [final] ).

cnf(i_0_18142,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9993]),
    [final] ).

cnf(i_0_18143,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10754]),
    [final] ).

cnf(i_0_18144,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11046]),
    [final] ).

cnf(i_0_18145,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Nitpick_Owf_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9968]),
    [final] ).

cnf(i_0_18146,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11047]),
    [final] ).

cnf(i_0_18147,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10754]),
    [final] ).

cnf(i_0_18148,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11046]),
    [final] ).

cnf(i_0_18149,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10979]),
    [final] ).

cnf(i_0_18150,plain,
    ( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10980]),
    [final] ).

cnf(i_0_18151,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[i_0_11048]),
    [final] ).

cnf(i_0_18152,plain,
    c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X1))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11049]),
    [final] ).

cnf(i_0_18153,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11050]),
    [final] ).

cnf(i_0_18154,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11051]),
    [final] ).

cnf(i_0_18155,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11052]),
    [final] ).

cnf(i_0_18156,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11053]),
    [final] ).

cnf(i_0_18157,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11054]),
    [final] ).

cnf(i_0_18158,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_11055]),
    [final] ).

cnf(i_0_18159,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11056]),
    [final] ).

cnf(i_0_18160,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11057]),
    [final] ).

cnf(i_0_18161,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11058]),
    [final] ).

cnf(i_0_18162,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11059]),
    [final] ).

cnf(i_0_18163,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1),
    inference(split_conjunct,[status(thm)],[i_0_11060]),
    [final] ).

cnf(i_0_18164,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11061]),
    [final] ).

cnf(i_0_18165,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11062]),
    [final] ).

cnf(i_0_18166,plain,
    ( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Osgn__if(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10083]),
    [final] ).

cnf(i_0_18167,plain,
    ( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11011]),
    [final] ).

cnf(i_0_18168,hypothesis,
    hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
    inference(split_conjunct,[status(thm)],[conj_1]),
    [final] ).

cnf(i_0_18169,plain,
    ( hAPP(c_List_Orev(X2),X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10995]),
    [final] ).

cnf(i_0_18170,plain,
    ( hAPP(c_List_Orotate1(X2),X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10996]),
    [final] ).

cnf(i_0_18171,plain,
    ( c_List_Olist_ONil(X2) = hAPP(c_List_Orev(X2),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10997]),
    [final] ).

cnf(i_0_18172,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(split_conjunct,[status(thm)],[fact_wf__pair__less]),
    [final] ).

cnf(i_0_18173,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(split_conjunct,[status(thm)],[fact_max__strict__def]),
    [final] ).

cnf(i_0_18174,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(split_conjunct,[status(thm)],[fact_min__strict__def]),
    [final] ).

cnf(i_0_18175,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(c_fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11063]),
    [final] ).

cnf(i_0_18176,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11064]),
    [final] ).

cnf(i_0_18177,plain,
    ( c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11065]),
    [final] ).

cnf(i_0_18178,plain,
    ( c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11066]),
    [final] ).

cnf(i_0_18179,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_nat__1]),
    [final] ).

cnf(i_0_18180,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | esk397_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9891]),
    [final] ).

cnf(i_0_18181,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11067]),
    [final] ).

cnf(i_0_18182,plain,
    hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11068]),
    [final] ).

cnf(i_0_18183,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_9870]),
    [final] ).

cnf(i_0_18184,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11069]),
    [final] ).

cnf(i_0_18185,plain,
    class_Nat_Osize(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11070]),
    [final] ).

cnf(i_0_18186,plain,
    class_Nat_Osize(tc_sum(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11071]),
    [final] ).

cnf(i_0_18187,plain,
    ( c_List_Olinorder__class_Osorted(X2,X1)
    | X1 != c_List_Olist_ONil(X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7369]),
    [final] ).

cnf(i_0_18188,plain,
    ( c_Int_Oiszero(X2,X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Osemiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11054]),
    [final] ).

cnf(i_0_18189,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11072]),
    [final] ).

cnf(i_0_18190,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11073]),
    [final] ).

cnf(i_0_18191,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11074]),
    [final] ).

cnf(i_0_18192,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11075]),
    [final] ).

cnf(i_0_18193,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11076]),
    [final] ).

cnf(i_0_18194,plain,
    ( c_List_Oremdups(X2,X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11061]),
    [final] ).

cnf(i_0_18195,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oremdups(X2,X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11062]),
    [final] ).

cnf(i_0_18196,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_11055]),
    [final] ).

cnf(i_0_18197,plain,
    hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11077]),
    [final] ).

cnf(i_0_18198,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11078]),
    [final] ).

cnf(i_0_18199,plain,
    c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11079]),
    [final] ).

cnf(i_0_18200,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11080]),
    [final] ).

cnf(i_0_18201,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11081]),
    [final] ).

cnf(i_0_18202,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11082]),
    [final] ).

cnf(i_0_18203,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11083]),
    [final] ).

cnf(i_0_18204,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11084]),
    [final] ).

cnf(i_0_18205,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11085]),
    [final] ).

cnf(i_0_18206,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_int__0]),
    [final] ).

cnf(i_0_18207,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_int__1]),
    [final] ).

cnf(i_0_18208,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I3_J]),
    [final] ).

cnf(i_0_18209,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat_Osize_I3_J]),
    [final] ).

cnf(i_0_18210,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_zminus__0]),
    [final] ).

cnf(i_0_18211,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]),
    [final] ).

cnf(i_0_18212,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]),
    [final] ).

cnf(i_0_18213,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11086]),
    [final] ).

cnf(i_0_18214,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11087]),
    [final] ).

cnf(i_0_18215,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_11088]),
    [final] ).

cnf(i_0_18216,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_11089]),
    [final] ).

cnf(i_0_18217,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1)
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11090]),
    [final] ).

cnf(i_0_18218,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11091]),
    [final] ).

cnf(i_0_18219,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_11092]),
    [final] ).

cnf(i_0_18220,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11093]),
    [final] ).

cnf(i_0_18221,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11094]),
    [final] ).

cnf(i_0_18222,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11095]),
    [final] ).

cnf(i_0_18223,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11096]),
    [final] ).

cnf(i_0_18224,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11097]),
    [final] ).

cnf(i_0_18225,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_10331]),
    [final] ).

cnf(i_0_18226,plain,
    ( hAPP(c_Code__Numeral_Oint__of,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_5275]),
    [final] ).

cnf(i_0_18227,plain,
    ( c_Nitpick_Onat__gcd(X2,X1) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10524]),
    [final] ).

cnf(i_0_18228,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_Int_OMin__def]),
    [final] ).

cnf(i_0_18229,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11098]),
    [final] ).

cnf(i_0_18230,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11099]),
    [final] ).

cnf(i_0_18231,plain,
    ( c_Random_Oinc__shift(X1,X2) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10870]),
    [final] ).

cnf(i_0_18232,plain,
    c_Quickcheck_Obeyond(X1,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[i_0_11100]),
    [final] ).

cnf(i_0_18233,plain,
    X1 = hAPP(c_Code__Numeral_Oof__nat,esk535_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10239]),
    [final] ).

cnf(i_0_18234,plain,
    X1 = hAPP(c_Int_OAbs__Integ,esk318_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_8888]),
    [final] ).

cnf(i_0_18235,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11101]),
    [final] ).

cnf(i_0_18236,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11102]),
    [final] ).

cnf(i_0_18237,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat__number__of__Pls]),
    [final] ).

cnf(i_0_18238,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_com_Osize_I9_J]),
    [final] ).

cnf(i_0_18239,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_bool_Osize_I3_J]),
    [final] ).

cnf(i_0_18240,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_bool_Osize_I4_J]),
    [final] ).

cnf(i_0_18241,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat__0]),
    [final] ).

cnf(i_0_18242,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__code]),
    [final] ).

cnf(i_0_18243,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_zero__is__num__zero]),
    [final] ).

cnf(i_0_18244,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_semiring__norm_I113_J]),
    [final] ).

cnf(i_0_18245,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__def]),
    [final] ).

cnf(i_0_18246,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]),
    [final] ).

cnf(i_0_18247,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_one__code__numeral__def]),
    [final] ).

cnf(i_0_18248,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]),
    [final] ).

cnf(i_0_18249,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_One__nat__def]),
    [final] ).

cnf(i_0_18250,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11103]),
    [final] ).

cnf(i_0_18251,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11104]),
    [final] ).

cnf(i_0_18252,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11105]),
    [final] ).

cnf(i_0_18253,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(X1))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11106]),
    [final] ).

cnf(i_0_18254,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11107]),
    [final] ).

cnf(i_0_18255,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_minus__Pls]),
    [final] ).

cnf(i_0_18256,plain,
    c_Equiv__Relations_Oequivp(X1,c_fequal),
    inference(split_conjunct,[status(thm)],[i_0_11108]),
    [final] ).

cnf(i_0_18257,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_trans__less__than]),
    [final] ).

cnf(i_0_18258,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
    [final] ).

cnf(i_0_18259,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
    [final] ).

cnf(i_0_18260,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11109]),
    [final] ).

cnf(i_0_18261,plain,
    class_Nat_Osize(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11110]),
    [final] ).

cnf(i_0_18262,plain,
    class_Nat_Osize(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11111]),
    [final] ).

cnf(i_0_18263,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11112]),
    [final] ).

cnf(i_0_18264,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat_Osize_I1_J]),
    [final] ).

cnf(i_0_18265,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I1_J]),
    [final] ).

cnf(i_0_18266,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]),
    [final] ).

cnf(i_0_18267,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]),
    [final] ).

cnf(i_0_18268,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]),
    [final] ).

cnf(i_0_18269,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_bool_Osize_I1_J]),
    [final] ).

cnf(i_0_18270,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]),
    [final] ).

cnf(i_0_18271,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_of__int__eq__id]),
    [final] ).

cnf(i_0_18272,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_com_Osize_I1_J]),
    [final] ).

cnf(i_0_18273,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_bot__nat__def]),
    [final] ).

cnf(i_0_18274,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_inf__nat__def]),
    [final] ).

cnf(i_0_18275,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_sup__nat__def]),
    [final] ).

cnf(i_0_18276,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_11113]),
    [final] ).

cnf(i_0_18277,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
    [final] ).

cnf(i_0_18278,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
    [final] ).

cnf(i_0_18279,plain,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Odvd]),
    [final] ).

cnf(i_0_18280,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
    [final] ).

cnf(i_0_18281,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
    [final] ).

cnf(i_0_18282,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]),
    [final] ).

cnf(i_0_18283,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy]),
    [final] ).

cnf(i_0_18284,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]),
    [final] ).

cnf(i_0_18285,plain,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]),
    [final] ).

cnf(i_0_18286,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(split_conjunct,[status(thm)],[arity_Com__Ocom__Nat_Osize]),
    [final] ).

cnf(i_0_18287,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]),
    [final] ).

cnf(i_0_18288,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]),
    [final] ).

cnf(i_0_18289,plain,
    class_Nat_Osize(tc_Com_Ostate),
    inference(split_conjunct,[status(thm)],[arity_Com__Ostate__Nat_Osize]),
    [final] ).

cnf(i_0_18290,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]),
    [final] ).

cnf(i_0_18291,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]),
    [final] ).

cnf(i_0_18292,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]),
    [final] ).

cnf(i_0_18293,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18294,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18295,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18296,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
    [final] ).

cnf(i_0_18297,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]),
    [final] ).

cnf(i_0_18298,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_18299,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_18300,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_18301,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18302,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18303,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18304,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_18305,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
    [final] ).

cnf(i_0_18306,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]),
    [final] ).

cnf(i_0_18307,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_18308,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
    [final] ).

cnf(i_0_18309,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18310,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18311,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18312,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]),
    [final] ).

cnf(i_0_18313,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18314,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18315,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18316,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]),
    [final] ).

cnf(i_0_18317,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]),
    [final] ).

cnf(i_0_18318,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]),
    [final] ).

cnf(i_0_18319,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
    [final] ).

cnf(i_0_18320,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]),
    [final] ).

cnf(i_0_18321,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18322,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18323,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18324,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]),
    [final] ).

cnf(i_0_18325,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]),
    [final] ).

cnf(i_0_18326,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]),
    [final] ).

cnf(i_0_18327,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]),
    [final] ).

cnf(i_0_18328,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]),
    [final] ).

cnf(i_0_18329,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]),
    [final] ).

cnf(i_0_18330,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]),
    [final] ).

cnf(i_0_18331,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]),
    [final] ).

cnf(i_0_18332,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]),
    [final] ).

cnf(i_0_18333,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18334,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18335,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18336,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]),
    [final] ).

cnf(i_0_18337,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]),
    [final] ).

cnf(i_0_18338,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]),
    [final] ).

cnf(i_0_18339,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_18340,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_18341,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_18342,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_18343,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]),
    [final] ).

cnf(i_0_18344,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]),
    [final] ).

cnf(i_0_18345,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18346,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18347,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18348,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_18349,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_18350,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_18351,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]),
    [final] ).

cnf(i_0_18352,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]),
    [final] ).

cnf(i_0_18353,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]),
    [final] ).

cnf(i_0_18354,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18355,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18356,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18357,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]),
    [final] ).

cnf(i_0_18358,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_18359,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_18360,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18361,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18362,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18363,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18364,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18365,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18366,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]),
    [final] ).

cnf(i_0_18367,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]),
    [final] ).

cnf(i_0_18368,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
    [final] ).

cnf(i_0_18369,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
    [final] ).

cnf(i_0_18370,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
    [final] ).

cnf(i_0_18371,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
    [final] ).

cnf(i_0_18372,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18373,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18374,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18375,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18376,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18377,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18378,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]),
    [final] ).

cnf(i_0_18379,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_18380,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_18381,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]),
    [final] ).

cnf(i_0_18382,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18383,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18384,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18385,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]),
    [final] ).

cnf(i_0_18386,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_18387,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]),
    [final] ).

cnf(i_0_18388,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
    [final] ).

cnf(i_0_18389,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
    [final] ).

cnf(i_0_18390,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
    [final] ).

cnf(i_0_18391,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_18392,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_18393,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_18394,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_18395,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
    [final] ).

cnf(i_0_18396,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]),
    [final] ).

cnf(i_0_18397,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]),
    [final] ).

cnf(i_0_18398,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]),
    [final] ).

cnf(i_0_18399,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]),
    [final] ).

cnf(i_0_18400,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
    [final] ).

cnf(i_0_18401,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
    [final] ).

cnf(i_0_18402,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_18403,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18404,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18405,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18406,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
    [final] ).

cnf(i_0_18407,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
    [final] ).

cnf(i_0_18408,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_18409,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_18410,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_18411,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_18412,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18413,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18414,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18415,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18416,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18417,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18418,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]),
    [final] ).

cnf(i_0_18419,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
    [final] ).

cnf(i_0_18420,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
    [final] ).

cnf(i_0_18421,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_18422,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18423,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18424,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_18425,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_18426,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_18427,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_18428,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_18429,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_18430,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_18431,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18432,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18433,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_18434,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_18435,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_18436,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_18437,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
    [final] ).

cnf(i_0_18438,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_18439,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_18440,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_18441,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]),
    [final] ).

cnf(i_0_18442,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_18443,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_18444,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_18445,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]),
    [final] ).

cnf(i_0_18446,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_18447,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_18448,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_18449,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18450,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18451,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18452,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18453,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18454,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18455,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18456,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_18457,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
    [final] ).

cnf(i_0_18458,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]),
    [final] ).

cnf(i_0_18459,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
    [final] ).

cnf(i_0_18460,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
    [final] ).

cnf(i_0_18461,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
    [final] ).

cnf(i_0_18462,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
    [final] ).

cnf(i_0_18463,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
    [final] ).

cnf(i_0_18464,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_18465,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_18466,plain,
    hBOOL(c_fTrue),
    inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
    [final] ).

cnf(i_0_18467,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[fact_subtract__code__numeral__def]),
    [final] ).

cnf(i_0_18468,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[fact_Code__Numeral_Oof__nat__code]),
    [final] ).

cnf(i_0_18469,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_18470,plain,
    c_Int_OMin != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
    [final] ).

cnf(i_0_18471,plain,
    c_Int_OPls != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
    [final] ).

cnf(i_0_18472,axiom,
    X1 = X1 ).

cnf(i_0_18473,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18474,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18475,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18476,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18477,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).

cnf(i_0_18478,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).

cnf(i_0_18479,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18480,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18481,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18482,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18483,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18484,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18485,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18486,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18487,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18488,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18489,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18490,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18491,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18492,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18493,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18494,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18495,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18496,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18497,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18498,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18499,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18500,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18501,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18502,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18503,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18504,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X1,X3,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18505,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X1,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18506,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X1,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18507,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X1,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18508,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X1,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18509,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X1) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18510,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18511,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18512,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18513,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18514,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18515,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18516,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18517,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18518,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18519,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18520,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18521,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18522,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18523,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18524,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18525,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18526,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18527,axiom,
    ( X1 != X2
    | esk531_6(X1,X3,X4,X5,X6,X7) = esk531_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18528,axiom,
    ( X1 != X2
    | esk531_6(X3,X1,X4,X5,X6,X7) = esk531_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18529,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X1,X5,X6,X7) = esk531_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18530,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X1,X6,X7) = esk531_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18531,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X6,X1,X7) = esk531_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18532,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X6,X7,X1) = esk531_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18533,axiom,
    ( X1 != X2
    | esk532_6(X1,X3,X4,X5,X6,X7) = esk532_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18534,axiom,
    ( X1 != X2
    | esk532_6(X3,X1,X4,X5,X6,X7) = esk532_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18535,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X1,X5,X6,X7) = esk532_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18536,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X1,X6,X7) = esk532_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18537,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X6,X1,X7) = esk532_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18538,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X6,X7,X1) = esk532_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18539,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osorted__list__of__set(X1,X3) = c_List_Olinorder__class_Osorted__list__of__set(X2,X3) ) ).

cnf(i_0_18540,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osorted__list__of__set(X3,X1) = c_List_Olinorder__class_Osorted__list__of__set(X3,X2) ) ).

cnf(i_0_18541,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18542,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18543,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18544,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18545,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18546,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18547,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18548,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18549,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18550,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18551,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18552,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18553,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_18554,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).

cnf(i_0_18555,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).

cnf(i_0_18556,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).

cnf(i_0_18557,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18558,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18559,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18560,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18561,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18562,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).

cnf(i_0_18563,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).

cnf(i_0_18564,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).

cnf(i_0_18565,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).

cnf(i_0_18566,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).

cnf(i_0_18567,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18568,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__decr__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18569,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__decr__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18570,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18571,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18572,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18573,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).

cnf(i_0_18574,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).

cnf(i_0_18575,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).

cnf(i_0_18576,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).

cnf(i_0_18577,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).

cnf(i_0_18578,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18579,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__decr__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18580,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__decr__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18581,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__decr__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18582,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3) ) ).

cnf(i_0_18583,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X1) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X2) ) ).

cnf(i_0_18584,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18585,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18586,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18587,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18588,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18589,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18590,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18591,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18592,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18593,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18594,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18595,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18596,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18597,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18598,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18599,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18600,axiom,
    ( X1 != X2
    | esk356_5(X1,X3,X4,X5,X6) = esk356_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18601,axiom,
    ( X1 != X2
    | esk356_5(X3,X1,X4,X5,X6) = esk356_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18602,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X1,X5,X6) = esk356_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18603,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X5,X1,X6) = esk356_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18604,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X5,X6,X1) = esk356_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18605,axiom,
    ( X1 != X2
    | esk357_5(X1,X3,X4,X5,X6) = esk357_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18606,axiom,
    ( X1 != X2
    | esk357_5(X3,X1,X4,X5,X6) = esk357_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18607,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X1,X5,X6) = esk357_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18608,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X5,X1,X6) = esk357_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18609,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X5,X6,X1) = esk357_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18610,axiom,
    ( X1 != X2
    | esk355_5(X1,X3,X4,X5,X6) = esk355_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18611,axiom,
    ( X1 != X2
    | esk355_5(X3,X1,X4,X5,X6) = esk355_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18612,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X1,X5,X6) = esk355_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18613,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X5,X1,X6) = esk355_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18614,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X5,X6,X1) = esk355_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18615,axiom,
    ( X1 != X2
    | esk354_5(X1,X3,X4,X5,X6) = esk354_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18616,axiom,
    ( X1 != X2
    | esk354_5(X3,X1,X4,X5,X6) = esk354_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18617,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X1,X5,X6) = esk354_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18618,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X5,X1,X6) = esk354_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18619,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X5,X6,X1) = esk354_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18620,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18621,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18622,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18623,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18624,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18625,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18626,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18627,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18628,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18629,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18630,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18631,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18632,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18633,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18634,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18635,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18636,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18637,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18638,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18639,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18640,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18641,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18642,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18643,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18644,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18645,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18646,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18647,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18648,axiom,
    ( X1 != X2
    | esk331_6(X1,X3,X4,X5,X6,X7) = esk331_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18649,axiom,
    ( X1 != X2
    | esk331_6(X3,X1,X4,X5,X6,X7) = esk331_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18650,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X1,X5,X6,X7) = esk331_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18651,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X1,X6,X7) = esk331_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18652,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X6,X1,X7) = esk331_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18653,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X6,X7,X1) = esk331_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18654,axiom,
    ( X1 != X2
    | esk330_6(X1,X3,X4,X5,X6,X7) = esk330_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18655,axiom,
    ( X1 != X2
    | esk330_6(X3,X1,X4,X5,X6,X7) = esk330_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18656,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X1,X5,X6,X7) = esk330_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18657,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X1,X6,X7) = esk330_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18658,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X6,X1,X7) = esk330_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18659,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X6,X7,X1) = esk330_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18660,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18661,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18662,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18663,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18664,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18665,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18666,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18667,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18668,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18669,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18670,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18671,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18672,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18673,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18674,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18675,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18676,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).

cnf(i_0_18677,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).

cnf(i_0_18678,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).

cnf(i_0_18679,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).

cnf(i_0_18680,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18681,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18682,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18683,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18684,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18685,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18686,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18687,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18688,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18689,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18690,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18691,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18692,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18693,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18694,axiom,
    ( X1 != X2
    | esk388_4(X1,X3,X4,X5) = esk388_4(X2,X3,X4,X5) ) ).

cnf(i_0_18695,axiom,
    ( X1 != X2
    | esk388_4(X3,X1,X4,X5) = esk388_4(X3,X2,X4,X5) ) ).

cnf(i_0_18696,axiom,
    ( X1 != X2
    | esk388_4(X3,X4,X1,X5) = esk388_4(X3,X4,X2,X5) ) ).

cnf(i_0_18697,axiom,
    ( X1 != X2
    | esk388_4(X3,X4,X5,X1) = esk388_4(X3,X4,X5,X2) ) ).

cnf(i_0_18698,axiom,
    ( X1 != X2
    | esk387_4(X1,X3,X4,X5) = esk387_4(X2,X3,X4,X5) ) ).

cnf(i_0_18699,axiom,
    ( X1 != X2
    | esk387_4(X3,X1,X4,X5) = esk387_4(X3,X2,X4,X5) ) ).

cnf(i_0_18700,axiom,
    ( X1 != X2
    | esk387_4(X3,X4,X1,X5) = esk387_4(X3,X4,X2,X5) ) ).

cnf(i_0_18701,axiom,
    ( X1 != X2
    | esk387_4(X3,X4,X5,X1) = esk387_4(X3,X4,X5,X2) ) ).

cnf(i_0_18702,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18703,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18704,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18705,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18706,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18707,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18708,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18709,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18710,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18711,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18712,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18713,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18714,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18715,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18716,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18717,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18718,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18719,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18720,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18721,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18722,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18723,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18724,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18725,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18726,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18727,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18728,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18729,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18730,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18731,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18732,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18733,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18734,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18735,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18736,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18737,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18738,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18739,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18740,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18741,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18742,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18743,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18744,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18745,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18746,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18747,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18748,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18749,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18750,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18751,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18752,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18753,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18754,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18755,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18756,axiom,
    ( X1 != X2
    | esk499_4(X1,X3,X4,X5) = esk499_4(X2,X3,X4,X5) ) ).

cnf(i_0_18757,axiom,
    ( X1 != X2
    | esk499_4(X3,X1,X4,X5) = esk499_4(X3,X2,X4,X5) ) ).

cnf(i_0_18758,axiom,
    ( X1 != X2
    | esk499_4(X3,X4,X1,X5) = esk499_4(X3,X4,X2,X5) ) ).

cnf(i_0_18759,axiom,
    ( X1 != X2
    | esk499_4(X3,X4,X5,X1) = esk499_4(X3,X4,X5,X2) ) ).

cnf(i_0_18760,axiom,
    ( X1 != X2
    | esk498_4(X1,X3,X4,X5) = esk498_4(X2,X3,X4,X5) ) ).

cnf(i_0_18761,axiom,
    ( X1 != X2
    | esk498_4(X3,X1,X4,X5) = esk498_4(X3,X2,X4,X5) ) ).

cnf(i_0_18762,axiom,
    ( X1 != X2
    | esk498_4(X3,X4,X1,X5) = esk498_4(X3,X4,X2,X5) ) ).

cnf(i_0_18763,axiom,
    ( X1 != X2
    | esk498_4(X3,X4,X5,X1) = esk498_4(X3,X4,X5,X2) ) ).

cnf(i_0_18764,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_18765,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_18766,axiom,
    ( X1 != X2
    | esk348_3(X1,X3,X4) = esk348_3(X2,X3,X4) ) ).

cnf(i_0_18767,axiom,
    ( X1 != X2
    | esk348_3(X3,X1,X4) = esk348_3(X3,X2,X4) ) ).

cnf(i_0_18768,axiom,
    ( X1 != X2
    | esk348_3(X3,X4,X1) = esk348_3(X3,X4,X2) ) ).

cnf(i_0_18769,axiom,
    ( X1 != X2
    | esk347_3(X1,X3,X4) = esk347_3(X2,X3,X4) ) ).

cnf(i_0_18770,axiom,
    ( X1 != X2
    | esk347_3(X3,X1,X4) = esk347_3(X3,X2,X4) ) ).

cnf(i_0_18771,axiom,
    ( X1 != X2
    | esk347_3(X3,X4,X1) = esk347_3(X3,X4,X2) ) ).

cnf(i_0_18772,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18773,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18774,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X1,X3,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18775,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X1,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18776,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X1,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18777,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X1,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18778,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X1) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18779,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18780,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18781,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18782,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18783,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18784,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18785,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__map(X2,X3,X4,X5) ) ).

cnf(i_0_18786,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__map(X3,X2,X4,X5) ) ).

cnf(i_0_18787,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__map(X3,X4,X2,X5) ) ).

cnf(i_0_18788,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__map(X3,X4,X5,X2) ) ).

cnf(i_0_18789,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18790,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18791,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18792,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__map(X2,X3,X4,X5) ) ).

cnf(i_0_18793,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__map(X3,X2,X4,X5) ) ).

cnf(i_0_18794,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__map(X3,X4,X2,X5) ) ).

cnf(i_0_18795,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__map(X3,X4,X5,X2) ) ).

cnf(i_0_18796,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18797,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18798,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18799,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18800,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18801,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18802,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18803,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18804,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18805,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18806,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18807,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18808,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18809,axiom,
    ( X1 != X2
    | esk74_5(X1,X3,X4,X5,X6) = esk74_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18810,axiom,
    ( X1 != X2
    | esk74_5(X3,X1,X4,X5,X6) = esk74_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18811,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X1,X5,X6) = esk74_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18812,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X5,X1,X6) = esk74_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18813,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X5,X6,X1) = esk74_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18814,axiom,
    ( X1 != X2
    | esk344_3(X1,X3,X4) = esk344_3(X2,X3,X4) ) ).

cnf(i_0_18815,axiom,
    ( X1 != X2
    | esk344_3(X3,X1,X4) = esk344_3(X3,X2,X4) ) ).

cnf(i_0_18816,axiom,
    ( X1 != X2
    | esk344_3(X3,X4,X1) = esk344_3(X3,X4,X2) ) ).

cnf(i_0_18817,axiom,
    ( X1 != X2
    | esk343_3(X1,X3,X4) = esk343_3(X2,X3,X4) ) ).

cnf(i_0_18818,axiom,
    ( X1 != X2
    | esk343_3(X3,X1,X4) = esk343_3(X3,X2,X4) ) ).

cnf(i_0_18819,axiom,
    ( X1 != X2
    | esk343_3(X3,X4,X1) = esk343_3(X3,X4,X2) ) ).

cnf(i_0_18820,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18821,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18822,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18823,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18824,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18825,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18826,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18827,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18828,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18829,axiom,
    ( X1 != X2
    | esk453_2(X1,X3) = esk453_2(X2,X3) ) ).

cnf(i_0_18830,axiom,
    ( X1 != X2
    | esk453_2(X3,X1) = esk453_2(X3,X2) ) ).

cnf(i_0_18831,axiom,
    ( X1 != X2
    | esk454_2(X1,X3) = esk454_2(X2,X3) ) ).

cnf(i_0_18832,axiom,
    ( X1 != X2
    | esk454_2(X3,X1) = esk454_2(X3,X2) ) ).

cnf(i_0_18833,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18834,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18835,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18836,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18837,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18838,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18839,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18840,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X1,X3,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18841,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X1,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18842,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X1,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18843,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X1,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18844,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X6,X1,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18845,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X1) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18846,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18847,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18848,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18849,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18850,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18851,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18852,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18853,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18854,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18855,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18856,axiom,
    ( X1 != X2
    | esk277_3(X1,X3,X4) = esk277_3(X2,X3,X4) ) ).

cnf(i_0_18857,axiom,
    ( X1 != X2
    | esk277_3(X3,X1,X4) = esk277_3(X3,X2,X4) ) ).

cnf(i_0_18858,axiom,
    ( X1 != X2
    | esk277_3(X3,X4,X1) = esk277_3(X3,X4,X2) ) ).

cnf(i_0_18859,axiom,
    ( X1 != X2
    | esk528_3(X1,X3,X4) = esk528_3(X2,X3,X4) ) ).

cnf(i_0_18860,axiom,
    ( X1 != X2
    | esk528_3(X3,X1,X4) = esk528_3(X3,X2,X4) ) ).

cnf(i_0_18861,axiom,
    ( X1 != X2
    | esk528_3(X3,X4,X1) = esk528_3(X3,X4,X2) ) ).

cnf(i_0_18862,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18863,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18864,axiom,
    ( X1 != X2
    | esk494_4(X1,X3,X4,X5) = esk494_4(X2,X3,X4,X5) ) ).

cnf(i_0_18865,axiom,
    ( X1 != X2
    | esk494_4(X3,X1,X4,X5) = esk494_4(X3,X2,X4,X5) ) ).

cnf(i_0_18866,axiom,
    ( X1 != X2
    | esk494_4(X3,X4,X1,X5) = esk494_4(X3,X4,X2,X5) ) ).

cnf(i_0_18867,axiom,
    ( X1 != X2
    | esk494_4(X3,X4,X5,X1) = esk494_4(X3,X4,X5,X2) ) ).

cnf(i_0_18868,axiom,
    ( X1 != X2
    | esk486_4(X1,X3,X4,X5) = esk486_4(X2,X3,X4,X5) ) ).

cnf(i_0_18869,axiom,
    ( X1 != X2
    | esk486_4(X3,X1,X4,X5) = esk486_4(X3,X2,X4,X5) ) ).

cnf(i_0_18870,axiom,
    ( X1 != X2
    | esk486_4(X3,X4,X1,X5) = esk486_4(X3,X4,X2,X5) ) ).

cnf(i_0_18871,axiom,
    ( X1 != X2
    | esk486_4(X3,X4,X5,X1) = esk486_4(X3,X4,X5,X2) ) ).

cnf(i_0_18872,axiom,
    ( X1 != X2
    | esk128_4(X1,X3,X4,X5) = esk128_4(X2,X3,X4,X5) ) ).

cnf(i_0_18873,axiom,
    ( X1 != X2
    | esk128_4(X3,X1,X4,X5) = esk128_4(X3,X2,X4,X5) ) ).

cnf(i_0_18874,axiom,
    ( X1 != X2
    | esk128_4(X3,X4,X1,X5) = esk128_4(X3,X4,X2,X5) ) ).

cnf(i_0_18875,axiom,
    ( X1 != X2
    | esk128_4(X3,X4,X5,X1) = esk128_4(X3,X4,X5,X2) ) ).

cnf(i_0_18876,axiom,
    ( X1 != X2
    | esk130_4(X1,X3,X4,X5) = esk130_4(X2,X3,X4,X5) ) ).

cnf(i_0_18877,axiom,
    ( X1 != X2
    | esk130_4(X3,X1,X4,X5) = esk130_4(X3,X2,X4,X5) ) ).

cnf(i_0_18878,axiom,
    ( X1 != X2
    | esk130_4(X3,X4,X1,X5) = esk130_4(X3,X4,X2,X5) ) ).

cnf(i_0_18879,axiom,
    ( X1 != X2
    | esk130_4(X3,X4,X5,X1) = esk130_4(X3,X4,X5,X2) ) ).

cnf(i_0_18880,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18881,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18882,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18883,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18884,axiom,
    ( X1 != X2
    | esk21_4(X1,X3,X4,X5) = esk21_4(X2,X3,X4,X5) ) ).

cnf(i_0_18885,axiom,
    ( X1 != X2
    | esk21_4(X3,X1,X4,X5) = esk21_4(X3,X2,X4,X5) ) ).

cnf(i_0_18886,axiom,
    ( X1 != X2
    | esk21_4(X3,X4,X1,X5) = esk21_4(X3,X4,X2,X5) ) ).

cnf(i_0_18887,axiom,
    ( X1 != X2
    | esk21_4(X3,X4,X5,X1) = esk21_4(X3,X4,X5,X2) ) ).

cnf(i_0_18888,axiom,
    ( X1 != X2
    | esk20_4(X1,X3,X4,X5) = esk20_4(X2,X3,X4,X5) ) ).

cnf(i_0_18889,axiom,
    ( X1 != X2
    | esk20_4(X3,X1,X4,X5) = esk20_4(X3,X2,X4,X5) ) ).

cnf(i_0_18890,axiom,
    ( X1 != X2
    | esk20_4(X3,X4,X1,X5) = esk20_4(X3,X4,X2,X5) ) ).

cnf(i_0_18891,axiom,
    ( X1 != X2
    | esk20_4(X3,X4,X5,X1) = esk20_4(X3,X4,X5,X2) ) ).

cnf(i_0_18892,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18893,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18894,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18895,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18896,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18897,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18898,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18899,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18900,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18901,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18902,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18903,axiom,
    ( X1 != X2
    | esk230_3(X1,X3,X4) = esk230_3(X2,X3,X4) ) ).

cnf(i_0_18904,axiom,
    ( X1 != X2
    | esk230_3(X3,X1,X4) = esk230_3(X3,X2,X4) ) ).

cnf(i_0_18905,axiom,
    ( X1 != X2
    | esk230_3(X3,X4,X1) = esk230_3(X3,X4,X2) ) ).

cnf(i_0_18906,axiom,
    ( X1 != X2
    | esk231_3(X1,X3,X4) = esk231_3(X2,X3,X4) ) ).

cnf(i_0_18907,axiom,
    ( X1 != X2
    | esk231_3(X3,X1,X4) = esk231_3(X3,X2,X4) ) ).

cnf(i_0_18908,axiom,
    ( X1 != X2
    | esk231_3(X3,X4,X1) = esk231_3(X3,X4,X2) ) ).

cnf(i_0_18909,axiom,
    ( X1 != X2
    | esk73_4(X1,X3,X4,X5) = esk73_4(X2,X3,X4,X5) ) ).

cnf(i_0_18910,axiom,
    ( X1 != X2
    | esk73_4(X3,X1,X4,X5) = esk73_4(X3,X2,X4,X5) ) ).

cnf(i_0_18911,axiom,
    ( X1 != X2
    | esk73_4(X3,X4,X1,X5) = esk73_4(X3,X4,X2,X5) ) ).

cnf(i_0_18912,axiom,
    ( X1 != X2
    | esk73_4(X3,X4,X5,X1) = esk73_4(X3,X4,X5,X2) ) ).

cnf(i_0_18913,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X1,X3,X4,X5) = c_List_Olinorder__class_Osort__key(X2,X3,X4,X5) ) ).

cnf(i_0_18914,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X1,X4,X5) = c_List_Olinorder__class_Osort__key(X3,X2,X4,X5) ) ).

cnf(i_0_18915,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X4,X1,X5) = c_List_Olinorder__class_Osort__key(X3,X4,X2,X5) ) ).

cnf(i_0_18916,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X4,X5,X1) = c_List_Olinorder__class_Osort__key(X3,X4,X5,X2) ) ).

cnf(i_0_18917,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18918,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18919,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18920,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18921,axiom,
    ( X1 != X2
    | esk228_3(X1,X3,X4) = esk228_3(X2,X3,X4) ) ).

cnf(i_0_18922,axiom,
    ( X1 != X2
    | esk228_3(X3,X1,X4) = esk228_3(X3,X2,X4) ) ).

cnf(i_0_18923,axiom,
    ( X1 != X2
    | esk228_3(X3,X4,X1) = esk228_3(X3,X4,X2) ) ).

cnf(i_0_18924,axiom,
    ( X1 != X2
    | esk227_3(X1,X3,X4) = esk227_3(X2,X3,X4) ) ).

cnf(i_0_18925,axiom,
    ( X1 != X2
    | esk227_3(X3,X1,X4) = esk227_3(X3,X2,X4) ) ).

cnf(i_0_18926,axiom,
    ( X1 != X2
    | esk227_3(X3,X4,X1) = esk227_3(X3,X4,X2) ) ).

cnf(i_0_18927,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_18928,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_18929,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_18930,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_18931,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18932,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18933,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18934,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18935,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18936,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18937,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18938,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18939,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18940,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18941,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18942,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18943,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18944,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18945,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18946,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18947,axiom,
    ( X1 != X2
    | esk519_2(X1,X3) = esk519_2(X2,X3) ) ).

cnf(i_0_18948,axiom,
    ( X1 != X2
    | esk519_2(X3,X1) = esk519_2(X3,X2) ) ).

cnf(i_0_18949,axiom,
    ( X1 != X2
    | esk518_2(X1,X3) = esk518_2(X2,X3) ) ).

cnf(i_0_18950,axiom,
    ( X1 != X2
    | esk518_2(X3,X1) = esk518_2(X3,X2) ) ).

cnf(i_0_18951,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18952,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18953,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18954,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18955,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18956,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18957,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18958,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18959,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18960,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18961,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18962,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18963,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18964,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18965,axiom,
    ( X1 != X2
    | esk137_3(X1,X3,X4) = esk137_3(X2,X3,X4) ) ).

cnf(i_0_18966,axiom,
    ( X1 != X2
    | esk137_3(X3,X1,X4) = esk137_3(X3,X2,X4) ) ).

cnf(i_0_18967,axiom,
    ( X1 != X2
    | esk137_3(X3,X4,X1) = esk137_3(X3,X4,X2) ) ).

cnf(i_0_18968,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18969,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18970,axiom,
    ( X1 != X2
    | esk495_4(X1,X3,X4,X5) = esk495_4(X2,X3,X4,X5) ) ).

cnf(i_0_18971,axiom,
    ( X1 != X2
    | esk495_4(X3,X1,X4,X5) = esk495_4(X3,X2,X4,X5) ) ).

cnf(i_0_18972,axiom,
    ( X1 != X2
    | esk495_4(X3,X4,X1,X5) = esk495_4(X3,X4,X2,X5) ) ).

cnf(i_0_18973,axiom,
    ( X1 != X2
    | esk495_4(X3,X4,X5,X1) = esk495_4(X3,X4,X5,X2) ) ).

cnf(i_0_18974,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18975,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18976,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18977,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18978,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18979,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18980,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18981,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18982,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18983,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18984,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18985,axiom,
    ( X1 != X2
    | esk328_2(X1,X3) = esk328_2(X2,X3) ) ).

cnf(i_0_18986,axiom,
    ( X1 != X2
    | esk328_2(X3,X1) = esk328_2(X3,X2) ) ).

cnf(i_0_18987,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18988,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18989,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18990,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18991,axiom,
    ( X1 != X2
    | esk427_2(X1,X3) = esk427_2(X2,X3) ) ).

cnf(i_0_18992,axiom,
    ( X1 != X2
    | esk427_2(X3,X1) = esk427_2(X3,X2) ) ).

cnf(i_0_18993,axiom,
    ( X1 != X2
    | esk428_2(X1,X3) = esk428_2(X2,X3) ) ).

cnf(i_0_18994,axiom,
    ( X1 != X2
    | esk428_2(X3,X1) = esk428_2(X3,X2) ) ).

cnf(i_0_18995,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X3,X4,X5) ) ).

cnf(i_0_18996,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X2,X4,X5) ) ).

cnf(i_0_18997,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X2,X5) ) ).

cnf(i_0_18998,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X2) ) ).

cnf(i_0_18999,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X1,X3,X4,X5) = c_Lazy__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_19000,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X1,X4,X5) = c_Lazy__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_19001,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X1,X5) = c_Lazy__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_19002,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X5,X1) = c_Lazy__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_19003,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_19004,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_19005,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_19006,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_19007,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_19008,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_19009,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_19010,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_19011,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_19012,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).

cnf(i_0_19013,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).

cnf(i_0_19014,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).

cnf(i_0_19015,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).

cnf(i_0_19016,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_19017,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_19018,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_19019,axiom,
    ( X1 != X2
    | esk415_2(X1,X3) = esk415_2(X2,X3) ) ).

cnf(i_0_19020,axiom,
    ( X1 != X2
    | esk415_2(X3,X1) = esk415_2(X3,X2) ) ).

cnf(i_0_19021,axiom,
    ( X1 != X2
    | esk127_3(X1,X3,X4) = esk127_3(X2,X3,X4) ) ).

cnf(i_0_19022,axiom,
    ( X1 != X2
    | esk127_3(X3,X1,X4) = esk127_3(X3,X2,X4) ) ).

cnf(i_0_19023,axiom,
    ( X1 != X2
    | esk127_3(X3,X4,X1) = esk127_3(X3,X4,X2) ) ).

cnf(i_0_19024,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_19025,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_19026,axiom,
    ( X1 != X2
    | esk129_3(X1,X3,X4) = esk129_3(X2,X3,X4) ) ).

cnf(i_0_19027,axiom,
    ( X1 != X2
    | esk129_3(X3,X1,X4) = esk129_3(X3,X2,X4) ) ).

cnf(i_0_19028,axiom,
    ( X1 != X2
    | esk129_3(X3,X4,X1) = esk129_3(X3,X4,X2) ) ).

cnf(i_0_19029,axiom,
    ( X1 != X2
    | esk90_3(X1,X3,X4) = esk90_3(X2,X3,X4) ) ).

cnf(i_0_19030,axiom,
    ( X1 != X2
    | esk90_3(X3,X1,X4) = esk90_3(X3,X2,X4) ) ).

cnf(i_0_19031,axiom,
    ( X1 != X2
    | esk90_3(X3,X4,X1) = esk90_3(X3,X4,X2) ) ).

cnf(i_0_19032,axiom,
    ( X1 != X2
    | esk89_3(X1,X3,X4) = esk89_3(X2,X3,X4) ) ).

cnf(i_0_19033,axiom,
    ( X1 != X2
    | esk89_3(X3,X1,X4) = esk89_3(X3,X2,X4) ) ).

cnf(i_0_19034,axiom,
    ( X1 != X2
    | esk89_3(X3,X4,X1) = esk89_3(X3,X4,X2) ) ).

cnf(i_0_19035,axiom,
    ( X1 != X2
    | esk493_3(X1,X3,X4) = esk493_3(X2,X3,X4) ) ).

cnf(i_0_19036,axiom,
    ( X1 != X2
    | esk493_3(X3,X1,X4) = esk493_3(X3,X2,X4) ) ).

cnf(i_0_19037,axiom,
    ( X1 != X2
    | esk493_3(X3,X4,X1) = esk493_3(X3,X4,X2) ) ).

cnf(i_0_19038,axiom,
    ( X1 != X2
    | esk485_3(X1,X3,X4) = esk485_3(X2,X3,X4) ) ).

cnf(i_0_19039,axiom,
    ( X1 != X2
    | esk485_3(X3,X1,X4) = esk485_3(X3,X2,X4) ) ).

cnf(i_0_19040,axiom,
    ( X1 != X2
    | esk485_3(X3,X4,X1) = esk485_3(X3,X4,X2) ) ).

cnf(i_0_19041,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X1,X3,X4,X5) = c_Quotient_OBabs(X2,X3,X4,X5) ) ).

cnf(i_0_19042,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X1,X4,X5) = c_Quotient_OBabs(X3,X2,X4,X5) ) ).

cnf(i_0_19043,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X1,X5) = c_Quotient_OBabs(X3,X4,X2,X5) ) ).

cnf(i_0_19044,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X5,X1) = c_Quotient_OBabs(X3,X4,X5,X2) ) ).

cnf(i_0_19045,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X1,X3) = c_Lazy__Sequence_Oflat(X2,X3) ) ).

cnf(i_0_19046,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X3,X1) = c_Lazy__Sequence_Oflat(X3,X2) ) ).

cnf(i_0_19047,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19048,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19049,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19050,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).

cnf(i_0_19051,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).

cnf(i_0_19052,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).

cnf(i_0_19053,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).

cnf(i_0_19054,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).

cnf(i_0_19055,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).

cnf(i_0_19056,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).

cnf(i_0_19057,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).

cnf(i_0_19058,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19059,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19060,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19061,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19062,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19063,axiom,
    ( X1 != X2
    | c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).

cnf(i_0_19064,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19065,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19066,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19067,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19068,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19069,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19070,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X3,X4,X5) ) ).

cnf(i_0_19071,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X4,X5) ) ).

cnf(i_0_19072,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X2,X5) ) ).

cnf(i_0_19073,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X2) ) ).

cnf(i_0_19074,axiom,
    ( X1 != X2
    | esk433_2(X1,X3) = esk433_2(X2,X3) ) ).

cnf(i_0_19075,axiom,
    ( X1 != X2
    | esk433_2(X3,X1) = esk433_2(X3,X2) ) ).

cnf(i_0_19076,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19077,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19078,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19079,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19080,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_19081,axiom,
    ( X1 != X2
    | esk402_2(X1,X3) = esk402_2(X2,X3) ) ).

cnf(i_0_19082,axiom,
    ( X1 != X2
    | esk402_2(X3,X1) = esk402_2(X3,X2) ) ).

cnf(i_0_19083,axiom,
    ( X1 != X2
    | esk401_2(X1,X3) = esk401_2(X2,X3) ) ).

cnf(i_0_19084,axiom,
    ( X1 != X2
    | esk401_2(X3,X1) = esk401_2(X3,X2) ) ).

cnf(i_0_19085,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19086,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19087,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19088,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19089,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19090,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19091,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19092,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19093,axiom,
    ( X1 != X2
    | esk496_3(X1,X3,X4) = esk496_3(X2,X3,X4) ) ).

cnf(i_0_19094,axiom,
    ( X1 != X2
    | esk496_3(X3,X1,X4) = esk496_3(X3,X2,X4) ) ).

cnf(i_0_19095,axiom,
    ( X1 != X2
    | esk496_3(X3,X4,X1) = esk496_3(X3,X4,X2) ) ).

cnf(i_0_19096,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19097,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19098,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).

cnf(i_0_19099,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).

cnf(i_0_19100,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).

cnf(i_0_19101,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19102,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19103,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19104,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19105,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).

cnf(i_0_19106,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).

cnf(i_0_19107,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).

cnf(i_0_19108,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19109,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19110,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19111,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19112,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19113,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19114,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19115,axiom,
    ( X1 != X2
    | esk460_2(X1,X3) = esk460_2(X2,X3) ) ).

cnf(i_0_19116,axiom,
    ( X1 != X2
    | esk460_2(X3,X1) = esk460_2(X3,X2) ) ).

cnf(i_0_19117,axiom,
    ( X1 != X2
    | esk397_1(X1) = esk397_1(X2) ) ).

cnf(i_0_19118,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19119,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19120,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19121,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19122,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19123,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19124,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19125,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19126,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19127,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19128,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19129,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19130,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19131,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19132,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19133,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19134,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19135,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19136,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19137,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19138,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19139,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19140,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19141,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19142,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19143,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19144,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19145,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19146,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19147,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19148,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19149,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19150,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19151,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19152,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19153,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19154,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19155,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19156,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19157,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19158,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19159,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19160,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19161,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19162,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19163,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19164,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19165,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19166,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19167,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19168,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19169,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19170,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19171,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19172,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19173,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19174,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19175,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19176,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19177,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19178,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19179,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19180,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19181,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19182,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19183,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19184,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19185,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19186,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19187,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19188,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19189,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19190,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19191,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19192,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19193,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19194,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19195,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19196,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19197,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19198,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19199,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19200,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19201,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19202,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19203,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19204,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19205,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19206,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19207,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19208,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19209,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19210,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19211,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19212,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X1,X3,X4,X5,X6)
    | c_Finite__Set_Ofolding__image(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19213,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X1,X4,X5,X6)
    | c_Finite__Set_Ofolding__image(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19214,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X1,X5,X6)
    | c_Finite__Set_Ofolding__image(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19215,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X1,X6)
    | c_Finite__Set_Ofolding__image(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19216,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X1)
    | c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19217,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19218,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19219,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19220,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19221,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19222,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19223,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19224,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19225,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19226,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19227,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19228,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19229,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19230,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19231,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19232,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19233,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19234,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19235,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19236,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19237,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19238,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19239,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19240,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19241,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19242,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19243,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19244,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19245,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19246,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19247,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19248,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19249,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19250,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19251,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19252,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19253,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19254,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19255,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19256,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19257,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19258,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19259,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19260,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19261,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19262,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19263,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19264,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19265,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19266,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19267,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19268,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19269,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19270,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19271,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19272,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19273,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19274,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19275,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19276,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19277,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19278,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19279,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19280,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19281,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19282,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19283,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19284,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19285,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19286,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19287,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19288,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19289,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19290,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19291,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19292,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19293,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19294,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19295,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19296,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19297,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19298,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19299,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19300,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19301,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19302,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19303,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19304,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19305,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19306,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19307,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19308,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19309,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19310,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19311,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19312,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19313,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19314,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19315,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19316,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19317,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19318,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).

cnf(i_0_19319,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).

cnf(i_0_19320,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).

cnf(i_0_19321,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19322,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19323,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19324,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19325,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19326,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19327,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19328,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19329,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19330,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19331,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19332,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_19333,axiom,
    ( X1 != X2
    | ~ class_Rings_Odvd(X1)
    | class_Rings_Odvd(X2) ) ).

cnf(i_0_19334,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19335,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19336,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19337,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19338,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19339,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19340,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19341,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19342,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19343,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19344,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19345,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19346,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19347,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19348,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19349,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19350,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19351,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19352,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19353,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19354,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19355,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19356,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19357,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19358,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19359,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19360,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19361,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19362,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19363,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X1,X3,X4,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19364,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X1,X4,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19365,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X1,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19366,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X1,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19367,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X1)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19368,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19369,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19370,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19371,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19372,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19373,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19374,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19375,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19376,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19377,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19378,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19379,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X1,X3,X4)
    | c_List_Oall__interval__nat(X2,X3,X4) ) ).

cnf(i_0_19380,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X1,X4)
    | c_List_Oall__interval__nat(X3,X2,X4) ) ).

cnf(i_0_19381,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X4,X1)
    | c_List_Oall__interval__nat(X3,X4,X2) ) ).

cnf(i_0_19382,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19383,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19384,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19385,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19386,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19387,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19388,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19389,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19390,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19391,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19392,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19393,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19394,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19395,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_18472_001,axiom,
    X1 = X1 ).

cnf(i_0_18473_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18474_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18475_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18476_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18477_006,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).

cnf(i_0_18478_007,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).

cnf(i_0_18479_008,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18480_009,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18481_010,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18482_011,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18483_012,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18484_013,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18485_014,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18486_015,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18487_016,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18488_017,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18489_018,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18490_019,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18491_020,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18492_021,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18493_022,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18494_023,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18495_024,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18496_025,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18497_026,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18498_027,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18499_028,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18500_029,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18501_030,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18502_031,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18503_032,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18504_033,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X1,X3,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18505_034,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X1,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18506_035,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X1,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18507_036,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X1,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18508_037,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X1,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18509_038,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X1) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18510_039,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18511_040,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18512_041,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18513_042,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18514_043,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18515_044,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18516_045,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18517_046,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18518_047,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18519_048,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18520_049,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18521_050,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18522_051,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18523_052,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18524_053,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18525_054,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18526_055,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18527_056,axiom,
    ( X1 != X2
    | esk531_6(X1,X3,X4,X5,X6,X7) = esk531_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18528_057,axiom,
    ( X1 != X2
    | esk531_6(X3,X1,X4,X5,X6,X7) = esk531_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18529_058,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X1,X5,X6,X7) = esk531_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18530_059,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X1,X6,X7) = esk531_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18531_060,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X6,X1,X7) = esk531_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18532_061,axiom,
    ( X1 != X2
    | esk531_6(X3,X4,X5,X6,X7,X1) = esk531_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18533_062,axiom,
    ( X1 != X2
    | esk532_6(X1,X3,X4,X5,X6,X7) = esk532_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18534_063,axiom,
    ( X1 != X2
    | esk532_6(X3,X1,X4,X5,X6,X7) = esk532_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18535_064,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X1,X5,X6,X7) = esk532_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18536_065,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X1,X6,X7) = esk532_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18537_066,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X6,X1,X7) = esk532_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18538_067,axiom,
    ( X1 != X2
    | esk532_6(X3,X4,X5,X6,X7,X1) = esk532_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18539_068,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osorted__list__of__set(X1,X3) = c_List_Olinorder__class_Osorted__list__of__set(X2,X3) ) ).

cnf(i_0_18540_069,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osorted__list__of__set(X3,X1) = c_List_Olinorder__class_Osorted__list__of__set(X3,X2) ) ).

cnf(i_0_18541_070,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18542_071,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18543_072,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18544_073,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18545_074,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18546_075,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18547_076,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18548_077,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18549_078,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18550_079,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18551_080,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18552_081,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18553_082,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_18554_083,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).

cnf(i_0_18555_084,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).

cnf(i_0_18556_085,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).

cnf(i_0_18557_086,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18558_087,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18559_088,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18560_089,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18561_090,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18562_091,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).

cnf(i_0_18563_092,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).

cnf(i_0_18564_093,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).

cnf(i_0_18565_094,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).

cnf(i_0_18566_095,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).

cnf(i_0_18567_096,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18568_097,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__decr__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18569_098,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__decr__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18570_099,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18571_100,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18572_101,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).

cnf(i_0_18573_102,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).

cnf(i_0_18574_103,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).

cnf(i_0_18575_104,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).

cnf(i_0_18576_105,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).

cnf(i_0_18577_106,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).

cnf(i_0_18578_107,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18579_108,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__decr__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18580_109,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__decr__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18581_110,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__decr__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18582_111,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3) ) ).

cnf(i_0_18583_112,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X1) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X2) ) ).

cnf(i_0_18584_113,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18585_114,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18586_115,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18587_116,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18588_117,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18589_118,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18590_119,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18591_120,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18592_121,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18593_122,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18594_123,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18595_124,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18596_125,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18597_126,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18598_127,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18599_128,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18600_129,axiom,
    ( X1 != X2
    | esk356_5(X1,X3,X4,X5,X6) = esk356_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18601_130,axiom,
    ( X1 != X2
    | esk356_5(X3,X1,X4,X5,X6) = esk356_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18602_131,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X1,X5,X6) = esk356_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18603_132,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X5,X1,X6) = esk356_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18604_133,axiom,
    ( X1 != X2
    | esk356_5(X3,X4,X5,X6,X1) = esk356_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18605_134,axiom,
    ( X1 != X2
    | esk357_5(X1,X3,X4,X5,X6) = esk357_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18606_135,axiom,
    ( X1 != X2
    | esk357_5(X3,X1,X4,X5,X6) = esk357_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18607_136,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X1,X5,X6) = esk357_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18608_137,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X5,X1,X6) = esk357_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18609_138,axiom,
    ( X1 != X2
    | esk357_5(X3,X4,X5,X6,X1) = esk357_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18610_139,axiom,
    ( X1 != X2
    | esk355_5(X1,X3,X4,X5,X6) = esk355_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18611_140,axiom,
    ( X1 != X2
    | esk355_5(X3,X1,X4,X5,X6) = esk355_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18612_141,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X1,X5,X6) = esk355_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18613_142,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X5,X1,X6) = esk355_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18614_143,axiom,
    ( X1 != X2
    | esk355_5(X3,X4,X5,X6,X1) = esk355_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18615_144,axiom,
    ( X1 != X2
    | esk354_5(X1,X3,X4,X5,X6) = esk354_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18616_145,axiom,
    ( X1 != X2
    | esk354_5(X3,X1,X4,X5,X6) = esk354_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18617_146,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X1,X5,X6) = esk354_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18618_147,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X5,X1,X6) = esk354_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18619_148,axiom,
    ( X1 != X2
    | esk354_5(X3,X4,X5,X6,X1) = esk354_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18620_149,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18621_150,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18622_151,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18623_152,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18624_153,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18625_154,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18626_155,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18627_156,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18628_157,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18629_158,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18630_159,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18631_160,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18632_161,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18633_162,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18634_163,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18635_164,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18636_165,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18637_166,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18638_167,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18639_168,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18640_169,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18641_170,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18642_171,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18643_172,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18644_173,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18645_174,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18646_175,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18647_176,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18648_177,axiom,
    ( X1 != X2
    | esk331_6(X1,X3,X4,X5,X6,X7) = esk331_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18649_178,axiom,
    ( X1 != X2
    | esk331_6(X3,X1,X4,X5,X6,X7) = esk331_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18650_179,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X1,X5,X6,X7) = esk331_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18651_180,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X1,X6,X7) = esk331_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18652_181,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X6,X1,X7) = esk331_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18653_182,axiom,
    ( X1 != X2
    | esk331_6(X3,X4,X5,X6,X7,X1) = esk331_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18654_183,axiom,
    ( X1 != X2
    | esk330_6(X1,X3,X4,X5,X6,X7) = esk330_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18655_184,axiom,
    ( X1 != X2
    | esk330_6(X3,X1,X4,X5,X6,X7) = esk330_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18656_185,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X1,X5,X6,X7) = esk330_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18657_186,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X1,X6,X7) = esk330_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18658_187,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X6,X1,X7) = esk330_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18659_188,axiom,
    ( X1 != X2
    | esk330_6(X3,X4,X5,X6,X7,X1) = esk330_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18660_189,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18661_190,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18662_191,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18663_192,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18664_193,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18665_194,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18666_195,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18667_196,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18668_197,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18669_198,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18670_199,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18671_200,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18672_201,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18673_202,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18674_203,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18675_204,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18676_205,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).

cnf(i_0_18677_206,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).

cnf(i_0_18678_207,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).

cnf(i_0_18679_208,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).

cnf(i_0_18680_209,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18681_210,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18682_211,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18683_212,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18684_213,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18685_214,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18686_215,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18687_216,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18688_217,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18689_218,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18690_219,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18691_220,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18692_221,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18693_222,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18694_223,axiom,
    ( X1 != X2
    | esk388_4(X1,X3,X4,X5) = esk388_4(X2,X3,X4,X5) ) ).

cnf(i_0_18695_224,axiom,
    ( X1 != X2
    | esk388_4(X3,X1,X4,X5) = esk388_4(X3,X2,X4,X5) ) ).

cnf(i_0_18696_225,axiom,
    ( X1 != X2
    | esk388_4(X3,X4,X1,X5) = esk388_4(X3,X4,X2,X5) ) ).

cnf(i_0_18697_226,axiom,
    ( X1 != X2
    | esk388_4(X3,X4,X5,X1) = esk388_4(X3,X4,X5,X2) ) ).

cnf(i_0_18698_227,axiom,
    ( X1 != X2
    | esk387_4(X1,X3,X4,X5) = esk387_4(X2,X3,X4,X5) ) ).

cnf(i_0_18699_228,axiom,
    ( X1 != X2
    | esk387_4(X3,X1,X4,X5) = esk387_4(X3,X2,X4,X5) ) ).

cnf(i_0_18700_229,axiom,
    ( X1 != X2
    | esk387_4(X3,X4,X1,X5) = esk387_4(X3,X4,X2,X5) ) ).

cnf(i_0_18701_230,axiom,
    ( X1 != X2
    | esk387_4(X3,X4,X5,X1) = esk387_4(X3,X4,X5,X2) ) ).

cnf(i_0_18702_231,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18703_232,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18704_233,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18705_234,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18706_235,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18707_236,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18708_237,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18709_238,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18710_239,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18711_240,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18712_241,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18713_242,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18714_243,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18715_244,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18716_245,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18717_246,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18718_247,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18719_248,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18720_249,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18721_250,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18722_251,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18723_252,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18724_253,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18725_254,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18726_255,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18727_256,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18728_257,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18729_258,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18730_259,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18731_260,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18732_261,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18733_262,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18734_263,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18735_264,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18736_265,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18737_266,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18738_267,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18739_268,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18740_269,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18741_270,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18742_271,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18743_272,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18744_273,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18745_274,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18746_275,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18747_276,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18748_277,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18749_278,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18750_279,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18751_280,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18752_281,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18753_282,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18754_283,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18755_284,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18756_285,axiom,
    ( X1 != X2
    | esk499_4(X1,X3,X4,X5) = esk499_4(X2,X3,X4,X5) ) ).

cnf(i_0_18757_286,axiom,
    ( X1 != X2
    | esk499_4(X3,X1,X4,X5) = esk499_4(X3,X2,X4,X5) ) ).

cnf(i_0_18758_287,axiom,
    ( X1 != X2
    | esk499_4(X3,X4,X1,X5) = esk499_4(X3,X4,X2,X5) ) ).

cnf(i_0_18759_288,axiom,
    ( X1 != X2
    | esk499_4(X3,X4,X5,X1) = esk499_4(X3,X4,X5,X2) ) ).

cnf(i_0_18760_289,axiom,
    ( X1 != X2
    | esk498_4(X1,X3,X4,X5) = esk498_4(X2,X3,X4,X5) ) ).

cnf(i_0_18761_290,axiom,
    ( X1 != X2
    | esk498_4(X3,X1,X4,X5) = esk498_4(X3,X2,X4,X5) ) ).

cnf(i_0_18762_291,axiom,
    ( X1 != X2
    | esk498_4(X3,X4,X1,X5) = esk498_4(X3,X4,X2,X5) ) ).

cnf(i_0_18763_292,axiom,
    ( X1 != X2
    | esk498_4(X3,X4,X5,X1) = esk498_4(X3,X4,X5,X2) ) ).

cnf(i_0_18764_293,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_18765_294,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_18766_295,axiom,
    ( X1 != X2
    | esk348_3(X1,X3,X4) = esk348_3(X2,X3,X4) ) ).

cnf(i_0_18767_296,axiom,
    ( X1 != X2
    | esk348_3(X3,X1,X4) = esk348_3(X3,X2,X4) ) ).

cnf(i_0_18768_297,axiom,
    ( X1 != X2
    | esk348_3(X3,X4,X1) = esk348_3(X3,X4,X2) ) ).

cnf(i_0_18769_298,axiom,
    ( X1 != X2
    | esk347_3(X1,X3,X4) = esk347_3(X2,X3,X4) ) ).

cnf(i_0_18770_299,axiom,
    ( X1 != X2
    | esk347_3(X3,X1,X4) = esk347_3(X3,X2,X4) ) ).

cnf(i_0_18771_300,axiom,
    ( X1 != X2
    | esk347_3(X3,X4,X1) = esk347_3(X3,X4,X2) ) ).

cnf(i_0_18772_301,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18773_302,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18774_303,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X1,X3,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18775_304,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X1,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18776_305,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X1,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18777_306,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X1,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18778_307,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X1) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18779_308,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18780_309,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18781_310,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18782_311,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18783_312,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18784_313,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18785_314,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__map(X2,X3,X4,X5) ) ).

cnf(i_0_18786_315,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__map(X3,X2,X4,X5) ) ).

cnf(i_0_18787_316,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__map(X3,X4,X2,X5) ) ).

cnf(i_0_18788_317,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__map(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__map(X3,X4,X5,X2) ) ).

cnf(i_0_18789_318,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18790_319,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18791_320,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18792_321,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__map(X2,X3,X4,X5) ) ).

cnf(i_0_18793_322,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__map(X3,X2,X4,X5) ) ).

cnf(i_0_18794_323,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__map(X3,X4,X2,X5) ) ).

cnf(i_0_18795_324,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__map(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__map(X3,X4,X5,X2) ) ).

cnf(i_0_18796_325,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18797_326,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18798_327,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18799_328,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18800_329,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18801_330,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18802_331,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18803_332,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18804_333,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18805_334,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18806_335,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18807_336,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18808_337,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18809_338,axiom,
    ( X1 != X2
    | esk74_5(X1,X3,X4,X5,X6) = esk74_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18810_339,axiom,
    ( X1 != X2
    | esk74_5(X3,X1,X4,X5,X6) = esk74_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18811_340,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X1,X5,X6) = esk74_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18812_341,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X5,X1,X6) = esk74_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18813_342,axiom,
    ( X1 != X2
    | esk74_5(X3,X4,X5,X6,X1) = esk74_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18814_343,axiom,
    ( X1 != X2
    | esk344_3(X1,X3,X4) = esk344_3(X2,X3,X4) ) ).

cnf(i_0_18815_344,axiom,
    ( X1 != X2
    | esk344_3(X3,X1,X4) = esk344_3(X3,X2,X4) ) ).

cnf(i_0_18816_345,axiom,
    ( X1 != X2
    | esk344_3(X3,X4,X1) = esk344_3(X3,X4,X2) ) ).

cnf(i_0_18817_346,axiom,
    ( X1 != X2
    | esk343_3(X1,X3,X4) = esk343_3(X2,X3,X4) ) ).

cnf(i_0_18818_347,axiom,
    ( X1 != X2
    | esk343_3(X3,X1,X4) = esk343_3(X3,X2,X4) ) ).

cnf(i_0_18819_348,axiom,
    ( X1 != X2
    | esk343_3(X3,X4,X1) = esk343_3(X3,X4,X2) ) ).

cnf(i_0_18820_349,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18821_350,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18822_351,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18823_352,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18824_353,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18825_354,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18826_355,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18827_356,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18828_357,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18829_358,axiom,
    ( X1 != X2
    | esk453_2(X1,X3) = esk453_2(X2,X3) ) ).

cnf(i_0_18830_359,axiom,
    ( X1 != X2
    | esk453_2(X3,X1) = esk453_2(X3,X2) ) ).

cnf(i_0_18831_360,axiom,
    ( X1 != X2
    | esk454_2(X1,X3) = esk454_2(X2,X3) ) ).

cnf(i_0_18832_361,axiom,
    ( X1 != X2
    | esk454_2(X3,X1) = esk454_2(X3,X2) ) ).

cnf(i_0_18833_362,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18834_363,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18835_364,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18836_365,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18837_366,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18838_367,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18839_368,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18840_369,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X1,X3,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18841_370,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X1,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18842_371,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X1,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18843_372,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X1,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18844_373,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X6,X1,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18845_374,axiom,
    ( X1 != X2
    | c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X1) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18846_375,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18847_376,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18848_377,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18849_378,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18850_379,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18851_380,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18852_381,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18853_382,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18854_383,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18855_384,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18856_385,axiom,
    ( X1 != X2
    | esk277_3(X1,X3,X4) = esk277_3(X2,X3,X4) ) ).

cnf(i_0_18857_386,axiom,
    ( X1 != X2
    | esk277_3(X3,X1,X4) = esk277_3(X3,X2,X4) ) ).

cnf(i_0_18858_387,axiom,
    ( X1 != X2
    | esk277_3(X3,X4,X1) = esk277_3(X3,X4,X2) ) ).

cnf(i_0_18859_388,axiom,
    ( X1 != X2
    | esk528_3(X1,X3,X4) = esk528_3(X2,X3,X4) ) ).

cnf(i_0_18860_389,axiom,
    ( X1 != X2
    | esk528_3(X3,X1,X4) = esk528_3(X3,X2,X4) ) ).

cnf(i_0_18861_390,axiom,
    ( X1 != X2
    | esk528_3(X3,X4,X1) = esk528_3(X3,X4,X2) ) ).

cnf(i_0_18862_391,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18863_392,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18864_393,axiom,
    ( X1 != X2
    | esk494_4(X1,X3,X4,X5) = esk494_4(X2,X3,X4,X5) ) ).

cnf(i_0_18865_394,axiom,
    ( X1 != X2
    | esk494_4(X3,X1,X4,X5) = esk494_4(X3,X2,X4,X5) ) ).

cnf(i_0_18866_395,axiom,
    ( X1 != X2
    | esk494_4(X3,X4,X1,X5) = esk494_4(X3,X4,X2,X5) ) ).

cnf(i_0_18867_396,axiom,
    ( X1 != X2
    | esk494_4(X3,X4,X5,X1) = esk494_4(X3,X4,X5,X2) ) ).

cnf(i_0_18868_397,axiom,
    ( X1 != X2
    | esk486_4(X1,X3,X4,X5) = esk486_4(X2,X3,X4,X5) ) ).

cnf(i_0_18869_398,axiom,
    ( X1 != X2
    | esk486_4(X3,X1,X4,X5) = esk486_4(X3,X2,X4,X5) ) ).

cnf(i_0_18870_399,axiom,
    ( X1 != X2
    | esk486_4(X3,X4,X1,X5) = esk486_4(X3,X4,X2,X5) ) ).

cnf(i_0_18871_400,axiom,
    ( X1 != X2
    | esk486_4(X3,X4,X5,X1) = esk486_4(X3,X4,X5,X2) ) ).

cnf(i_0_18872_401,axiom,
    ( X1 != X2
    | esk128_4(X1,X3,X4,X5) = esk128_4(X2,X3,X4,X5) ) ).

cnf(i_0_18873_402,axiom,
    ( X1 != X2
    | esk128_4(X3,X1,X4,X5) = esk128_4(X3,X2,X4,X5) ) ).

cnf(i_0_18874_403,axiom,
    ( X1 != X2
    | esk128_4(X3,X4,X1,X5) = esk128_4(X3,X4,X2,X5) ) ).

cnf(i_0_18875_404,axiom,
    ( X1 != X2
    | esk128_4(X3,X4,X5,X1) = esk128_4(X3,X4,X5,X2) ) ).

cnf(i_0_18876_405,axiom,
    ( X1 != X2
    | esk130_4(X1,X3,X4,X5) = esk130_4(X2,X3,X4,X5) ) ).

cnf(i_0_18877_406,axiom,
    ( X1 != X2
    | esk130_4(X3,X1,X4,X5) = esk130_4(X3,X2,X4,X5) ) ).

cnf(i_0_18878_407,axiom,
    ( X1 != X2
    | esk130_4(X3,X4,X1,X5) = esk130_4(X3,X4,X2,X5) ) ).

cnf(i_0_18879_408,axiom,
    ( X1 != X2
    | esk130_4(X3,X4,X5,X1) = esk130_4(X3,X4,X5,X2) ) ).

cnf(i_0_18880_409,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18881_410,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18882_411,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18883_412,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18884_413,axiom,
    ( X1 != X2
    | esk21_4(X1,X3,X4,X5) = esk21_4(X2,X3,X4,X5) ) ).

cnf(i_0_18885_414,axiom,
    ( X1 != X2
    | esk21_4(X3,X1,X4,X5) = esk21_4(X3,X2,X4,X5) ) ).

cnf(i_0_18886_415,axiom,
    ( X1 != X2
    | esk21_4(X3,X4,X1,X5) = esk21_4(X3,X4,X2,X5) ) ).

cnf(i_0_18887_416,axiom,
    ( X1 != X2
    | esk21_4(X3,X4,X5,X1) = esk21_4(X3,X4,X5,X2) ) ).

cnf(i_0_18888_417,axiom,
    ( X1 != X2
    | esk20_4(X1,X3,X4,X5) = esk20_4(X2,X3,X4,X5) ) ).

cnf(i_0_18889_418,axiom,
    ( X1 != X2
    | esk20_4(X3,X1,X4,X5) = esk20_4(X3,X2,X4,X5) ) ).

cnf(i_0_18890_419,axiom,
    ( X1 != X2
    | esk20_4(X3,X4,X1,X5) = esk20_4(X3,X4,X2,X5) ) ).

cnf(i_0_18891_420,axiom,
    ( X1 != X2
    | esk20_4(X3,X4,X5,X1) = esk20_4(X3,X4,X5,X2) ) ).

cnf(i_0_18892_421,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18893_422,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18894_423,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18895_424,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18896_425,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18897_426,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18898_427,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18899_428,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18900_429,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18901_430,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18902_431,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18903_432,axiom,
    ( X1 != X2
    | esk230_3(X1,X3,X4) = esk230_3(X2,X3,X4) ) ).

cnf(i_0_18904_433,axiom,
    ( X1 != X2
    | esk230_3(X3,X1,X4) = esk230_3(X3,X2,X4) ) ).

cnf(i_0_18905_434,axiom,
    ( X1 != X2
    | esk230_3(X3,X4,X1) = esk230_3(X3,X4,X2) ) ).

cnf(i_0_18906_435,axiom,
    ( X1 != X2
    | esk231_3(X1,X3,X4) = esk231_3(X2,X3,X4) ) ).

cnf(i_0_18907_436,axiom,
    ( X1 != X2
    | esk231_3(X3,X1,X4) = esk231_3(X3,X2,X4) ) ).

cnf(i_0_18908_437,axiom,
    ( X1 != X2
    | esk231_3(X3,X4,X1) = esk231_3(X3,X4,X2) ) ).

cnf(i_0_18909_438,axiom,
    ( X1 != X2
    | esk73_4(X1,X3,X4,X5) = esk73_4(X2,X3,X4,X5) ) ).

cnf(i_0_18910_439,axiom,
    ( X1 != X2
    | esk73_4(X3,X1,X4,X5) = esk73_4(X3,X2,X4,X5) ) ).

cnf(i_0_18911_440,axiom,
    ( X1 != X2
    | esk73_4(X3,X4,X1,X5) = esk73_4(X3,X4,X2,X5) ) ).

cnf(i_0_18912_441,axiom,
    ( X1 != X2
    | esk73_4(X3,X4,X5,X1) = esk73_4(X3,X4,X5,X2) ) ).

cnf(i_0_18913_442,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X1,X3,X4,X5) = c_List_Olinorder__class_Osort__key(X2,X3,X4,X5) ) ).

cnf(i_0_18914_443,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X1,X4,X5) = c_List_Olinorder__class_Osort__key(X3,X2,X4,X5) ) ).

cnf(i_0_18915_444,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X4,X1,X5) = c_List_Olinorder__class_Osort__key(X3,X4,X2,X5) ) ).

cnf(i_0_18916_445,axiom,
    ( X1 != X2
    | c_List_Olinorder__class_Osort__key(X3,X4,X5,X1) = c_List_Olinorder__class_Osort__key(X3,X4,X5,X2) ) ).

cnf(i_0_18917_446,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18918_447,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18919_448,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18920_449,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18921_450,axiom,
    ( X1 != X2
    | esk228_3(X1,X3,X4) = esk228_3(X2,X3,X4) ) ).

cnf(i_0_18922_451,axiom,
    ( X1 != X2
    | esk228_3(X3,X1,X4) = esk228_3(X3,X2,X4) ) ).

cnf(i_0_18923_452,axiom,
    ( X1 != X2
    | esk228_3(X3,X4,X1) = esk228_3(X3,X4,X2) ) ).

cnf(i_0_18924_453,axiom,
    ( X1 != X2
    | esk227_3(X1,X3,X4) = esk227_3(X2,X3,X4) ) ).

cnf(i_0_18925_454,axiom,
    ( X1 != X2
    | esk227_3(X3,X1,X4) = esk227_3(X3,X2,X4) ) ).

cnf(i_0_18926_455,axiom,
    ( X1 != X2
    | esk227_3(X3,X4,X1) = esk227_3(X3,X4,X2) ) ).

cnf(i_0_18927_456,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_18928_457,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_18929_458,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_18930_459,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_18931_460,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18932_461,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18933_462,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18934_463,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18935_464,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18936_465,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18937_466,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18938_467,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18939_468,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18940_469,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18941_470,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18942_471,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18943_472,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18944_473,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18945_474,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18946_475,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18947_476,axiom,
    ( X1 != X2
    | esk519_2(X1,X3) = esk519_2(X2,X3) ) ).

cnf(i_0_18948_477,axiom,
    ( X1 != X2
    | esk519_2(X3,X1) = esk519_2(X3,X2) ) ).

cnf(i_0_18949_478,axiom,
    ( X1 != X2
    | esk518_2(X1,X3) = esk518_2(X2,X3) ) ).

cnf(i_0_18950_479,axiom,
    ( X1 != X2
    | esk518_2(X3,X1) = esk518_2(X3,X2) ) ).

cnf(i_0_18951_480,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18952_481,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18953_482,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18954_483,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18955_484,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18956_485,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18957_486,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18958_487,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18959_488,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18960_489,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18961_490,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18962_491,axiom,
    ( X1 != X2
    | c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18963_492,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18964_493,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18965_494,axiom,
    ( X1 != X2
    | esk137_3(X1,X3,X4) = esk137_3(X2,X3,X4) ) ).

cnf(i_0_18966_495,axiom,
    ( X1 != X2
    | esk137_3(X3,X1,X4) = esk137_3(X3,X2,X4) ) ).

cnf(i_0_18967_496,axiom,
    ( X1 != X2
    | esk137_3(X3,X4,X1) = esk137_3(X3,X4,X2) ) ).

cnf(i_0_18968_497,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18969_498,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18970_499,axiom,
    ( X1 != X2
    | esk495_4(X1,X3,X4,X5) = esk495_4(X2,X3,X4,X5) ) ).

cnf(i_0_18971_500,axiom,
    ( X1 != X2
    | esk495_4(X3,X1,X4,X5) = esk495_4(X3,X2,X4,X5) ) ).

cnf(i_0_18972_501,axiom,
    ( X1 != X2
    | esk495_4(X3,X4,X1,X5) = esk495_4(X3,X4,X2,X5) ) ).

cnf(i_0_18973_502,axiom,
    ( X1 != X2
    | esk495_4(X3,X4,X5,X1) = esk495_4(X3,X4,X5,X2) ) ).

cnf(i_0_18974_503,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18975_504,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18976_505,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18977_506,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18978_507,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18979_508,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18980_509,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18981_510,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18982_511,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18983_512,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18984_513,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18985_514,axiom,
    ( X1 != X2
    | esk328_2(X1,X3) = esk328_2(X2,X3) ) ).

cnf(i_0_18986_515,axiom,
    ( X1 != X2
    | esk328_2(X3,X1) = esk328_2(X3,X2) ) ).

cnf(i_0_18987_516,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18988_517,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18989_518,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18990_519,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18991_520,axiom,
    ( X1 != X2
    | esk427_2(X1,X3) = esk427_2(X2,X3) ) ).

cnf(i_0_18992_521,axiom,
    ( X1 != X2
    | esk427_2(X3,X1) = esk427_2(X3,X2) ) ).

cnf(i_0_18993_522,axiom,
    ( X1 != X2
    | esk428_2(X1,X3) = esk428_2(X2,X3) ) ).

cnf(i_0_18994_523,axiom,
    ( X1 != X2
    | esk428_2(X3,X1) = esk428_2(X3,X2) ) ).

cnf(i_0_18995_524,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X3,X4,X5) ) ).

cnf(i_0_18996_525,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X2,X4,X5) ) ).

cnf(i_0_18997_526,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X2,X5) ) ).

cnf(i_0_18998_527,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X2) ) ).

cnf(i_0_18999_528,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X1,X3,X4,X5) = c_Lazy__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_19000_529,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X1,X4,X5) = c_Lazy__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_19001_530,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X1,X5) = c_Lazy__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_19002_531,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X5,X1) = c_Lazy__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_19003_532,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_19004_533,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_19005_534,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_19006_535,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_19007_536,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_19008_537,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_19009_538,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_19010_539,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_19011_540,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_19012_541,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).

cnf(i_0_19013_542,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).

cnf(i_0_19014_543,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).

cnf(i_0_19015_544,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).

cnf(i_0_19016_545,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_19017_546,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_19018_547,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_19019_548,axiom,
    ( X1 != X2
    | esk415_2(X1,X3) = esk415_2(X2,X3) ) ).

cnf(i_0_19020_549,axiom,
    ( X1 != X2
    | esk415_2(X3,X1) = esk415_2(X3,X2) ) ).

cnf(i_0_19021_550,axiom,
    ( X1 != X2
    | esk127_3(X1,X3,X4) = esk127_3(X2,X3,X4) ) ).

cnf(i_0_19022_551,axiom,
    ( X1 != X2
    | esk127_3(X3,X1,X4) = esk127_3(X3,X2,X4) ) ).

cnf(i_0_19023_552,axiom,
    ( X1 != X2
    | esk127_3(X3,X4,X1) = esk127_3(X3,X4,X2) ) ).

cnf(i_0_19024_553,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_19025_554,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_19026_555,axiom,
    ( X1 != X2
    | esk129_3(X1,X3,X4) = esk129_3(X2,X3,X4) ) ).

cnf(i_0_19027_556,axiom,
    ( X1 != X2
    | esk129_3(X3,X1,X4) = esk129_3(X3,X2,X4) ) ).

cnf(i_0_19028_557,axiom,
    ( X1 != X2
    | esk129_3(X3,X4,X1) = esk129_3(X3,X4,X2) ) ).

cnf(i_0_19029_558,axiom,
    ( X1 != X2
    | esk90_3(X1,X3,X4) = esk90_3(X2,X3,X4) ) ).

cnf(i_0_19030_559,axiom,
    ( X1 != X2
    | esk90_3(X3,X1,X4) = esk90_3(X3,X2,X4) ) ).

cnf(i_0_19031_560,axiom,
    ( X1 != X2
    | esk90_3(X3,X4,X1) = esk90_3(X3,X4,X2) ) ).

cnf(i_0_19032_561,axiom,
    ( X1 != X2
    | esk89_3(X1,X3,X4) = esk89_3(X2,X3,X4) ) ).

cnf(i_0_19033_562,axiom,
    ( X1 != X2
    | esk89_3(X3,X1,X4) = esk89_3(X3,X2,X4) ) ).

cnf(i_0_19034_563,axiom,
    ( X1 != X2
    | esk89_3(X3,X4,X1) = esk89_3(X3,X4,X2) ) ).

cnf(i_0_19035_564,axiom,
    ( X1 != X2
    | esk493_3(X1,X3,X4) = esk493_3(X2,X3,X4) ) ).

cnf(i_0_19036_565,axiom,
    ( X1 != X2
    | esk493_3(X3,X1,X4) = esk493_3(X3,X2,X4) ) ).

cnf(i_0_19037_566,axiom,
    ( X1 != X2
    | esk493_3(X3,X4,X1) = esk493_3(X3,X4,X2) ) ).

cnf(i_0_19038_567,axiom,
    ( X1 != X2
    | esk485_3(X1,X3,X4) = esk485_3(X2,X3,X4) ) ).

cnf(i_0_19039_568,axiom,
    ( X1 != X2
    | esk485_3(X3,X1,X4) = esk485_3(X3,X2,X4) ) ).

cnf(i_0_19040_569,axiom,
    ( X1 != X2
    | esk485_3(X3,X4,X1) = esk485_3(X3,X4,X2) ) ).

cnf(i_0_19041_570,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X1,X3,X4,X5) = c_Quotient_OBabs(X2,X3,X4,X5) ) ).

cnf(i_0_19042_571,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X1,X4,X5) = c_Quotient_OBabs(X3,X2,X4,X5) ) ).

cnf(i_0_19043_572,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X1,X5) = c_Quotient_OBabs(X3,X4,X2,X5) ) ).

cnf(i_0_19044_573,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X5,X1) = c_Quotient_OBabs(X3,X4,X5,X2) ) ).

cnf(i_0_19045_574,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X1,X3) = c_Lazy__Sequence_Oflat(X2,X3) ) ).

cnf(i_0_19046_575,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X3,X1) = c_Lazy__Sequence_Oflat(X3,X2) ) ).

cnf(i_0_19047_576,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19048_577,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19049_578,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19050_579,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).

cnf(i_0_19051_580,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).

cnf(i_0_19052_581,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).

cnf(i_0_19053_582,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).

cnf(i_0_19054_583,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).

cnf(i_0_19055_584,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).

cnf(i_0_19056_585,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).

cnf(i_0_19057_586,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).

cnf(i_0_19058_587,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19059_588,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19060_589,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19061_590,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19062_591,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19063_592,axiom,
    ( X1 != X2
    | c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).

cnf(i_0_19064_593,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19065_594,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19066_595,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19067_596,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19068_597,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19069_598,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19070_599,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X3,X4,X5) ) ).

cnf(i_0_19071_600,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X4,X5) ) ).

cnf(i_0_19072_601,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X2,X5) ) ).

cnf(i_0_19073_602,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X2) ) ).

cnf(i_0_19074_603,axiom,
    ( X1 != X2
    | esk433_2(X1,X3) = esk433_2(X2,X3) ) ).

cnf(i_0_19075_604,axiom,
    ( X1 != X2
    | esk433_2(X3,X1) = esk433_2(X3,X2) ) ).

cnf(i_0_19076_605,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19077_606,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19078_607,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19079_608,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19080_609,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_19081_610,axiom,
    ( X1 != X2
    | esk402_2(X1,X3) = esk402_2(X2,X3) ) ).

cnf(i_0_19082_611,axiom,
    ( X1 != X2
    | esk402_2(X3,X1) = esk402_2(X3,X2) ) ).

cnf(i_0_19083_612,axiom,
    ( X1 != X2
    | esk401_2(X1,X3) = esk401_2(X2,X3) ) ).

cnf(i_0_19084_613,axiom,
    ( X1 != X2
    | esk401_2(X3,X1) = esk401_2(X3,X2) ) ).

cnf(i_0_19085_614,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19086_615,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19087_616,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19088_617,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19089_618,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19090_619,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19091_620,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19092_621,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19093_622,axiom,
    ( X1 != X2
    | esk496_3(X1,X3,X4) = esk496_3(X2,X3,X4) ) ).

cnf(i_0_19094_623,axiom,
    ( X1 != X2
    | esk496_3(X3,X1,X4) = esk496_3(X3,X2,X4) ) ).

cnf(i_0_19095_624,axiom,
    ( X1 != X2
    | esk496_3(X3,X4,X1) = esk496_3(X3,X4,X2) ) ).

cnf(i_0_19096_625,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19097_626,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19098_627,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).

cnf(i_0_19099_628,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).

cnf(i_0_19100_629,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).

cnf(i_0_19101_630,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19102_631,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19103_632,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19104_633,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19105_634,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).

cnf(i_0_19106_635,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).

cnf(i_0_19107_636,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).

cnf(i_0_19108_637,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19109_638,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19110_639,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19111_640,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19112_641,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19113_642,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19114_643,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19115_644,axiom,
    ( X1 != X2
    | esk460_2(X1,X3) = esk460_2(X2,X3) ) ).

cnf(i_0_19116_645,axiom,
    ( X1 != X2
    | esk460_2(X3,X1) = esk460_2(X3,X2) ) ).

cnf(i_0_19117_646,axiom,
    ( X1 != X2
    | esk397_1(X1) = esk397_1(X2) ) ).

cnf(i_0_19118_647,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19119_648,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19120_649,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19121_650,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19122_651,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19123_652,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19124_653,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19125_654,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19126_655,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19127_656,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19128_657,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19129_658,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19130_659,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19131_660,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19132_661,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19133_662,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19134_663,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19135_664,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19136_665,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19137_666,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19138_667,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19139_668,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19140_669,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19141_670,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19142_671,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19143_672,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19144_673,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19145_674,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19146_675,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19147_676,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19148_677,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19149_678,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19150_679,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19151_680,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19152_681,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19153_682,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19154_683,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19155_684,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19156_685,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19157_686,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19158_687,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19159_688,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19160_689,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19161_690,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19162_691,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19163_692,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19164_693,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19165_694,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19166_695,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19167_696,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19168_697,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19169_698,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19170_699,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19171_700,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19172_701,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19173_702,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19174_703,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19175_704,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19176_705,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19177_706,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19178_707,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19179_708,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19180_709,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19181_710,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19182_711,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19183_712,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19184_713,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19185_714,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19186_715,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19187_716,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19188_717,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19189_718,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19190_719,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19191_720,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19192_721,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19193_722,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19194_723,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19195_724,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19196_725,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19197_726,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19198_727,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19199_728,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19200_729,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19201_730,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19202_731,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19203_732,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
    | c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19204_733,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19205_734,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19206_735,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19207_736,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19208_737,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19209_738,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19210_739,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19211_740,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19212_741,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X1,X3,X4,X5,X6)
    | c_Finite__Set_Ofolding__image(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19213_742,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X1,X4,X5,X6)
    | c_Finite__Set_Ofolding__image(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19214_743,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X1,X5,X6)
    | c_Finite__Set_Ofolding__image(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19215_744,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X1,X6)
    | c_Finite__Set_Ofolding__image(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19216_745,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X1)
    | c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19217_746,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19218_747,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19219_748,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19220_749,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19221_750,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19222_751,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
    | c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19223_752,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19224_753,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19225_754,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19226_755,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19227_756,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19228_757,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19229_758,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19230_759,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19231_760,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19232_761,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19233_762,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19234_763,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19235_764,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19236_765,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19237_766,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19238_767,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19239_768,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19240_769,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19241_770,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19242_771,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19243_772,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19244_773,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19245_774,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19246_775,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19247_776,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19248_777,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19249_778,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19250_779,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19251_780,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19252_781,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19253_782,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19254_783,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19255_784,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19256_785,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19257_786,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19258_787,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19259_788,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19260_789,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19261_790,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19262_791,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19263_792,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19264_793,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19265_794,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19266_795,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19267_796,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19268_797,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19269_798,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19270_799,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19271_800,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19272_801,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19273_802,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19274_803,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19275_804,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19276_805,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19277_806,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19278_807,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19279_808,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19280_809,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19281_810,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19282_811,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19283_812,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19284_813,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19285_814,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19286_815,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19287_816,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19288_817,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19289_818,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19290_819,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19291_820,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19292_821,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19293_822,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19294_823,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19295_824,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19296_825,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19297_826,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19298_827,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19299_828,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19300_829,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19301_830,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19302_831,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19303_832,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19304_833,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19305_834,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19306_835,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19307_836,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19308_837,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19309_838,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19310_839,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19311_840,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19312_841,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19313_842,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19314_843,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19315_844,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19316_845,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19317_846,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19318_847,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).

cnf(i_0_19319_848,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).

cnf(i_0_19320_849,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).

cnf(i_0_19321_850,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19322_851,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19323_852,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19324_853,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19325_854,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19326_855,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19327_856,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19328_857,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19329_858,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19330_859,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19331_860,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19332_861,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_19333_862,axiom,
    ( X1 != X2
    | ~ class_Rings_Odvd(X1)
    | class_Rings_Odvd(X2) ) ).

cnf(i_0_19334_863,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19335_864,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19336_865,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19337_866,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19338_867,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19339_868,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19340_869,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19341_870,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19342_871,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19343_872,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19344_873,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19345_874,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19346_875,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19347_876,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19348_877,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19349_878,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19350_879,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19351_880,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19352_881,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19353_882,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19354_883,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19355_884,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19356_885,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19357_886,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19358_887,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19359_888,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19360_889,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19361_890,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19362_891,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19363_892,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X1,X3,X4,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19364_893,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X1,X4,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19365_894,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X1,X5,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19366_895,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X1,X6)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19367_896,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X1)
    | c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19368_897,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19369_898,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19370_899,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19371_900,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19372_901,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19373_902,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19374_903,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19375_904,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19376_905,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19377_906,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19378_907,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19379_908,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X1,X3,X4)
    | c_List_Oall__interval__nat(X2,X3,X4) ) ).

cnf(i_0_19380_909,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X1,X4)
    | c_List_Oall__interval__nat(X3,X2,X4) ) ).

cnf(i_0_19381_910,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X4,X1)
    | c_List_Oall__interval__nat(X3,X4,X2) ) ).

cnf(i_0_19382_911,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19383_912,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19384_913,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19385_914,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19386_915,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19387_916,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19388_917,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19389_918,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19390_919,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19391_920,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19392_921,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19393_922,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19394_923,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19395_924,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19396,plain,
    ( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | X4 = X4
    | ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X3,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk265_7(X4,X4,X6,X5,X3,X2,X1)),esk266_7(X4,X4,X6,X5,X3,X2,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
    inference(equality_inference,[],[11148]) ).

cnf(i_0_19397,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ class_Groups_Ocomm__monoid__mult(X5)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X5),X6),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X7),X4)
    | hBOOL(hAPP(hAPP(c_member(X1),esk332_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11164]) ).

cnf(i_0_19398,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ class_Groups_Ocomm__monoid__add(X5)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X5),X6),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X7),X4)
    | hBOOL(hAPP(hAPP(c_member(X1),esk35_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11165]) ).

cnf(i_0_19399,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),esk395_4(X3,X2,X2,X1))) ),
    inference(equality_inference,[],[11189]) ).

cnf(i_0_19400,plain,
    ( X1 = X1
    | ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
    | ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
    | hBOOL(hAPP(hAPP(c_member(X2),esk266_7(X1,X1,X6,X5,X4,X3,X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
    inference(equality_inference,[],[11247]) ).

cnf(i_0_19401,plain,
    ( X1 = X1
    | ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
    | ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
    | hBOOL(hAPP(hAPP(c_member(X2),esk265_7(X1,X1,X6,X5,X4,X3,X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
    inference(equality_inference,[],[11248]) ).

cnf(i_0_19402,plain,
    ( ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
    | hAPP(hAPP(X5,X6),X7) = hAPP(hAPP(X5,X6),X7)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(equality_inference,[],[11271]) ).

cnf(i_0_19403,plain,
    X1 = X1,
    inference(equality_inference,[],[11292]) ).

cnf(i_0_19404,plain,
    ( X1 = X1
    | ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
    | ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
    | hAPP(X6,esk265_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk266_7(X1,X1,X6,X5,X4,X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
    inference(equality_inference,[],[11305]) ).

cnf(i_0_19405,plain,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X5,esk165_6(X4,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3),X5,X3,X2,X1))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))) ),
    inference(equality_inference,[],[11366]) ).

cnf(i_0_19406,plain,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
    | hBOOL(hAPP(hAPP(c_member(X2),esk165_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
    inference(equality_inference,[],[11430]) ).

cnf(i_0_19407,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk459_5(X2,X3,X1,X3,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk459_5(X2,X3,X1,X3,X1)))) ),
    inference(equality_inference,[],[11432]) ).

cnf(i_0_19408,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk424_5(X3,X3,X2,X1,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk424_5(X3,X3,X2,X1,X1)))) ),
    inference(equality_inference,[],[11433]) ).

cnf(i_0_19409,plain,
    ( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk434_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
    inference(equality_inference,[],[11442]) ).

cnf(i_0_19410,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk386_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk386_4(X3,X2,X2,X1)))),X3)) ),
    inference(equality_inference,[],[11454]) ).

cnf(i_0_19411,plain,
    ( ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),X5),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),X5),X3) ),
    inference(equality_inference,[],[11497]) ).

cnf(i_0_19412,plain,
    hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
    inference(equality_inference,[],[11505]) ).

cnf(i_0_19413,plain,
    hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
    inference(equality_inference,[],[11506]) ).

cnf(i_0_19414,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    inference(equality_inference,[],[11529]) ).

cnf(i_0_19415,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5) = hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5),
    inference(equality_inference,[],[11579]) ).

cnf(i_0_19416,plain,
    hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5) = hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5),
    inference(equality_inference,[],[11580]) ).

cnf(i_0_19417,plain,
    ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X2)),
    inference(equality_inference,[],[11600]) ).

cnf(i_0_19418,plain,
    ( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))
    | ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
    inference(equality_inference,[],[11664]) ).

cnf(i_0_19419,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | X2 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(equality_inference,[],[11667]) ).

cnf(i_0_19420,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))) ),
    inference(equality_inference,[],[11764]) ).

cnf(i_0_19421,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk425_5(X2,X3,X3,X1,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
    inference(equality_inference,[],[11765]) ).

cnf(i_0_19422,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk423_5(X3,X3,X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
    inference(equality_inference,[],[11766]) ).

cnf(i_0_19423,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X5)) ),
    inference(equality_inference,[],[11782]) ).

cnf(i_0_19424,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_5(X2,X3,X1,X3,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11787]) ).

cnf(i_0_19425,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk424_5(X3,X3,X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11788]) ).

cnf(i_0_19426,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)) ),
    inference(equality_inference,[],[11832]) ).

cnf(i_0_19427,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk408_5(X2,X3,X2,X3,X1)),X2) = X2
    | X2 = hAPP(hAPP(c_List_Oappend(X1),esk409_5(X2,X3,X2,X3,X1)),X2) ),
    inference(equality_inference,[],[11873]) ).

cnf(i_0_19428,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2),esk425_5(X2,X3,X3,X1,X1))) ),
    inference(equality_inference,[],[11879]) ).

cnf(i_0_19429,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2),esk423_5(X3,X3,X2,X1,X1))) ),
    inference(equality_inference,[],[11880]) ).

cnf(i_0_19430,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),X4) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk24_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
    inference(equality_inference,[],[11892]) ).

cnf(i_0_19431,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X4))),X3)) ),
    inference(equality_inference,[],[11920]) ).

cnf(i_0_19432,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)) ),
    inference(equality_inference,[],[11932]) ).

cnf(i_0_19433,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[11933]) ).

cnf(i_0_19434,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[11934]) ).

cnf(i_0_19435,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[11935]) ).

cnf(i_0_19436,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
    inference(equality_inference,[],[11970]) ).

cnf(i_0_19437,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk409_5(X3,X2,X3,X2,X1)) = X2
    | hAPP(hAPP(c_List_Oappend(X1),esk408_5(X3,X2,X3,X2,X1)),X3) = X3 ),
    inference(equality_inference,[],[11994]) ).

cnf(i_0_19438,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk408_5(X3,X1,X3,X1,X2))
    | X3 = hAPP(hAPP(c_List_Oappend(X2),esk409_5(X3,X1,X3,X1,X2)),X3) ),
    inference(equality_inference,[],[11995]) ).

cnf(i_0_19439,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))),c_Int_Ointrel)),
    inference(equality_inference,[],[12027]) ).

cnf(i_0_19440,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X4),X3))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))) ),
    inference(equality_inference,[],[12032]) ).

cnf(i_0_19441,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))) ),
    inference(equality_inference,[],[12033]) ).

cnf(i_0_19442,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))) ),
    inference(equality_inference,[],[12034]) ).

cnf(i_0_19443,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olexord(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))) ),
    inference(equality_inference,[],[12035]) ).

cnf(i_0_19444,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olex(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olex(X1,X5))) ),
    inference(equality_inference,[],[12036]) ).

cnf(i_0_19445,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5)) ),
    inference(equality_inference,[],[12057]) ).

cnf(i_0_19446,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olex(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)) ),
    inference(equality_inference,[],[12103]) ).

cnf(i_0_19447,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)) ),
    inference(equality_inference,[],[12110]) ).

cnf(i_0_19448,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[12163]) ).

cnf(i_0_19449,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3))),
    inference(equality_inference,[],[12175]) ).

cnf(i_0_19450,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[12180]) ).

cnf(i_0_19451,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[12181]) ).

cnf(i_0_19452,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X1)),c_Int_Ointrel)),
    inference(equality_inference,[],[12182]) ).

cnf(i_0_19453,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ class_Groups_Ocomm__monoid__add(X2)
    | ~ class_Groups_Ocomm__monoid__mult(X2)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X2),X3),X1) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X2),X4),X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk209_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12195]) ).

cnf(i_0_19454,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ class_Groups_Ocomm__monoid__add(X2)
    | ~ class_Groups_Ocomm__monoid__mult(X2)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2),X3),X1) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2),X4),X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk218_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12196]) ).

cnf(i_0_19455,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk408_5(X3,X1,X3,X1,X2))
    | hAPP(hAPP(c_List_Oappend(X2),X1),esk409_5(X3,X1,X3,X1,X2)) = X1 ),
    inference(equality_inference,[],[12199]) ).

cnf(i_0_19456,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk395_4(X3,X2,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)))) ),
    inference(equality_inference,[],[12202]) ).

cnf(i_0_19457,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X2)) ),
    inference(equality_inference,[],[12292]) ).

cnf(i_0_19458,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olex(X1,X3))) ),
    inference(equality_inference,[],[12295]) ).

cnf(i_0_19459,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_List_Omeasures(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X3)))) ),
    inference(equality_inference,[],[12338]) ).

cnf(i_0_19460,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk386_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[12343]) ).

cnf(i_0_19461,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(equality_inference,[],[12384]) ).

cnf(i_0_19462,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ c_List_Olist__all2(X1,X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4),hAPP(hAPP(c_List_Oappend(X1),X3),X5)) ),
    inference(equality_inference,[],[12429]) ).

cnf(i_0_19463,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X4)
    | ~ c_List_Olist__all2(X1,X1,X2,hAPP(hAPP(c_List_Oappend(X1),X5),X3),hAPP(hAPP(c_List_Oappend(X1),X5),X4)) ),
    inference(equality_inference,[],[12430]) ).

cnf(i_0_19464,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_Oimage(X3,X2,X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_Oimage(X3,X2,X4),X5))) ),
    inference(equality_inference,[],[12445]) ).

cnf(i_0_19465,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)) ),
    inference(equality_inference,[],[12508]) ).

cnf(i_0_19466,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Fun_Oinj__on(X3,X2,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),X1)),hAPP(c_List_Oset(X3),X1)))
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))
    | ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X3,X2),X4),X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))) ),
    inference(equality_inference,[],[12523]) ).

cnf(i_0_19467,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1))) ),
    inference(equality_inference,[],[12560]) ).

cnf(i_0_19468,plain,
    ( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X4)),X3)) ),
    inference(equality_inference,[],[12561]) ).

cnf(i_0_19469,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X5)) = X5
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4))) ),
    inference(equality_inference,[],[12570]) ).

cnf(i_0_19470,plain,
    ( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
    inference(equality_inference,[],[12593]) ).

cnf(i_0_19471,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk181_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))) ),
    inference(equality_inference,[],[12718]) ).

cnf(i_0_19472,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))) ),
    inference(equality_inference,[],[12719]) ).

cnf(i_0_19473,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),c_List_Olexord(X1,X5))),
    inference(equality_inference,[],[12760]) ).

cnf(i_0_19474,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
    inference(equality_inference,[],[12763]) ).

cnf(i_0_19475,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X2),X3) = hAPP(hAPP(c_List_Otake(X1),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[12800]) ).

cnf(i_0_19476,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)) ),
    inference(equality_inference,[],[12813]) ).

cnf(i_0_19477,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),c_Nat_OSuc),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk128_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(equality_inference,[],[12816]) ).

cnf(i_0_19478,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12818]) ).

cnf(i_0_19479,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk180_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12819]) ).

cnf(i_0_19480,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(equality_inference,[],[12835]) ).

cnf(i_0_19481,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
    inference(equality_inference,[],[12868]) ).

cnf(i_0_19482,plain,
    ( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
    inference(equality_inference,[],[12880]) ).

cnf(i_0_19483,plain,
    ( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1)
    | hBOOL(hAPP(hAPP(c_member(X1),esk451_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3))) ),
    inference(equality_inference,[],[12903]) ).

cnf(i_0_19484,plain,
    ( X1 = X1
    | ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X6))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X6)) ),
    inference(equality_inference,[],[12905]) ).

cnf(i_0_19485,plain,
    hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3),
    inference(equality_inference,[],[12907]) ).

cnf(i_0_19486,plain,
    ( ~ class_Rings_Oring(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)) ),
    inference(equality_inference,[],[12944]) ).

cnf(i_0_19487,plain,
    ( ~ class_Rings_Oring(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5) ),
    inference(equality_inference,[],[12945]) ).

cnf(i_0_19488,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(c_Fun_Ocomp(X7,X2,X8,X4),X5),X6),
    inference(equality_inference,[],[12957]) ).

cnf(i_0_19489,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
    inference(equality_inference,[],[13008]) ).

cnf(i_0_19490,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)) ),
    inference(equality_inference,[],[13009]) ).

cnf(i_0_19491,plain,
    ( X1 = esk73_4(hAPP(X2,X1),X2,X3,X4)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
    inference(equality_inference,[],[13086]) ).

cnf(i_0_19492,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)) ),
    inference(equality_inference,[],[13122]) ).

cnf(i_0_19493,plain,
    ( X1 = X1
    | ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
    inference(equality_inference,[],[13129]) ).

cnf(i_0_19494,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)) ),
    inference(equality_inference,[],[13134]) ).

cnf(i_0_19495,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk182_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk181_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3)) ),
    inference(equality_inference,[],[13139]) ).

cnf(i_0_19496,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
    | X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk180_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk179_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)) ),
    inference(equality_inference,[],[13140]) ).

cnf(i_0_19497,plain,
    ( c_Fun_Obij__betw(X1,X1,esk537_4(X2,X1,X2,X1),X2,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(equality_inference,[],[13154]) ).

cnf(i_0_19498,plain,
    ( ~ class_Rings_Oring(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)),X3)),X4) = X4 ),
    inference(equality_inference,[],[13162]) ).

cnf(i_0_19499,plain,
    ( ~ class_Rings_Oring(X1)
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X3)),X4)),X2) ),
    inference(equality_inference,[],[13163]) ).

cnf(i_0_19500,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),c_List_Olexord(X1,X4))),
    inference(equality_inference,[],[13172]) ).

cnf(i_0_19501,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk396_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
    inference(equality_inference,[],[13174]) ).

cnf(i_0_19502,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk451_4(hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),X1,X2,X3))) ),
    inference(equality_inference,[],[13180]) ).

cnf(i_0_19503,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)),X2)),X3) = X3 ),
    inference(equality_inference,[],[13217]) ).

cnf(i_0_19504,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)),X3)),X2) ),
    inference(equality_inference,[],[13218]) ).

cnf(i_0_19505,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3))))),
    inference(equality_inference,[],[13236]) ).

cnf(i_0_19506,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4)) ),
    inference(equality_inference,[],[13237]) ).

cnf(i_0_19507,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[13319]) ).

cnf(i_0_19508,plain,
    hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
    inference(equality_inference,[],[13323]) ).

cnf(i_0_19509,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X3)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(equality_inference,[],[13329]) ).

cnf(i_0_19510,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[13346]) ).

cnf(i_0_19511,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[13347]) ).

cnf(i_0_19512,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[13348]) ).

cnf(i_0_19513,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_List_Oset(X2),X1)),hAPP(c_List_Oset(X2),X1))) ),
    inference(equality_inference,[],[13473]) ).

cnf(i_0_19514,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),
    inference(equality_inference,[],[13531]) ).

cnf(i_0_19515,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5)) ),
    inference(equality_inference,[],[13553]) ).

cnf(i_0_19516,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X2)),X3) = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[13574]) ).

cnf(i_0_19517,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))) ),
    inference(equality_inference,[],[13596]) ).

cnf(i_0_19518,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[13697]) ).

cnf(i_0_19519,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(equality_inference,[],[13725]) ).

cnf(i_0_19520,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
    inference(equality_inference,[],[13780]) ).

cnf(i_0_19521,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(equality_inference,[],[13795]) ).

cnf(i_0_19522,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
    inference(equality_inference,[],[13807]) ).

cnf(i_0_19523,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13809]) ).

cnf(i_0_19524,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13810]) ).

cnf(i_0_19525,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(equality_inference,[],[13821]) ).

cnf(i_0_19526,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk396_3(X2,X1,X1))) ),
    inference(equality_inference,[],[13825]) ).

cnf(i_0_19527,plain,
    c_List_Olist__all2(X1,X1,c_fequal,X2,X2),
    inference(equality_inference,[],[13831]) ).

cnf(i_0_19528,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))) ),
    inference(equality_inference,[],[13884]) ).

cnf(i_0_19529,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4),
    inference(equality_inference,[],[13887]) ).

cnf(i_0_19530,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)))
    | hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Orderings_Oord__class_Omax(X1)),X2),hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))) = X2 ),
    inference(equality_inference,[],[13903]) ).

cnf(i_0_19531,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[13926]) ).

cnf(i_0_19532,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4 ),
    inference(equality_inference,[],[13976]) ).

cnf(i_0_19533,plain,
    X1 = X1,
    inference(equality_inference,[],[13978]) ).

cnf(i_0_19534,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
    inference(equality_inference,[],[14002]) ).

cnf(i_0_19535,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1))))) ),
    inference(equality_inference,[],[14021]) ).

cnf(i_0_19536,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(equality_inference,[],[14023]) ).

cnf(i_0_19537,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(equality_inference,[],[14024]) ).

cnf(i_0_19538,plain,
    ( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(equality_inference,[],[14049]) ).

cnf(i_0_19539,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)),
    inference(equality_inference,[],[14066]) ).

cnf(i_0_19540,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
    inference(equality_inference,[],[14120]) ).

cnf(i_0_19541,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
    inference(equality_inference,[],[14132]) ).

cnf(i_0_19542,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(equality_inference,[],[14177]) ).

cnf(i_0_19543,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)))),
    inference(equality_inference,[],[14220]) ).

cnf(i_0_19544,plain,
    ( c_Fun_Oinj__on(X1,X2,esk24_4(X3,X2,X1,hAPP(c_Set_Oimage(X2,X1,X4),X3)),hAPP(c_Set_Oimage(X2,X1,X4),X3))
    | hAPP(c_Set_Oimage(X2,X1,X4),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(equality_inference,[],[14231]) ).

cnf(i_0_19545,plain,
    ( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)) ),
    inference(equality_inference,[],[14233]) ).

cnf(i_0_19546,plain,
    ( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)) ),
    inference(equality_inference,[],[14234]) ).

cnf(i_0_19547,plain,
    ( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ),
    inference(equality_inference,[],[14281]) ).

cnf(i_0_19548,plain,
    ( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ),
    inference(equality_inference,[],[14282]) ).

cnf(i_0_19549,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(equality_inference,[],[14346]) ).

cnf(i_0_19550,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = X4,
    inference(equality_inference,[],[14358]) ).

cnf(i_0_19551,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = X4,
    inference(equality_inference,[],[14359]) ).

cnf(i_0_19552,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1)) ),
    inference(equality_inference,[],[14373]) ).

cnf(i_0_19553,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
    inference(equality_inference,[],[14400]) ).

cnf(i_0_19554,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
    inference(equality_inference,[],[14425]) ).

cnf(i_0_19555,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1))
    | ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),X1))) ),
    inference(equality_inference,[],[14461]) ).

cnf(i_0_19556,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))) ),
    inference(equality_inference,[],[14483]) ).

cnf(i_0_19557,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14513]) ).

cnf(i_0_19558,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
    inference(equality_inference,[],[14514]) ).

cnf(i_0_19559,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),X2)),
    inference(equality_inference,[],[14552]) ).

cnf(i_0_19560,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
    inference(equality_inference,[],[14558]) ).

cnf(i_0_19561,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
    inference(equality_inference,[],[14574]) ).

cnf(i_0_19562,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
    inference(equality_inference,[],[14575]) ).

cnf(i_0_19563,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(equality_inference,[],[14586]) ).

cnf(i_0_19564,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[14588]) ).

cnf(i_0_19565,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[14589]) ).

cnf(i_0_19566,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14590]) ).

cnf(i_0_19567,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14591]) ).

cnf(i_0_19568,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14592]) ).

cnf(i_0_19569,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14593]) ).

cnf(i_0_19570,plain,
    ( hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X2) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[14596]) ).

cnf(i_0_19571,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_List_Olists(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
    inference(equality_inference,[],[14645]) ).

cnf(i_0_19572,plain,
    X1 = X1,
    inference(equality_inference,[],[14694]) ).

cnf(i_0_19573,plain,
    X1 = X1,
    inference(equality_inference,[],[14695]) ).

cnf(i_0_19574,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk415_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
    inference(equality_inference,[],[14698]) ).

cnf(i_0_19575,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))
    | hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4))) ),
    inference(equality_inference,[],[14699]) ).

cnf(i_0_19576,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
    inference(equality_inference,[],[14702]) ).

cnf(i_0_19577,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5)) ),
    inference(equality_inference,[],[14711]) ).

cnf(i_0_19578,plain,
    ( hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3) = X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[14718]) ).

cnf(i_0_19579,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14729]) ).

cnf(i_0_19580,plain,
    ( X1 = X1
    | ~ class_Rings_Olinordered__semidom(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(equality_inference,[],[14767]) ).

cnf(i_0_19581,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk389_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(equality_inference,[],[14775]) ).

cnf(i_0_19582,plain,
    ( ~ class_Rings_Oidom(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))) ),
    inference(equality_inference,[],[14829]) ).

cnf(i_0_19583,plain,
    ( ~ class_Rings_Oidom(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1)))) ),
    inference(equality_inference,[],[14830]) ).

cnf(i_0_19584,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
    inference(equality_inference,[],[14851]) ).

cnf(i_0_19585,plain,
    X1 = X1,
    inference(equality_inference,[],[14903]) ).

cnf(i_0_19586,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))),X2)) ),
    inference(equality_inference,[],[14924]) ).

cnf(i_0_19587,plain,
    hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4)) = hAPP(c_Set_OPow(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)),
    inference(equality_inference,[],[15000]) ).

cnf(i_0_19588,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk249_3(X1,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
    inference(equality_inference,[],[15027]) ).

cnf(i_0_19589,plain,
    ( X1 = X1
    | ~ class_Rings_Olinordered__semidom(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ),
    inference(equality_inference,[],[15057]) ).

cnf(i_0_19590,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),
    inference(equality_inference,[],[15105]) ).

cnf(i_0_19591,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X3) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X3)) ),
    inference(equality_inference,[],[15179]) ).

cnf(i_0_19592,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(equality_inference,[],[15180]) ).

cnf(i_0_19593,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)))) ),
    inference(equality_inference,[],[15194]) ).

cnf(i_0_19594,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[15204]) ).

cnf(i_0_19595,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))) ),
    inference(equality_inference,[],[15215]) ).

cnf(i_0_19596,plain,
    ( hAPP(X1,X2) = hAPP(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
    inference(equality_inference,[],[15220]) ).

cnf(i_0_19597,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(equality_inference,[],[15268]) ).

cnf(i_0_19598,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[15353]) ).

cnf(i_0_19599,plain,
    hAPP(hAPP(c_List_Ozip(X1,X1),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Orev(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),
    inference(equality_inference,[],[15360]) ).

cnf(i_0_19600,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
    inference(equality_inference,[],[15373]) ).

cnf(i_0_19601,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
    inference(equality_inference,[],[15374]) ).

cnf(i_0_19602,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
    inference(equality_inference,[],[15375]) ).

cnf(i_0_19603,plain,
    hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4) = hAPP(c_Product__Type_OPair(X1,X2),X4),
    inference(equality_inference,[],[15381]) ).

cnf(i_0_19604,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(equality_inference,[],[15395]) ).

cnf(i_0_19605,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,X1),X1),c_Product__Type_Ofst(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)) = X2,
    inference(equality_inference,[],[15488]) ).

cnf(i_0_19606,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(X1,X1),X1),c_Product__Type_Osnd(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)) = X2,
    inference(equality_inference,[],[15489]) ).

cnf(i_0_19607,plain,
    X1 = X1,
    inference(equality_inference,[],[15505]) ).

cnf(i_0_19608,plain,
    X1 = X1,
    inference(equality_inference,[],[15506]) ).

cnf(i_0_19609,plain,
    ( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[15520]) ).

cnf(i_0_19610,plain,
    hBOOL(hAPP(hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X2)),
    inference(equality_inference,[],[15537]) ).

cnf(i_0_19611,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[15544]) ).

cnf(i_0_19612,plain,
    hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Lazy__Sequence_Oempty(X2),
    inference(equality_inference,[],[15547]) ).

cnf(i_0_19613,plain,
    hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Lazy__Sequence_Ohit__bound(X2),
    inference(equality_inference,[],[15548]) ).

cnf(i_0_19614,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) = c_List_Obutlast(X1,X2),
    inference(equality_inference,[],[15649]) ).

cnf(i_0_19615,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) = X3 ),
    inference(equality_inference,[],[15674]) ).

cnf(i_0_19616,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3)) ),
    inference(equality_inference,[],[15699]) ).

cnf(i_0_19617,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1)) ),
    inference(equality_inference,[],[15700]) ).

cnf(i_0_19618,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[15737]) ).

cnf(i_0_19619,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),
    inference(equality_inference,[],[15750]) ).

cnf(i_0_19620,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(equality_inference,[],[15791]) ).

cnf(i_0_19621,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X3))) ),
    inference(equality_inference,[],[15821]) ).

cnf(i_0_19622,plain,
    ~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[15837]) ).

cnf(i_0_19623,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))) ),
    inference(equality_inference,[],[15849]) ).

cnf(i_0_19624,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
    inference(equality_inference,[],[15876]) ).

cnf(i_0_19625,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))))),
    inference(equality_inference,[],[15881]) ).

cnf(i_0_19626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(equality_inference,[],[15889]) ).

cnf(i_0_19627,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[15898]) ).

cnf(i_0_19628,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[15899]) ).

cnf(i_0_19629,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(equality_inference,[],[15975]) ).

cnf(i_0_19630,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(equality_inference,[],[16003]) ).

cnf(i_0_19631,plain,
    hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X4) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X1),c_List_Olist_ONil(X2)),X4),
    inference(equality_inference,[],[16052]) ).

cnf(i_0_19632,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(equality_inference,[],[16068]) ).

cnf(i_0_19633,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(equality_inference,[],[16069]) ).

cnf(i_0_19634,plain,
    X1 = X1,
    inference(equality_inference,[],[16078]) ).

cnf(i_0_19635,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[16091]) ).

cnf(i_0_19636,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | X2 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3)) ),
    inference(equality_inference,[],[16092]) ).

cnf(i_0_19637,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[16095]) ).

cnf(i_0_19638,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[16109]) ).

cnf(i_0_19639,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(equality_inference,[],[16124]) ).

cnf(i_0_19640,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)))),
    inference(equality_inference,[],[16126]) ).

cnf(i_0_19641,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X1)
    | X1 = X1 ),
    inference(equality_inference,[],[16137]) ).

cnf(i_0_19642,plain,
    X1 = X1,
    inference(equality_inference,[],[16138]) ).

cnf(i_0_19643,plain,
    X1 = X1,
    inference(equality_inference,[],[16139]) ).

cnf(i_0_19644,plain,
    X1 = X1,
    inference(equality_inference,[],[16140]) ).

cnf(i_0_19645,plain,
    ( ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) ),
    inference(equality_inference,[],[16161]) ).

cnf(i_0_19646,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
    inference(equality_inference,[],[16211]) ).

cnf(i_0_19647,plain,
    X1 = hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X1),X4)),
    inference(equality_inference,[],[16216]) ).

cnf(i_0_19648,plain,
    X1 = hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X1)),
    inference(equality_inference,[],[16217]) ).

cnf(i_0_19649,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(equality_inference,[],[16253]) ).

cnf(i_0_19650,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)))) ),
    inference(equality_inference,[],[16270]) ).

cnf(i_0_19651,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(equality_inference,[],[16298]) ).

cnf(i_0_19652,plain,
    X1 = X1,
    inference(equality_inference,[],[16318]) ).

cnf(i_0_19653,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[16331]) ).

cnf(i_0_19654,plain,
    hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[16360]) ).

cnf(i_0_19655,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
    inference(equality_inference,[],[16362]) ).

cnf(i_0_19656,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(equality_inference,[],[16363]) ).

cnf(i_0_19657,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(equality_inference,[],[16385]) ).

cnf(i_0_19658,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(equality_inference,[],[16390]) ).

cnf(i_0_19659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(equality_inference,[],[16411]) ).

cnf(i_0_19660,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(equality_inference,[],[16417]) ).

cnf(i_0_19661,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16493]) ).

cnf(i_0_19662,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16494]) ).

cnf(i_0_19663,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(equality_inference,[],[16495]) ).

cnf(i_0_19664,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(equality_inference,[],[16500]) ).

cnf(i_0_19665,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2))))),
    inference(equality_inference,[],[16502]) ).

cnf(i_0_19666,plain,
    X1 = X1,
    inference(equality_inference,[],[16503]) ).

cnf(i_0_19667,plain,
    X1 = X1,
    inference(equality_inference,[],[16505]) ).

cnf(i_0_19668,plain,
    X1 = X1,
    inference(equality_inference,[],[16507]) ).

cnf(i_0_19669,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(equality_inference,[],[16511]) ).

cnf(i_0_19670,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(equality_inference,[],[16535]) ).

cnf(i_0_19671,plain,
    ( ~ class_Fields_Ofield(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) ),
    inference(equality_inference,[],[16537]) ).

cnf(i_0_19672,plain,
    ( ~ class_Fields_Ofield(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
    inference(equality_inference,[],[16538]) ).

cnf(i_0_19673,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X3,
    inference(equality_inference,[],[16601]) ).

cnf(i_0_19674,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X2,
    inference(equality_inference,[],[16602]) ).

cnf(i_0_19675,plain,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(equality_inference,[],[16637]) ).

cnf(i_0_19676,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
    inference(equality_inference,[],[16660]) ).

cnf(i_0_19677,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
    inference(equality_inference,[],[16661]) ).

cnf(i_0_19678,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(equality_inference,[],[16682]) ).

cnf(i_0_19679,plain,
    X1 = hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(hAPP(c_List_Oappend(X2),X3),X1)),
    inference(equality_inference,[],[16694]) ).

cnf(i_0_19680,plain,
    X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(hAPP(c_List_Oappend(X2),X1),X3)),
    inference(equality_inference,[],[16695]) ).

cnf(i_0_19681,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1))) ),
    inference(equality_inference,[],[16713]) ).

cnf(i_0_19682,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
    inference(equality_inference,[],[16728]) ).

cnf(i_0_19683,plain,
    X1 = X1,
    inference(equality_inference,[],[16729]) ).

cnf(i_0_19684,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | X2 = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(equality_inference,[],[16742]) ).

cnf(i_0_19685,plain,
    hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3,
    inference(equality_inference,[],[16779]) ).

cnf(i_0_19686,plain,
    ( X1 = X1
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(equality_inference,[],[16805]) ).

cnf(i_0_19687,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(equality_inference,[],[16812]) ).

cnf(i_0_19688,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(equality_inference,[],[16837]) ).

cnf(i_0_19689,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(equality_inference,[],[16838]) ).

cnf(i_0_19690,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) = c_Int_OMin,
    inference(equality_inference,[],[16893]) ).

cnf(i_0_19691,plain,
    c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin),
    inference(equality_inference,[],[16894]) ).

cnf(i_0_19692,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[16913]) ).

cnf(i_0_19693,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
    inference(equality_inference,[],[16951]) ).

cnf(i_0_19694,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
    inference(equality_inference,[],[16973]) ).

cnf(i_0_19695,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | X2 = esk460_2(hAPP(c_List_Oset(X1),X2),X1)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))) ),
    inference(equality_inference,[],[16991]) ).

cnf(i_0_19696,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(equality_inference,[],[16997]) ).

cnf(i_0_19697,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(equality_inference,[],[17000]) ).

cnf(i_0_19698,plain,
    ( hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
    inference(equality_inference,[],[17011]) ).

cnf(i_0_19699,plain,
    ( X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
    inference(equality_inference,[],[17012]) ).

cnf(i_0_19700,plain,
    ( c_Nitpick_Onorm__frac(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(equality_inference,[],[17013]) ).

cnf(i_0_19701,plain,
    ( c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(equality_inference,[],[17014]) ).

cnf(i_0_19702,plain,
    X1 = X1,
    inference(equality_inference,[],[17015]) ).

cnf(i_0_19703,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17023]) ).

cnf(i_0_19704,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17024]) ).

cnf(i_0_19705,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17025]) ).

cnf(i_0_19706,plain,
    ( ~ class_Rings_Odvd(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
    inference(equality_inference,[],[17082]) ).

cnf(i_0_19707,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
    inference(equality_inference,[],[17101]) ).

cnf(i_0_19708,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(equality_inference,[],[17105]) ).

cnf(i_0_19709,plain,
    hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[17106]) ).

cnf(i_0_19710,plain,
    hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[17107]) ).

cnf(i_0_19711,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(equality_inference,[],[17110]) ).

cnf(i_0_19712,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
    inference(equality_inference,[],[17111]) ).

cnf(i_0_19713,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
    inference(equality_inference,[],[17177]) ).

cnf(i_0_19714,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(equality_inference,[],[17178]) ).

cnf(i_0_19715,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17182]) ).

cnf(i_0_19716,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17183]) ).

cnf(i_0_19717,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17184]) ).

cnf(i_0_19718,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17185]) ).

cnf(i_0_19719,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17190]) ).

cnf(i_0_19720,plain,
    c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),
    inference(equality_inference,[],[17204]) ).

cnf(i_0_19721,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17206]) ).

cnf(i_0_19722,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[17207]) ).

cnf(i_0_19723,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17209]) ).

cnf(i_0_19724,plain,
    X1 = X1,
    inference(equality_inference,[],[17210]) ).

cnf(i_0_19725,plain,
    X1 = X1,
    inference(equality_inference,[],[17211]) ).

cnf(i_0_19726,plain,
    X1 = X1,
    inference(equality_inference,[],[17212]) ).

cnf(i_0_19727,plain,
    X1 = X1,
    inference(equality_inference,[],[17213]) ).

cnf(i_0_19728,plain,
    X1 = X1,
    inference(equality_inference,[],[17214]) ).

cnf(i_0_19729,plain,
    X1 = X1,
    inference(equality_inference,[],[17215]) ).

cnf(i_0_19730,plain,
    X1 = X1,
    inference(equality_inference,[],[17216]) ).

cnf(i_0_19731,plain,
    X1 = X1,
    inference(equality_inference,[],[17217]) ).

cnf(i_0_19732,plain,
    X1 = X1,
    inference(equality_inference,[],[17218]) ).

cnf(i_0_19733,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(equality_inference,[],[17224]) ).

cnf(i_0_19734,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)) = hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
    inference(equality_inference,[],[17225]) ).

cnf(i_0_19735,plain,
    hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[17226]) ).

cnf(i_0_19736,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
    inference(equality_inference,[],[17240]) ).

cnf(i_0_19737,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2),
    inference(equality_inference,[],[17241]) ).

cnf(i_0_19738,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
    inference(equality_inference,[],[17242]) ).

cnf(i_0_19739,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(equality_inference,[],[17245]) ).

cnf(i_0_19740,plain,
    X1 = X1,
    inference(equality_inference,[],[17253]) ).

cnf(i_0_19741,plain,
    X1 = X1,
    inference(equality_inference,[],[17254]) ).

cnf(i_0_19742,plain,
    X1 = X1,
    inference(equality_inference,[],[17255]) ).

cnf(i_0_19743,plain,
    X1 = X1,
    inference(equality_inference,[],[17256]) ).

cnf(i_0_19744,plain,
    c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(equality_inference,[],[17280]) ).

cnf(i_0_19745,plain,
    hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[17289]) ).

cnf(i_0_19746,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[17312]) ).

cnf(i_0_19747,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[17319]) ).

cnf(i_0_19748,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
    inference(equality_inference,[],[17327]) ).

cnf(i_0_19749,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17331]) ).

cnf(i_0_19750,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17332]) ).

cnf(i_0_19751,plain,
    c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(equality_inference,[],[17335]) ).

cnf(i_0_19752,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17338]) ).

cnf(i_0_19753,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17340]) ).

cnf(i_0_19754,plain,
    hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Ohd(X1),X2),
    inference(equality_inference,[],[17341]) ).

cnf(i_0_19755,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3 ),
    inference(equality_inference,[],[17349]) ).

cnf(i_0_19756,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) = X3 ),
    inference(equality_inference,[],[17350]) ).

cnf(i_0_19757,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3 ),
    inference(equality_inference,[],[17352]) ).

cnf(i_0_19758,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) = X3 ),
    inference(equality_inference,[],[17353]) ).

cnf(i_0_19759,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) ),
    inference(equality_inference,[],[17354]) ).

cnf(i_0_19760,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) ),
    inference(equality_inference,[],[17355]) ).

cnf(i_0_19761,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) ),
    inference(equality_inference,[],[17357]) ).

cnf(i_0_19762,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) ),
    inference(equality_inference,[],[17358]) ).

cnf(i_0_19763,plain,
    ( ~ c_Equiv__Relations_Oequivp(X1,X2)
    | hBOOL(hAPP(hAPP(X2,X3),X3)) ),
    inference(equality_inference,[],[17365]) ).

cnf(i_0_19764,plain,
    X1 = X1,
    inference(equality_inference,[],[17375]) ).

cnf(i_0_19765,plain,
    X1 = X1,
    inference(equality_inference,[],[17376]) ).

cnf(i_0_19766,plain,
    X1 = X1,
    inference(equality_inference,[],[17377]) ).

cnf(i_0_19767,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17383]) ).

cnf(i_0_19768,plain,
    ( ~ class_Rings_Oidom(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
    inference(equality_inference,[],[17391]) ).

cnf(i_0_19769,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17400]) ).

cnf(i_0_19770,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Olast(X1,X2),
    inference(equality_inference,[],[17419]) ).

cnf(i_0_19771,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Obutlast(X1,X2),
    inference(equality_inference,[],[17420]) ).

cnf(i_0_19772,plain,
    c_Divides_Opdivmod(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),
    inference(equality_inference,[],[17425]) ).

cnf(i_0_19773,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
    inference(equality_inference,[],[17433]) ).

cnf(i_0_19774,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17451]) ).

cnf(i_0_19775,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17452]) ).

cnf(i_0_19776,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[17474]) ).

cnf(i_0_19777,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[17475]) ).

cnf(i_0_19778,plain,
    ( ~ epred1_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(equality_inference,[],[17477]) ).

cnf(i_0_19779,plain,
    c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17478]) ).

cnf(i_0_19780,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17481]) ).

cnf(i_0_19781,plain,
    X1 = X1,
    inference(equality_inference,[],[17482]) ).

cnf(i_0_19782,plain,
    ( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17486]) ).

cnf(i_0_19783,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(equality_inference,[],[17487]) ).

cnf(i_0_19784,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
    inference(equality_inference,[],[17491]) ).

cnf(i_0_19785,plain,
    ( ~ epred2_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | hBOOL(hAPP(X1,X2)) ),
    inference(equality_inference,[],[17508]) ).

cnf(i_0_19786,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17539]) ).

cnf(i_0_19787,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17540]) ).

cnf(i_0_19788,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17541]) ).

cnf(i_0_19789,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odivmod__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) ),
    inference(equality_inference,[],[17589]) ).

cnf(i_0_19790,plain,
    c_Divides_Odivmod__int(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(equality_inference,[],[17594]) ).

cnf(i_0_19791,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[17606]) ).

cnf(i_0_19792,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(equality_inference,[],[17631]) ).

cnf(i_0_19793,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17632]) ).

cnf(i_0_19794,plain,
    c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17633]) ).

cnf(i_0_19795,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(equality_inference,[],[17638]) ).

cnf(i_0_19796,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X1) = X1,
    inference(equality_inference,[],[17660]) ).

cnf(i_0_19797,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
    inference(equality_inference,[],[17664]) ).

cnf(i_0_19798,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[17665]) ).

cnf(i_0_19799,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17670]) ).

cnf(i_0_19800,plain,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17674]) ).

cnf(i_0_19801,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17680]) ).

cnf(i_0_19802,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(equality_inference,[],[17712]) ).

cnf(i_0_19803,plain,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[17729]) ).

cnf(i_0_19804,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[17733]) ).

cnf(i_0_19805,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17787]) ).

cnf(i_0_19806,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[17789]) ).

cnf(i_0_19807,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17832]) ).

cnf(i_0_19808,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17833]) ).

cnf(i_0_19809,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17834]) ).

cnf(i_0_19810,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17835]) ).

cnf(i_0_19811,plain,
    ( ~ class_Nat_Osemiring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17836]) ).

cnf(i_0_19812,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17837]) ).

cnf(i_0_19813,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17838]) ).

cnf(i_0_19814,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17839]) ).

cnf(i_0_19815,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[17848]) ).

cnf(i_0_19816,plain,
    ( ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17849]) ).

cnf(i_0_19817,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[17850]) ).

cnf(i_0_19818,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17851]) ).

cnf(i_0_19819,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17852]) ).

cnf(i_0_19820,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17853]) ).

cnf(i_0_19821,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[17854]) ).

cnf(i_0_19822,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17869]) ).

cnf(i_0_19823,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[17870]) ).

cnf(i_0_19824,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[17882]) ).

cnf(i_0_19825,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17883]) ).

cnf(i_0_19826,plain,
    ( ~ class_Groups_Oab__group__add(X1)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[17884]) ).

cnf(i_0_19827,plain,
    hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[17885]) ).

cnf(i_0_19828,plain,
    X1 = X1,
    inference(equality_inference,[],[17908]) ).

cnf(i_0_19829,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17915]) ).

cnf(i_0_19830,plain,
    c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17920]) ).

cnf(i_0_19831,plain,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
    inference(equality_inference,[],[17921]) ).

cnf(i_0_19832,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17933]) ).

cnf(i_0_19833,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2 ),
    inference(equality_inference,[],[17935]) ).

cnf(i_0_19834,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) ),
    inference(equality_inference,[],[17937]) ).

cnf(i_0_19835,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(equality_inference,[],[17939]) ).

cnf(i_0_19836,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(equality_inference,[],[17940]) ).

cnf(i_0_19837,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17941]) ).

cnf(i_0_19838,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17942]) ).

cnf(i_0_19839,plain,
    X1 = X1,
    inference(equality_inference,[],[17991]) ).

cnf(i_0_19840,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[17992]) ).

cnf(i_0_19841,plain,
    hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[17993]) ).

cnf(i_0_19842,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(equality_inference,[],[17995]) ).

cnf(i_0_19843,plain,
    X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
    inference(equality_inference,[],[17996]) ).

cnf(i_0_19844,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[18002]) ).

cnf(i_0_19845,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(equality_inference,[],[18003]) ).

cnf(i_0_19846,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[18005]) ).

cnf(i_0_19847,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[18006]) ).

cnf(i_0_19848,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(equality_inference,[],[18017]) ).

cnf(i_0_19849,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
    inference(equality_inference,[],[18046]) ).

cnf(i_0_19850,plain,
    c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
    inference(equality_inference,[],[18047]) ).

cnf(i_0_19851,plain,
    X1 = X1,
    inference(equality_inference,[],[18054]) ).

cnf(i_0_19852,plain,
    X1 = X1,
    inference(equality_inference,[],[18055]) ).

cnf(i_0_19853,plain,
    X1 = X1,
    inference(equality_inference,[],[18056]) ).

cnf(i_0_19854,plain,
    X1 = X1,
    inference(equality_inference,[],[18057]) ).

cnf(i_0_19855,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(equality_inference,[],[18080]) ).

cnf(i_0_19856,plain,
    X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(equality_inference,[],[18085]) ).

cnf(i_0_19857,plain,
    X1 = X1,
    inference(equality_inference,[],[18091]) ).

cnf(i_0_19858,plain,
    X1 = X1,
    inference(equality_inference,[],[18092]) ).

cnf(i_0_19859,plain,
    X1 = X1,
    inference(equality_inference,[],[18093]) ).

cnf(i_0_19860,plain,
    X1 = X1,
    inference(equality_inference,[],[18095]) ).

cnf(i_0_19861,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18104]) ).

cnf(i_0_19862,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18105]) ).

cnf(i_0_19863,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18106]) ).

cnf(i_0_19864,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18133]) ).

cnf(i_0_19865,plain,
    ( ~ class_Rings_Oring__1(X1)
    | hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18134]) ).

cnf(i_0_19866,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(equality_inference,[],[18135]) ).

cnf(i_0_19867,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18149]) ).

cnf(i_0_19868,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18150]) ).

cnf(i_0_19869,plain,
    ( ~ class_Groups_Osgn__if(X1)
    | c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18166]) ).

cnf(i_0_19870,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[18167]) ).

cnf(i_0_19871,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18169]) ).

cnf(i_0_19872,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18170]) ).

cnf(i_0_19873,plain,
    c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18171]) ).

cnf(i_0_19874,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1)) ),
    inference(equality_inference,[],[18187]) ).

cnf(i_0_19875,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18188]) ).

cnf(i_0_19876,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18194]) ).

cnf(i_0_19877,plain,
    c_List_Olist_ONil(X1) = c_List_Oremdups(X1,c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18195]) ).

cnf(i_0_19878,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[18196]) ).

cnf(i_0_19879,plain,
    c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[18225]) ).

cnf(i_0_19880,plain,
    hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[18226]) ).

cnf(i_0_19881,plain,
    c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(equality_inference,[],[18227]) ).

cnf(i_0_19882,plain,
    c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(equality_inference,[],[18231]) ).

cnf(i_0_19883,plain,
    $false,
    inference(scs_inference,[],[i_0_12427,i_0_12923,i_0_12068]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW323+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32  % Computer : n027.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
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 06:37:35 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 31.84/22.38  % Version  : CSE_E---1.7
% 31.84/22.38  % Problem  : theBenchmark.p
% 31.84/22.38  % SZS status Theorem for theBenchmark.p
% 31.84/22.38  % SZS output start CNFRefutation
% See solution above
% 32.80/22.85  % Total time : 22.017s
%------------------------------------------------------------------------------